DEVELOPMENT OF MULTI ATTRIBUTE DECISION MAKING …€¦ · a) GTU is permitted to archive,...

DEVELOPMENT OF MULTI ATTRIBUTE DECISION

MAKING TECHNIQUE FOR IMPROVED

PERFORMANCE IN MANUFACTURING AND SUPPLY

CHAIN FUNCTION

A Thesis submitted to Gujarat Technological University

for the Award of

Doctor of Philosophy

in

Mechanical Engineering

by

Nirmal Nital Pravinbhai

Enrollment No. 129990919012

under supervision of

Prof. Dr. Mangal G. Bhatt

Gujarat Technological University, Ahmedabad

September, 2019

ii

DEVELOPMENT OF MULTI ATTRIBUTE DECISION

MAKING TECHNIQUE FOR IMPROVED

PERFORMANCE IN MANUFACTURING AND SUPPLY

CHAIN FUNCTION

A Thesis submitted to Gujarat Technological University

for the Award of

Doctor of Philosophy

in

Mechanical Engineering

by

Nirmal Nital Pravinbhai

Enrollment No. 129990919012

under supervision of

Prof. Dr. Mangal G. Bhatt

Gujarat Technological University, Ahmedabad

September, 2019

iii

@ Nirmal Nital Pravinbhai

iv

DECLARATION

I declare that the thesis entitled “Development of Multi Attribute Decision Making

Technique for Improved Performance in Manufacturing and Supply Chain

Function” submitted by me for the degree of Doctor of Philosophy is the record of

research work is carried out by me during the period from 2012 to 2019 under the

supervision of Prof. Dr. Mangal G. Bhatt, Principal at Shantilal Shah Engineering

College, Bhavnagar, Gujarat and this has not formed the basis for the award of any

degree, diploma, associateship, fellowship, titles in this or any other University or other

institution of higher learning.

I further declare that the material obtained from other sources has been duly acknowledged

in the thesis. I shall be solely responsible for any plagiarism or other irregularities, if

noticed in the thesis.

Signature of the Research Scholar: ………………………… Date:………………….

Name of Research Scholar: Nirmal Nital Pravinbhai (Enrollment No. 129990919012)

Place: Bhavnagar

v

CERTIFICATE

I certify that the work incorporated in the thesis “Development of Multi Attribute

Decision Making Technique for Improved Performance in Manufacturing and

Supply Chain Function” submitted by Kum. Nirmal Nital Pravinbhai (Enrollment No.

129990919012) was is carried out by the candidate under my supervision/guidance. To the

best of my knowledge: (i) the candidate has not submitted the same research work to any

other institution for any degree/diploma, Associateship, Fellowship or other similar titles

(ii) the thesis submitted is a record of original research work done by the Research Scholar

during the period of study under my supervision, and (iii) the thesis represents independent

research work on the part of the Research Scholar.

Signature of Supervisor: ……………………………………Date: ………….………

Name of Supervisor: Prof. Dr. Mangal G. Bhatt

Place: Bhavnagar

vi

Course-work Completion Certificate

This is to certify that Kum. Nirmal Nital Pravinbhai Enrollment no. 129990919012 is a

Ph. D. scholar enrolled for PhD program in the branch Mechanical Engineering of

Gujarat Technological University, Ahmedabad.

(Pleases tick the relevant option(s))

She has been exempted from the course-work (successfully completed during M.

Phil Course)

She has been exempted from Research Methodology Course only(Successfully

completed during M. Phil Course)

She has successfully completed the PhD course work for the partial requirement for

the award of PhD Degree. His/ Her performance in the course work is as follows-

Grade Obtained in

Research Methodology (PH001)

Grade Obtained in Self-study Course

(Core Subject) (PH002)

BB AB

Supervisor‘s Sign: ………………………


vii

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Technique for Improved Performance in Manufacturing and Supply Chain

Function” by Nirmal Nital Pravinbhai (Enrollment No. 129990919012) has been

examined by us. We undertake the following:

a. Thesis has significant new work / knowledge as compared already published or are

under consideration to be published elsewhere. No sentence, equation, diagram,

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issued from time to time (i.e. permitted similarity index <=25%).

Signature of the Research Scholar: …………………………… Date: ….………

Name of Research Scholar: Nirmal Nital Pravinbhai

Place: Shantilal Shah Engineering College, Bhavnagar

Signature of Supervisor: ……………………………… Date: ……………


Place: Shantilal Shah Engineering College, Bhavnagar

viii

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PhD THESIS Non-Exclusive License to

GUJARAT TECHNOLOGICAL UNIVERSITY

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xi

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all policy matters related to authorship and plagiarism.

Signature of the Research Scholar:____________________

Name of Research Scholar: Miss. Nirmal Nital Pravinbhai

Date:_______________ Place: Bhavnagar

Signature of Supervisor: ____________________


Date: _______________ Place: Bhavnagar

Seal:

xii

Thesis Approval Form

The viva-voce of the PhD Thesis submitted by Kum. Nirmal Nital Pravinbhai (Enrollment

No. 129990919012) entitled ―Development of Multi Attribute Decision Making Technique

for Improved Performance in Manufacturing and Supply Chain Function‖ was conducted

on 13.09.2019 at Gujarat Technological University.

(Please tick any one of the following option)

The performance of the candidate was satisfactory. We recommend that he/she be

awarded the PhD degree.

Any further modifications in research work recommended by the panel after 3

months from the date of first viva-voce upon request of the Supervisor or request

of Independent Research Scholar after which viva-voce can be re-conducted by the

same panel again

(Briefly specify the modifications suggested by the panel)

The performance of the candidate was unsatisfactory. We recommend that he/she

should not be awarded the PhD degree.

(The panel must give justifications for rejecting the research work)

_________________________________

Research Supervisor: Prof. Dr. M. G. Bhatt

__________________________________

External Examiner 1: Prof. Dr. H. K. Raval

_________________________________

External Examiner 2: Prof. Dr. R. S. Prabhu

Gaonkar

__________________________________

External Examiner 3: Prof. Dr. Puran Chandra

Tewari

xiii

ABSTRACT

Due to globalization decision making are very important if growth of product

variation, reduction in product life cycle, splitting of supply chain, changing

technologies and sustainability. Decision making is a part of operation research. When

there are numbers of alternatives rank according to consider the complex criteria

(beneficial/ non-beneficial and with different units), it is very difficult to make a

transparent decision without favoritism to meet the objective. There are several techniques

proposed by various researchers for solving through multi attribute decision making

(MADM). A major criticism of MADMs is that different techniques may yield different

ranking solution when applied to same problem; there are several limitations of current

MADM with various mathematical set theories. Here the fundamental research is carried

out, where the issues and limitations of current MADM techniques are tried to be resolved.

The Single Valued Neutrosophic Set (SVNS) is an ideal set of Neutrosophic theory, which

incorporates the data in level of truthness, level of indeterminacy and level of falsehood.

Here, Three new approaches for MADMs are tried to investigate (i) Fuzzy Single Valued

Neutrosophic Set Novel MADM(F-SVNS N- MADM), (ii) Fuzzy Single Valued

Neutrosophic Set Entropy Weight Based MADMD (F-SVNS EW-MADM) and (iii) Fuzzy

Single Valued Neutrosophic Set Advanced Correlation Coefficient MADM (F-SVNS

ACC-MADM); which works with conversion on crisp/ fuzzy set into single valued

Neutrosophic set. The proposed methodologies are implanted with same input information

in some case examples published in various peer reviewed journals and books in the field

of manufacturing and supply chain management. Validation is carried out with two stages

(i) Comparison with published result of MADM and (ii) Spearman rank correlation

coefficient sensitivity analysis of three methodologies with various normalization methods.

The outcome of implementation shows that proposed methodologies give more accurate

result with less calculation with compared to existing MADMs. The positive effect of two

of the methodologies among the three is that they give the solution without calculating

attributes weight which is impossible in any other MADM approach. The same set theory

is applied to F-SVNS EW-MADM methodology and it also shows the better ranking

solution by considering attribute weight criteria. The validation through spearman

correlation coefficient‘s ranking sensitivity analysis shows that, F-SVNS N-MADM

technique gives better ranking solution with less calculation among proposed

xiv

methodologies. Proposed techniques give the better solution by considering indeterminate,

uncertain, imprecise and inconsistent information by converting input information in to the

degree of truthness, degree of indeterminacy and degree of falsity.

xv

Acknowledgements

I would like to express gratitude to my research supervisor Prof. Dr. Mangal G.

Bhatt, Principal of Shantilal Shah Engineering College, Bhavnagar. I am having

gratitude to him for trust me and encourage me in each and every phase of research

journey. I also oblige to having both DPC members Prof. Dr. Darshak A. Desai,

Professor and Head of Mechanical Engineering, G. H. Patel College of Engineering,

Vallabhvidhyanagar, Anand and Prof. Dr. Harshit K. Dave, Associate Professor,

Mechanical Engineering Department, SVNIT, Surat for their constant inspirations and

directional suggestion for improvement in the research work.

I profoundly thank Prof. Dr. Florentin Smarandache, Professor of Mathematics

and Science Department, University of New Mexico, USA to give his value added

assistance and unconditional guidance for Neutrosophic set-the new era of mathematics.

I also thank to Neutrosophic Science International Association for kind support. I also

thankful to Prof. Dr. Debabrata Datta, Bhabha Atomic Research Centre, Mumbai to

give insight to work in the field of Neutrosophic set. I would also like to express

gratitude to Prof. Dr. M. N. Qureshi, King Khalid University Saudi Arabia for

encouragement to do research in the field of SCM.

I am thankful to Prof. Dr. Ashish V. Gohil, Head of Production Engineering

Department and colleagues of Production Engineering for their encouragement and

inspiration at each stage of the research work. I also thank to research week experts,

Prof. Dr. Himanshu Chaudhari, MNIT-Jaipur, Prof. Dr. Rajbir Bhatti, PTU- Jalandhar,

Prof. Dr. Jeetendra A. Vadhar, GEC, Palanpur, Gujarat, Prof. Dr. R. K. Agarwal,

Washington University- USA, Prof. Dr. Mukul Shukla, MNNIT- Allahabad, Prof. Dr. C.

K. Biswas, NIT- Rourkela, Prof. Dr. Mitesh Popat, Adani Institute of Infrastructure-

Ahmedabad and others for their kind suggestions, corrections and motivation.

I am also thankful to Prof. Dr. Uday Chhaya, Prof. Devangi Desai, Prof. Dr.

Dhwani Vaishnav and Prof. Vinay Parikh for final proofreading of the thesis and support.

I am also thankful to Dr. Rajubhai Mobarsa, SSEC Bhavnagar and Dr. Kadambhai

Mashruwala, Sr. Librarian at IIT, Bombay for plagiarism check. I genuinely thank

Honorable Commissionerate of Technical Education Gandhinagar for giving permission

xvi

for the PhD research work. I also acknowledge Honorable Vice Chancellor PhD section

of GTU, Dean and an entire team of PhD section for their assistance and kind support.

To give it a great focus and importance, I have reserved my gratitude for them for

the last, what normally should have been first in my text, it is all my Papa, Mummy

Rakesh, Reena, Parita and entire family without their encouragement, moral support and

help, I would not have been able to pursue my research work. I thank them from the

bottom of my heart.

Last but not the least, this research journey could not have been possible without

unconditional blessings from my gurus Mirra Alfassa Mother, Maharishi Aurobindo and

the Devine Mother. My research work is offering at lotus feet of Maa.

(Nirmal Nital Pravinbhai)

xvii

List of Contents

DECLARATION iv

CERTIFICATE v

COURSE-WORK COMPLETION CERTIFICATE vi

ORIGINALITY REPORT CERTIFICATE vii

PHD THESIS NON-EXCLUSIVE LICENSE TO GUJARAT TECHNOLOGICAL

UNIVERSITY

x

THESIS APPROVAL FORM xii

ABSTRACT xiii

ACKNOWLEDGEMENT xv

LIST OF CONTENTS xvii

LIST OF ABBREVIATION xxiii

LIST OF SYMBOLS xxv

LIST OF FIGURES xxvi

LIST OF TABLES xxvii

LIST OF APPENDICES xxxii

CHAPTER NO.1 INTRODUCTION 1

1.1 Importance of Decision Making in SCM 3

1.2 Decision Making through MADM 4

1.3 Functioning of MADM 5

1.4 Advantages of MADM 6

1.5 Objective and Scope of Research Work 7

1.6 Research Assumptions 9

1.7 Research Work Flow 9

1.8 Outline of the Thesis 12

CHAPTER NO 2: LITERATURE REVIEW 14

2.1 MADM Techniques 17

2.1.1 Analytical Hierarchy Process (AHP) 17

2.1.2 Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) 20

2.1.3 VIseKriterijuska OptimizacijaI Komoromisno Resenji (VIKOR) 23

2.1.4 ELimination and Choice Expressing Reality (ELECTRE) 25

xviii

2.1.5 Preference Ranking Organization Method for Enrichment Evaluations

(PROMETHEE)

27

2.1.6 Gray Relational Model (GRA) 30

2.1.7 Complex Proportional Assessment (COPRAS) 32

2.1.8 Preference Selection Index (PSI) Method 34

2.2 The Significance of Mathematical Set in MADMs 39

2.2.1 Crisp Set 39

2.2.2 Fuzzy Set (FS) (Linguistic Information) 41

2.2.3 Intuitionistic Fuzzy Set (IFS) 44

2.2.4 Interval Valued Intuitionistic Fuzzy Set (IVIFS) 46

2.2.5 Single Valued Neutrosophic Set (SVNS) 48

2.3 Selection Processes for Improving Performance in Manufacturing and Supply

Chain Areas

51

2.3.1 Material Selection 52

2.3.2 Machine Tool Selection 53

2.3.3 Rapid Prototype Selection 54

2.3.4 Non-Traditional Machining Process (NTMP) Selection 55

2.3.5 Automated Guided Vehicle (AGV) Selection 56

2.3.6 Robot Selection 56

2.3.7 Metal Stamping Layout Selection 58

2.3.8 Electro Chemical Machining (ECM) Program Selection 58

2.3.9 Cutting Fluid (Coolant) Selection 59

2.3.10 Supplier Selection 59

2.3.11 Third Party Reverse Logistic Provider‘s (TPRLP) Selection 61

2.4 Brief Conclusion of Literature Review 62

CHAPTER NO.3 PROPOSED MADM TECHNIQUES 66

3.1 Proposed Method-1: Fuzzy-Single Valued Neutrosophic Set Novel MADM (F-

SVNS-N-MADM)

68

3.2 Proposed Method-2: Fuzzy Single Valued Neutrosophic Set Entropy Weight based

MADM (F-SVNS EW-MADM)

71

3.3 Proposed Method-3: Fuzzy Single Valued Neutrosophic Set SVNS Advance

Correlation Coefficient MADM (F-SVNS-ACC-MADM)

74

xix

3.4 Demonstration of Proposed Methodologies 77

3.4.1 Industrial Case Example 1: Supplier Selection 77

3.4.2 Industrial Case Example 2: Material Provider‘s Selection 85

CHAPTER NO.4 IMPLEMENTATION AND VALIDATION 94

4.1 Collected Case Example 1: Material Selection 96

4.1.1 Proposed Method 1: F-SVNS-N-MADM for Material Selection 97

4.1.2 Proposed Method 2: F-SVNS-EW-MADM for Material Selection 98

4.1.3 Proposed Method 3: F-SVNS-ACC-MADM for Material Selection 99

4.1.4 Performance Measures Comparison: Material Ranking 99

4.2 Collected Case Example 2: Machine Tool Selection 101

4.2.1 Proposed Method 1: F-SVNS-N-MADM for Machine Tool Selection 102

4.2.2 Proposed Method 2: F-SVNS-EW-MADM for Machine Tool Selection 103

4.2.3 Proposed Method 3: F-SVNS-ACC-MADM for Machine Tool Selection 103

4.2.4 Performance Measures Comparison: Machine Tool Ranking 104

4.3 Collected Case Example 3: Rapid Prototype Selection 105

4.3.1 Proposed Method 1: F-SVNS-N-MADM for Rapid Prototype Selection 107

4.3.2 Proposed Method 2: F-SVNS-EW-MADM for Rapid Prototype Selection 108

4.3.3 Proposed Method 3: F-SVNS-ACC-MADM for Rapid Prototype

Selection

108

4.3.4 Performance Measures Comparison: Rapid Prototype Ranking 109

4.4 Collected Case Example 4: Non-Traditional Machining Processes (NTMP)

Selection

111

4.4.1 Proposed Method 1: F-SVNS-N-MADM for NTMP Selection 112

4.4.2 Proposed Method 2: F-SVNS-EW-MADM for NTMP Selection 113

4.4.3 Proposed Method 3: F-SVNS-ACC-MADM for NTMP Selection 113

4.4.4 Performance Measures Comparison: NTMP Ranking 114

4.5 Collected Case Example 5: Automated guided Vehicle (AGV) Selection 115

4.5.1 Proposed Method 1: F-SVNS-N-MADM for AGV Selection 117

4.5.2 Proposed Method 2: F-SVNS-EW-MADM for AGV Selection 117

4.5.3 Proposed Method 3: F-SVNS-ACC-MADM for AGV Selection 118

4.5.4 Performance Measures Comparison: AGV Ranking 119

4.6 Collected Case Example 6: Robot Selection 121

xx

4.6.1 Proposed Method 1: F-SVNS-N-MADM for Robot Selection 123

4.6.2 Proposed Method 2: F-SVNS-EW-MADM for Robot Selection 125

4.6.3 Proposed Method 3: F-SVNS-ACC-MADM for Robot Selection 127

4.6.4 Performance Measures Comparison: Robot Ranking 128

4.7 Collected Case Example 7: Metal Stamping Layout Selection 130

4.7.1 Proposed Method 1: F-SVNS-N-MADM for Metal Stamping Layout

Selection

132

4.7.2 Proposed Method 2: F-SVNS-EW-MADM for Metal Stamping Layout

Selection

133

4.7.3 Proposed Method 3: F-SVNS-ACC-MADM for Metal Stamping Layout

Selection

133

4.7.4 Performance Measures Comparison: Metal Stamping Layout Ranking 134

4.8 Collected Case Example 8: Electro Chemical Machining (ECM) Programming

Selection

135

4.8.1 Proposed Method 1: F-SVNS-N-MADM for ECM Programming

Selection

137

4.8.2 Proposed Method 2: F-SVNS-EW-MADM for ECM Programming

Selection

138

4.8.3 Proposed Method 3: F-SVNS-ACC-MADM for ECM Programming

Selection

140

4.8.4 Performance Measures Comparison: ECM Program Ranking 141

4.9 Collected Case Example 9: Cutting Fluid (Coolant) Selection 143

4.9.1 Proposed Method 1: F-SVNS-N-MADM for Cutting Fluid (Coolant)

Selection

144

4.9.2 Proposed Method 2: F-SVNS-EW-MADM for Cutting Fluid (Coolant)

Selection

145

4.9.3 Proposed Method 3: F-SVNS-ACC-MADM for Cutting Fluid (Coolant)

Selection

145

4.9.4 Performance Measures Comparison: Cutting Fluids Ranking 146

4.10 Collected Case Example 10: Supplier Selection 147

4.10.1 Proposed Method 1: F-SVNS-N-MADM for Supplier Selection 149

4.10.2 Proposed Method 2: F-SVNS-EW-MADM for Supplier Selection 151

4.10.3 Proposed Method 3: F-SVNS-ACC-MADM for Supplier Selection 152

xxi

4.10.4 Performance Measures Comparison: Suppliers Ranking 153

4.11 Collected Case Example 11: Third Party Reverse Logistics Provider‘s (TPRLP)

selection

155

4.11.1 Proposed Method 1: F-SVNS-N-MADM for TPRLP Selection 157

4.11.2 Proposed Method 2: F-SVNS-EW-MADM for TPRLP Selection 158

4.11.3 Proposed Method 3: F-SVNS-ACC-MADM for TPRLP Selection 159

4.11.4 Performance Measures Comparison: TPRLP Ranking 160

4.12 Comparative Performance of Proposed MADM Techniques 162

CHAPTER NO.5 SENSITIVITY ANALYSIS 165

5.1 Introduction 166

5.2 Classification of Sensitivity Analysis 166

5.3 Spearman Correlation Coefficient 167

5.4 Sensitivity Analysis of Proposed MADMs for Collected Case Examples 167

5.4.1 Sensitivity Analysis of Proposed MADMs for Case Example 1: Material

Selection

169

5.4.2 Sensitivity Analysis of Proposed MADMs for Case Example 2: Machine

Tool Selection

171

5.4.3 Sensitivity Analysis of Proposed MADMs for Case Example 3: Rapid

Prototype Selection

173

5.4.4 Sensitivity Analysis of Proposed MADMs for Case Example 4: NTMP

Selection

175

5.4.5 Sensitivity Analysis of Proposed MADMs for Case Example 5: AGV

Selection

177

5.4.6 Sensitivity Analysis of Proposed MADMs for Case Example 6: Robot

Selection

179

5.4.7 Sensitivity Analysis of Proposed MADMs for Case Example 7: Metal

Stamping Layout Selection

182

5.4.8 Sensitivity Analysis of Proposed MADMs for Case Example 8: ECM

Programming Selection

184

5.4.9 Sensitivity Analysis of Proposed MADMs for Case Example 9: Cutting

Fluid (Coolant) Selection

186

5.4.10 Sensitivity Analysis of Proposed MADMs for Case Example 10: Supplier 188

xxii

Selection

5.4.11 Sensitivity Analysis of Proposed MADMs for Case Example 11: TPRLP

Selection

190

5.5 Outcome of Sensitivity Analysis 192

CHAPTER NO.6 CONCLUSION AND FUTURE SCOPE 195

6.1 Actual Contribution of the Thesis 197

6.2 Advantage of Proposed Methodology 199

6.3 Future Scope 200

LIST OF REFERENCES 201

Appendix -A: F-SVNS N-MADM Detailed Calculations 222

Annexure -B: F-SVNS EW-MADM Detailed Calculations 229

Annexure -C: F-SVNS ACC-MADM Detailed Calculations 243

Annexure -D: Spearman Correlation Coefficient Detailed Calculations 252

Annexure -E: Investigated MADM‘s MATLAB Coding 263

LIST OF PUBLICATIONS 293

xxiii

List of Abbreviations

AGV Automated Guided Vehicle

AHP Analytical Hierarchy Process

ANP Analytic Network Process

COPRAS COmplex PRoportional ASsessment

DEA Data Envelopment Analysis

ELECTRE ELimination and Choice Expressing Reality

ERP Enterprise Resource Planning

F- PROMETHEE Fuzzy- Preference Ranking Organization Method for Enrichment

Evaluations

FMS Flexible Manufacturing System

F-PSI Fuzzy Preference Selection Index

FS Fuzzy Set

F-SVNS Fuzzy- Single Value Neutrosophic Sett

F-SVNS-ACC-MADM Fuzzy Single Valued Neutrosophic Set SVNS Advance Correlation

Coefficient MADM

F-SVNS EW- MADM Fuzzy Single Valued Neutrosophic Set Entropy Weight based MADM

F-SVNS-N-MADM Fuzzy-Single Valued Neutrosophic Set Novel MADM

F-TOPSIS Fuzzy- Technique for Order Preference by Similarity to Ideal Solution

F-VIKOR Fuzzy- VlseKriterijuska OptimizacijaI Komoromisno Resenje

GRA Gray Relational Analysis

GTMA Graph Theory and Matrix Approach

IFS Intuitionistic Fuzzy Set

IFS –ELECTRE Intuitionistic Fuzzy Set - ELimination and Choice Expressing Reality

IFS –TOPSIS Intuitionistic Fuzzy Set - Technique for Order Preference by Similarity to

Ideal Solution

IFV Intuitionistic Fuzzy Value

IVIFS Interval Valued Intuitionistic Fuzzy Set

LSTMM Linear Scale Transformation, Max Method

LSTMMM Linear Scale Transformation, Max- Min Method

LSTSM Linear Scale Transformation Sum Method

MADM Multi Attribute Decision Making

xxiv

MAGDM Multi Attribute Group Decision Making

MHE Material Handling Equipment

NDA Net Dominance of Alternative

NOF Negative Outranking Flow

NPD New Product Development

NTMP Non Traditional Machining Processes

PM Performance Measurement

POF Positive Outranking Flow

PROMETHEE Preference Ranking Organization Method for Enrichment Evaluations

PSI Preference Selection Index

SAW Simple Additive Weighting

SC Supply Chain

SCM Supply Chain Management

SM Selection Methodology

SVNS Single Valued Neutrosophic Set

TOPSIS Technique for Order preference by Similarity to Ideal Solution

TPL (3PL) Third Party Logistics

VIKOR VlseKriterijuska OptimizacijaI Komoromisno Resenje

VNM Vector Normalization Method

WPM Weighted Product Model

xxv

List of Symbols

Symbol Contain

A Set of alternatives

Priority weight of alternatives with respective to attribute

Concordance Index

discordance Index

GM Geometric Mean

Significance of alternative

Preference selection index of alternative

Number of alternatives

Number of attributes

Overall or composite performance score of the alternatives

Preference variation value

Quantitative performance of alternative when it examined with attribute

Normalized value of attributes

Relative importance between attributes

Separation of each alternatives from the ideal one

Weighted normalized rating

Weight of the attribute

Maximizing normalized indices

Minimizing normalized indices

Grey correlated coefficient

Utility degree

Preference function

Deviation in preference value of selection attribute

Positive outranking flow

Negative outranking flow

Net outranking flow

Overall preference value of selection criteria or attribute

Grey relation grad

xxvi

List of Figures

Fig

No. Contain

Page

No.

1.1 Flow chart of Research Work 11

2.1 Literature Review Screening Methodology 15

2.2 Outline of Literature Review 16

2.3 Fuzzy Eleventh Point Scales 35

5.1 Effect of Normalization Methods on Material Selection Case Example 1 170

5.2 Effect of Normalization Methods on Machine Tool Selection Case

Example 2

172

5.3 Effect of Normalization Methods on Rapid Prototype Selection Case

Example 3

174

5.4 Effect of Normalization Methods on NTMP Selection Case Example 4 176

5.5 Effect of Normalization Methods on AGV Selection Case Example 5 178

5.6 Effect of Normalization Methods on Robot Selection Case Example 6 180

5.7 Effect of Normalization Methods on Metal Stamping Layout Selection

Case Example 7

182

5.8 Effect of Normalization Methods on ECM Programming Selection Case

Example 8

184

5.9 Effect of Normalization Methods on Cutting Fluid Selection Case Example

9

187

5.10 Effect of Normalization Methods on Supplier Selection Case Example 10 189

5.11 Effect of Normalization Methods on Third Party Reverse Logistic

Provider‘s Selection Case Example 11

191

5.12 Flow of Sensitivity Analysis for Proposed Methodologies 193

xxvii

List of Tables

Table

No.

Description Page

No.

1.1 Decision Matrix for MADM Methodology 6

2.1 TOP 10 Cited Journals for Multi Attribute Decision Making Technique 15

2.2 Decision Matrix for AHP Methodology 18

2.3 Random Index (RI) Values for AHP Technique 19

2.4 Decision Matrix for TOPSIS Methodology 21

2.5 Decision Matrix for VIKOR Methodology 23

2.6 Decision Matrix for ELECTRE Methodology 26

2.7 Decision Matrix for PROMETHEE Methodology 28

2.8 Decision Matrix for GRA Methodology 30

2.9 Decision Matrix for COPRAS Methodology 32

2.10 Decision Matrix for PSI Methodology 35

2.11 Lingustic to Crisp Value Conversion Table 36

2.12 Normalized Decision Matrix for PSI Technique 36

2.13 Comparative Performance of Existing MADM Technique 38

2.14 Crisp Value of Selection Attributes 42

2.15 Lingustic to IFV Value Conversion Investigated in 2013 44

2.16 Lingustic to IFV Value Conversion Investigated in 2017 45

2.17 Conversion of Linguistic Value to Corresponding IVIFS 47

2.18 Conversion of Linguistic Value to Corresponding SVNS 49

3.1 Decision Matrix for F-SVNS N-MADM 68

3.2 Conversion of Linguistic Terms in to Classic (Crisp) Set 69

3.3 Normalized Decision Matrix for F-SVNS N-MADM 70

3.4 SVNS Normalized Decision Matrix for F-SVNS N-MADM 70

3.5 Decision Matrix for F-SVNS EW-MADM 72

3.6 Normalized Decision Matrix for F-SVNS EW-MADM 72

3.7 SVNS Normalized Decision Matrix for F-SVNS EW-MADM 73

3.8 Decision Matrix for F-SVNS ACC-MADM 75

3.9 Normalized Decision Matrix for F-SVNS ACC-MADM 75

3.10 SVNS Normalized Decision Matrix for F-SVNS ACC-MADM 76

3.11 Decision Matrix for F-SVNS MADM for Industrial Case Example-I 77

xxviii

3.12 Normalized Decision Matrix for F-SVNS MADM 78

3.13 SVNS Normalized Decision Matrix for Industrial Case Example-I 79

3.14 F-SVNS N-MADM Ranking for Industrial Case Example-I 80

3.15 F-SVNS EW-MADM Ranking for Industrial Case Example-I 82

3.16 F-SVNS ACC-MADM Ranking for Industrial Case Example-I 84

3.17 F-SVNS MADMs Ranking for Industrial Case Example-I 85

3.18 Decision Matrix for F-SVNS MADM for Industrial Case Example-II 85

3.19 Normalized Decision Matrix of F-SVNS MADM for Industrial Case

Example- II

86

3.20 SVNS Normalized Decision Matrix for Industrial Case Example-II 87

3.21 F-SVNS N-MADM Ranking for Industrial Case Example-II 88

3.22 F-SVNS EW-MADM Ranking for Industrial Case Example-II 90

3.23 F-SVNS ACC-MADM Ranking for Industrial Case Example-II 92

3.24 F-SVNS MADMs Ranking for Industrial Case Example-II 93

4.1 Collected Random Samples from the Peer Reviewed Journal/Book 95

4.2 Material Selection Input Matrix (Collected Case Example) 96

4.3 Material Selection Converted Input Matrix (Qualitative to Quantitative

Form)

96

4.4 Material Selection Normalized Matrix using VNM 97

4.5 F-SVNS N-MADM Ranking for Material Selection 98

4.6 F-SVNS EW-MADM Ranking for Material Selection 98

4.7 F-SVNS ACC-MADM Ranking for Material Selection 99

4.8 Material Selection Performance Measures Comparison 100

4.9 Machine Tool Selection Input Matrix (Collected Case Example) 101

4.10 Machine Tool Selection Normalized Matrix using VNM 101

4.11 F-SVNS N-MADM Ranking for Machine Tool Selection 102

4.12 F-SVNS EW-MADM Ranking for Machine Tool Selection 103

4.13 F-SVNS ACC-MADM Ranking for Machine Tool Selection 103

4.14 Machine Tool Selection Performance Measures Comparison 104

4.15 Rapid Prototype Selection Input Matrix (Collected Case Example) 106

4.16 Rapid Prototype Selection Normalized Matrix using VNM 106

4.17 F-SVNS N-MADM Ranking for Rapid Prototype Selection 107

4.18 F-SVNS-EW-MADM Ranking for Rapid Prototype Selection 108

xxix

4.19 F-SVNS ACC-MADM Ranking for Rapid Prototype Selection 109

4.20 Rapid Prototype Selection Performance Measures Comparison 109

4.21 NTMP Selection Input Matrix (Collected Case Example) 111

4.22 NTMP Selection Normalized Matrix using VNM 111

4.23 F-SVNS N-MADM Ranking for NTMP Selection 112

4.24 F-SVNS EW-MADM Ranking for NTMP Selection 113

4.25 F-SVNS ACC-MADM Ranking for NTMP Selection 113

4.26 NTMP Selection Performance Measures Comparison 114

4.27 AGV Selection Input Matrix (Collected Case Example) 115

4.28 AGV Selection Normalized Matrix using VNM 116

4.29 F-SVNS N-MADM Ranking for AGV Selection 117

4.30 F-SVNS EW-MADM Ranking for AGV Selection 118

4.31 F-SVNS ACC-MADM Ranking for AGV Selection 118

4.32 AGV Selection Performance Measures Comparison 119

4.33 Robot Selection Input Matrix (Collected Case Example) 121

4.34 Robot Selection Normalized Matrix using VNM 122

4.35 F-SVNS N-MADM Ranking for Robot Selection 123

4.36 F-SVNS EW-MADM Ranking for Robot Selection 125

4.37 F-SVNS ACC-MADM Ranking for Robot Selection 127

4.38 Robot Selection Performance Measures Comparison 129

4.39 Metal Stamping Layout Selection Input Matrix (Collected Case Example) 131

4.40 Metal Stamping Layout Selection Normalized Matrix using VNM 131

4.41 F-SVNS N-MADM Ranking for Metal Stamping Layout Selection 132

4.42 F-SVNS EW-MADM Ranking for Metal Stamping Layout Selection 133

4.43 F-SVNS ACC-MADM Ranking for Metal Stamping Layout Selection 133

4.44 Metal Stamping Layout Selection Performance Measures Comparison 134

4.45 ECM programming Selection Input Matrix (Collected Case Example) 136

4.46 ECM programming Selection Normalized Matrix using VNM 136

4.47 F-SVNS N-MADM Ranking for ECM Programming Selection 138

4.48 F-SVNS EW-MADM Ranking for ECM Programming Selection 139

4.49 F-SVNS ACC-MADM Ranking for ECM Programming Selection 140

4.50 ECM programming Selection Performance Measures Comparison 141

4.51 Cutting Fluid Selection Input Matrix (Collected Case Example) 143

xxx

4.52 Cutting Fluid Selection Normalized Matrix using VNM 143

4.53 F-SVNS N-MADM Ranking for Cutting Fluid Selection 144

4.54 F-SVNS EW-MADM Ranking for Cutting Fluid Selection 145

4.55 F-SVNS ACC-MADM Ranking for Cutting Fluid Selection 145

4.56 Cutting Fluid Selection Performance Measures Comparison 146

4.57 Supplier Selection Input Matrix (Collected Case Example) 148

4.58 Supplier Selection Normalized Matrix using VNM 149

4.59 F-SVNS N-MADM Ranking for Supplier Selection 150

4.60 F-SVNS EW-MADM Ranking for Supplier Selection 151

4.61 F-SVNS ACC-MADM Ranking for Supplier Selection 152

4.62 Supplier Selection Performance Measures Comparison 154

4.63 TPRLP Selection Input Matrix (Collected Case Example) 156

4.64 TPRLP Selection Normalized Matrix using VNM 156

4.65 F-SVNS N-MADM Ranking for TPRLP Selection 157

4.66 F-SVNS EW-MADM Ranking for TPRLP Selection 158

4.67 F-SVNS ACC-MADM Ranking for TPRLP Selection 159

4.68 TPRLP Selection Performance Measures Comparison 161

4.69 First Ranking Similarity in Percentage of Proposed Methodologies with

Published Results

163

5.1 Various Normalization Approaches for Beneficial and Non-beneficial

Values

168

5.2 Relative Normalization Equations for Proposed Methods 168

5.3 Average Spearman Rank Correlation Coefficient for Collective Case

Example of Material Selection

171


Example of Machine Tool Selection

173


Example of Rapid Prototype Selection

174


Example of NTMP Selection

176


Example of AGV Selection

178

5.8 Average Spearman Rank Correlation Coefficient for Collective Case 181

xxxi

Example of Robot Selection


Example of Metal Stamping Layout Selection

183


Example of Electro Chemical Machining Programming Selection

185


Example of Cutting Fluid (Coolant) Selection

187


Example of Supplier Selection

190


Example of Reverse Logistics Providers selection

192

5.14 Conclusion Validation of the Proposed Methodology using Sensitivity

Analysis

194

xxxii

List of Appendices

Appendix A F-SVNS N-MADM Detail Calculations

Appendix B F-SVNS EW-MADM Detail Calculations

Appendix C F-SVNS ACC-MADM Detail Calculations

Appendix D Spearman Correlation Coefficient Detail Calculations

Appendix E Investigated MADM‘s MATLAB Coding

Chapter 1: Introduction

1


2

CHAPTER: 1

Introduction

“Supply chain is like nature, it is all around us”

(Mohanty and Deshmukh 2009) described that ―A supply chain is a network of facilities

and distribution options that performs the functions of procurement of materials,

transportation of these materials into intermediate and finished products and the

distribution of these finished products to customers. Supply chains exist in both

service and manufacturing organization, although the complexity of the chain may

vary greatly from industry to industry and firm to firm‖. Though there are varieties of

definitions are available in literature. (Mohanty; and Deshmukh 2011) expressed the

summarizing forms of supply chain definition with their explanations as follows.

Supply chain basically involves integration of business processes.

Supply chain establishes linkages with suppliers, customers and within the

value chain of business unit. It also establishes linkages across business unit

value chains within the firm.

Supply chain encompasses all activities involved in the flow and

transformation of goods from the raw material stage to the finished product, as

well as associated with information flows, cash flows and product flows in

organization. Raw materials enter a manufacturing organization via a supply

chain system and are transformed into finished goods. The finished goods are

then supplied to consumers through a distribution system.

Supply chain can be viewed as a decision making structure which makes it

possible for a real cooperation among various decision making units operating

concurrently.

It is also known as value chains or demand chains. Supply chain management

(SCM) is the integrated process of production value for the end user or ultimate

consumers.

The main objectives of supply chain management are as below.


3

o To reduce inventory at all sites of SC

o To reduce costs

o Faster processing speeds

o To reduce lead time

o To reduce warehouse cost

o To reduce transportation cost

o To reduce obsolescence

o Greater responsiveness to customer demand

o Links to suppliers and customers

o Continuous flow of products and information

1.1 Importance of Decision Making in SCM

Due to globalization decision making are very important if growth of product

variation, reduction in product life cycle, splitting of supply chain, changing

technologies and sustainability. (Mohanty and Deshmukh 2009) explained the strategic

choices include: the selection of goals and objectives, the choice of products and

services to offer, the design and the configuration of polices determining how the firm

positions it to complete in the product market, the choice of an appropriate level of

scope and diversity; and the design of organization structure, administrative system

and policies. (Nirmal and Bhatt 2019), (Kahraman and Otay 2019) explained that the

decision plays a vital role for smoothly running of SC network, right decision also

directly/ indirectly leads to improve performance of manufacturing and supply chain

functions. (Mohanty and Deshmukh 2009) explained that the decisions for SCM can be

organized into broad categories as below.

(i) Strategic decision,

(ii) Tactical decision and

(iii) Operational decision

Strategic decisions: They are considered as long term decisions as follows.

Location decision: They are concerned with the size, number and

geographic location of the supply chain entities such as plants, inventories

or distribution centers.

1.2 Decision Making through MADM

4

Production or manufacturing decisions: Production/ manufacturing is heart

and key driver of supply chain. Manufacturing defined as making of good

by hand and/or machine. It works with raw or semi-finished component part

of a larger product. (Mohanty; and Deshmukh 2011) explained that huge

investment is taking place in appropriate manufacturing technologies such

as CAD/ CAM/CIM, rapid prototyping, robotics, FMS, non-conventional

machining processes etc. Production/ manufacturing decisions are meant to

determine which material to select, which products to produce, which

machine tool to select, which cutting fluid to use, where to produce, which

machining programming to select, which suppliers to select, from which

plants to supply distribution centers and so on.

Inventory/ material decisions: They are concerned with the way to

managing inventories and selection of material in supply chain.

Transportation decisions: They are made on the modes of transport to use,

selection of third party logistics providers, selection of transportation

network, selection of material handling equipment etc.

Tactical decisions: They are considered as medium term decisions, such as weekly

demand forecast, distribution and transportation plan, production planning and

material requirement planning (MRP).

Operational decisions: They are considered as very short term decisions made from

day to day to run supply chain, such as detailed production scheduling, master

production scheduling, scheduling production on machines and equipment

maintenance.

Here, in the current research work, focus is on improving the strategic decision where

selection of right alternative among the list of various alternatives and the conflicting

criteria are considered.

1.2 Decision Making through MADM

Decision making is a part of operation research. When there are numbers of alternative

with complex criteria (beneficial/ non-beneficial and with different units), it is very


5

difficult to make a transparent decision without favoritism. In general decision making

problem contains various alternatives, various criteria (objectives) and relative alternative

performance with respect to criteria (Payoff). In this research work focuses on the better

ranking of alternatives where there are numbers of criteria to be considered at the time of

selection, which directly/ indirectly leads to improve the performance of manufacturing

and supply chain functions (Nirmal and Bhatt 2019), (Kahraman and Otay 2019), this

procedure of selection is known as multi attribute decision making (MADM). MADM is

one of the branches in Operation research (OR) and Decision making (DM). Here,

there are number of alternatives and relative criteria considered for ranking purpose.

(Kahraman and Otay 2019), (Nirmal and Bhatt 2019), (Kahraman and Otay 2019),

(Hwang and Masud 2012) have developed the characteristics of MADM as shown below.

Alternatives: Different choices available for decision makers

Multi-attribute: Each problem is having different criteria (attributes). For each

selection problem decision maker must generate relevant alternatives and attributes

information.

Conflict among the attributes: multi attribute usually conflict. Some of them have

qualitative information, while some have quantitative information. Some attributes

are beneficial like quality of product, speed of machine, etc. while other attributes

are non-beneficial attributes like, price, delivery, etc.

Specific units: each attribute is having different units of measurement, i.e.

price/cost in Rs., speed in rpm, accuracy in mm, tensile strength (MPa), surface

roughness (micro mm), weight (kg), and diameter (mm).

Normalization: The normalization is attempted to convert the units of different

attributes information in the comparable scale.

Methodology/ Selection: The problem needs to be solved for ranking or best

alternatives by considering each alternative and attribute.

1.3 Functioning of MADM

MADM flows through the steps as below.

Step 1. To identify the objective of MADM for selection/ ranking/ sorting/ evaluation

for decision making.

Step 2. Collection of various alternatives and attributes involved in selection procedure.

1.4 Advantages of MADM

6

Step 3. Prepare a matrix ( ) with alternatives ( ) and attributes ( ), which is

known as decision matrix. Let consider set of alternatives as { } &

set of criteria as { }. Here, shows the relative performance

measures between alternatives and attributes which are also known as payoff are

having qualitative/ quantitative values. Table 2.1 shows the decision matrix.

TABLE 1.1: Decision Matrix for MADM Methodology

…..

…..

…..

…..

…. ….. ….. ….. ….. …..

…..

Step 4. Conversion of qualitative data in to quantitative data

Sometime the input matrix payoff is having linguistic (qualitative) data which is

converted in to crisp (quantitative) data.

Step 5. Generalization/ normalization of matrix

Each relative attribute of alternative are having different values with different units for that

purpose normalization is carried out. It makes the matrix (performance measure value) in a

similar range.

Step 6. Calculation of criteria weight for giving specific weightage of criteria.

Criteria weight is calculated in MADM or it is predetermined by the experts/ decision

makers/ researchers.

Step 7. Ranking of alternatives

Alternative weight is calculated with the MADM technique, the alternatives rank is

obtained according to descending order. i.e. highest alternative weight is considered as first

rank, while, lowest alternative weight is considered as last rank.

1.4 Advantages of MADM

MADM define as a technique which makes the decision making easier and able to

handle various kind of multi criteria (attribute) and find the best alternative for


7

selection process. MADM methods provide quantitative calculations to aid decision

making solution. Some advantages of MADMs are as follows.

Applicability in decision making environment

Ability to handle different criteria simultaneously

Ability to handle conflicting (Beneficial/ Non beneficial) criteria

Ability to handle criteria with different units

The matrix itself works as effective guiding tool to decision maker

Practical decision making

Transparent ranking

Avoiding personal favoritism in Ranking solution

Improve better understanding of goal and challenges

Payoff (Alternatives performance with respect to criteria)

Countless impact on practical decision making

1.5 Objective and Scope of Research Work

In the outcome of the literature review in chapter 2 shows that existing MADM such as

AHP, TOPSIS, VIKOR, ELECTRE, PROMETHREE, GRA, COPRAS, PSI, etc. are

applied for finding the best alternative for a given application in the field of manufacturing

and supply chain environment. While considering existing MADM with affiliated

mathematical set, there are some drawbacks or limitation of existing MADM methods also

reported at the end of literature review chapter 2.

The main objective of the present research work is to propose a new MADM approach as

the resolution of weaknesses of existing MADM methods, which result better ranking

solution.

To learn existing mathematical set which is applied in MADM and identify the

importance of single valued neutrosophic set (SVNS) compared to existing

mathematical set.

Investigate technique which is used to convert input information crisp/ lingustic set

(exact thinking) to earlier investigated mathematical set which is known as SVNS

1.5 Objective and Scope of Research Work

8

(Human behavioral thinking) which having the information in degree of truthness,

degree of indeterminacy and degree of falsehood, which leads to improve the

ranking solution.

To cover up the limitations of existing MADMs by proposing three new

approaches for MADMs.

(i) Fuzzy Single Valued Neutrosophic Set Novel MADM (F-SVNS N-

MADM),

(ii) Fuzzy Single Valued Neutrosophic Set Entropy Weight Based MADM (F-

SVNS EW-MADM) and

(iii) Fuzzy Single Valued Neutrosophic Set Advanced Correlation Coefficient

MADM (F-SVNS ACC-MADM)

To ensure the soundness of ranking solution of proposed MADMs.

To ensure that developed method can handle a large number of qualitative and

quantitative information with beneficial/ non-beneficial criteria as well as large

number of alternatives.

To implement the proposed methodologies in eleven domains through random case

example collected in each domain with peer reviewed journal/ book. Random

eleven domains are identified where, best selection process one of the keys to

improve performance of manufacturing and supply chain. The names of random

domains which are related to manufacturing and supply chain multi criteria

decision making are as under.

o Material selection

o Machine tool selection

o Rapid prototype selection

o Nontraditional machining process (NTMP) selection

o Automated guided vehicle (AGV) selection

o Robot selection

o Metal stamping layout selection

o Electro chemical machining (ECM) programming selection

o Cutting fluid (Coolant) selection

o Supplier selection

o Third party reverse logistics providers (TPRLP) selection


9

To study and explore general ranking solution of proposed MADMs with published

ranking results.

To test and analyze sensitivity analysis to check the soundness of proposed

MADMs solutions with same case examples of eleven domains through (i)

different normalization methods and (ii) spearman correlation coefficient.

To identify the best MADM from the proposed methods through average of all

eleven domain spearman correlation coefficient sensitivity analysis and less

calculations.

1.6 Research Assumptions

The success of manufacturing and supply chain decision problem depends on right

decision in right time. Some assumptions and research boundary are considered during the

current research work are as under.

Wherever multi attribute selection is carried out in manufacturing and supply chain

environment, the best ranking solution leads to improve performance.

For implementation and initial validation purpose, proposed methodologies

methodology are applied to collected case examples (from peer reviewed journal/

book) and compared and explained with published ranking results.

Research is constrained with classic MADM techniques with its application in

manufacturing and supply chain field.

During implementation phase the collection of input information in crisp value

quantitative/ qualitative mode and conversion in to Fuzzy Single Valued

Neutrosophic (F-SVNS) value.

1.7 Research Work Flow

Fig. 1.1 shows the research work flow in flow chart.

1.7 Research Work Flow

10

Start

Identify the Selection Process is one of the area to Improve Performance in

Manufacturing and Supply Chain Functions

Literature survey to study various ―Multi Attribute Decision Making

Techniques‖ for Ranking and Selection

Explanation of each MADM Methodological Steps, Application and Limitation

―F-SVNS-N-MADM Technique‖ ―F-SVNS-EW-MADM Technique‖ ―F-SVNS-ACC-MADM

Technique‖

1

Survey on random sample in MADM

applications

(1) Material Selection

(2) Machine Tool Selection

(3) Rapid Prototyping Selection

(4) Non Traditional Machining Process

Selection

(5) Automated Guided Vehicle Selection

(6) Robot Selection

(7) Metal Stamping Layout Selection

(8) Electro Chemical Machining process

Selection

(9) Cutting Fluid Selection

(10) Supplier Selection/ Vendor Selection

(11) Third Party Logistics Providers Selection

Literature survey is carried out to study various ―Mathematical Set‖ applied in ―Multi

Attribute Decision Making Techniques‖ for decision making

Explain and Identify Set Theory, Application, Advantage and Drawback

Investigate THREE New MADM‘s

(With Conversion Principle of Crisp value to F-SVNS Value)


11

FIGURE 1.1: Flow Chart of Research Work

1

Application in Manufacturing and Supply chain Supply Chain Environment Data Collect

Implementation of Methods in Collected Case

Examples (Random Sample)

(1) Material Selection

(2) Machine Tool Selection

(3) Rapid Prototyping Selection

(4) Non Traditional Machining Process Selection

(5) Automated Guided Vehicle Selection

(6) Robot Selection

(7) Metal Stamping Layout Selection

(8) Electro Chemical Machining Programming

Selection

(9) Cutting Fluid Selection

(10) Supplier Selection/ Vendor Selection

(11) Third Party Reverse Logistics Providers

Selection

Linear Scale

Transformation Max

Method (LSTMM)

Linear Scale

Transformation Max Min

Method (LSTMMM)

Vector Normalization

Method (VNM)

Linear Scale

Transformation Sum

Method (LSTSM)

Validation of Proposed MADM with various Normalizing Techniques

Identified the Best MADM methodology as F-SVNS-N-MADM Technique among proposed MADMs

End

Ranking Validation of each case examples with Published Results

Identify the best Method using ―Spearman Correlation Coefficient‖ Test

1.8 Outline of the Thesis

12

1.8 Outline of the Thesis

The entire thesis has been organized in six chapters. Framework of each chapter is as

under.

Chapter 2:

This chapter discusses the existing MADM techniques with history, method and

implementation in manufacturing and supply chain functions with its limitations. The

chapter also elaborates how to improve performance in manufacturing and supply chain

function through MADM selection. Moreover, this chapter also comprises of various

mathematical set theories, their applications, advantages and drawbacks.

Chapter 3:

This chapter is the core part of the thesis. It shows the three new methodologies of MADM

(i) Fuzzy Single Valued Neutrosophic Set Novel Multi Attribute Decision Making

(F-SVNS N-MADM)

(ii) Fuzzy Single Valued Neutrosophic Set Entropy Weight based MADM (F-

SVNS EW-MADM)

(iii) Fuzzy Single Valued Neutrosophic Set Advance Correlation Coefficient

MADM (F-SVNS ACC- MADM)

Chapter 4:

This chapter includes the application of proposed methodologies in various manufacturing

and supply chain area to improve the performance of selection process as shown below.

The proposed methodologies implemented in following collected case examples which is

published in various peer reviewed journals/ books in manufacturing and supplier chain

environment.



o Rapid prototyping selection

o Non-traditional machining process selection

o Automated guided vehicle selection

o Robot selection


13


o Electro chemical machining process selection

o Cutting Fluid Selection

o Supplier Selection/ Vendor Selection

o Third Party Logistics (TPL) providers Selection

Chapter 5:

This chapter shows the validation through sensitivity analysis using various normalization

methods for beneficial and non-beneficial attributes of selection through proposed

MADM‘s with the help of ―Spearman Correlation Coefficient Test‖ and proves F-SVNS

N-MADM technique gives better result among proposed methodology.

Chapter 6:

This chapter contains major conclusions including advantages of proposed methodologies,

actual contribution by the thesis and future scope of research.

14

Chapter 2: Literature Review


15

CHAPTER: 2

Literature Review

Here, the literature review follow with the meta-search (initial) phase research papers are

collected throughout the research journey through given key words and applications. Then

examination with elimination of duplication work/ similarity of applications and they are

ignored. Then remaining abstract analysis carried out to identify the area of work related to

manufacturing/ supply chain, mathematical set and so on. The detail study of scrutinized

research papers with methodology, application and explanation of comparison is carried

out which are covered in the citation. The literature screening methodology is as shown in

Fig 2.1.

FIGURE 2.1: Literature Review Screening Methodology

In this literature review, the applications of various MADM are also collected from the

TOP 10 cited journals for MADM techniques as shown in Table 2.1.

TABLE 2.1: Top 10 Cited Journals for Multi Attribute Decision Making Technique

Sr. No. Name of the Journal Citation

2016 Publisher

1 Knowledge-Based Systems 5.35 Elsevier

2 Materials and Design 4.90 Elsevier

3 Expert Systems with Applications 4.70 Elsevier

4 International Journal of Production Economics 4.28 Elsevier

5 European Journal of Operational Research 3.83 Elsevier

6 Journal of Materials Processing Technology 3.62 Elsevier

7 International Journal of Production Research 2.67 Taylor & Francis

8 International Journal of Advanced Manufacturing

Technology 2.30 Springer Nature

9 Decision Sciences 1.86 Wiley-Blackwell

10 Proceedings of the Institution of Mechanical Engineers, 0.99 Professional Engineering

Meta Search Elimination of Duplication / Similarity of Applications

Abstract Analysis Full Paper Analysis

Key words

[Selection Methodology, MADM,

Mathematical Set]

Google Scholar, IEEE, Emerald

insight, Elsevier, Springer, Science

Direct, Top Cited Peer Reviewed

Journal, International Books from

Year 1960 to 2019

16

Part B: Journal of Engineering and Manufacturing. Publishing Ltd.

Data collected from SCOPUS scores April, 2017.

In this chapter literature review is classified in three major topics (i) Existing literature on

MADM with their individual history, methodology, applications, advantages and

limitations (ii) Existing literature about mathematical set with their theory steps,

applications, advantages and limitations, (iii) The random case examples of selection

carried out in manufacturing and supply chain environment. The outline of the literature

review is as shown in Fig. 2.2

FIGURE 2.2: Outline of Literature Review

Literature Review

Existing Mathematics Set

Theory Step

Application

Advantages

Limitation

Existing MADM

Methodology Step

Application

Advantages

Limitation (Research Gap)

Random case examples of

selection carried out in

manufacturing and supply

chain environment.

Analytical Hierarchy Process

investigated by (Saaty 1994)

Technique for Order Preference by

Similarity to Ideal Solution developed

(Chen and Hwang 1992a)

VIseKriterijuska OptimizacijaI

Komoromisno Resenje(VIKOR)

investigated by (Opricovic 1998), (Rao

2008b)

Preference Ranking Organization

Method for Enrichment Evaluations

(PROMETHEE)

proposed by (Brans and Vincke 1985)

Gray Relational Model (GRA) Method

investigated by (Ju-Long 1982)

Complex Proportional Assessment

(COPRAS)

investigated by(Zavadskas et al. 1994)

Preference Selection Index (PSI)

Method investigated by (Maniya and

Bhatt 2010)

Crisp Set

Classical set

Fuzzy Set (FS)

investigated by (Zadeh 1996)

Intuitionistic fuzzy set (IFS)

developed by (Zadeh 1996),

(Atanassov 1986)

Interval Valued Intuitionistic

Fuzzy Set (IVIFS) investigated by

(Atanassov and Gargov 1989)

Neutrosophic (NS) developed by

(Smarandache 2005)

Single Valued Neutrosophic Set

(SVNS)

investigated by (Wang et al. 2010),

(Ye 2013)

Material Selection

Machine Tool Selection

Rapid Prototype Selection

Non-Traditional Machining

process Selection

Automated guided Vehicle

(AGV) Selection

Robot Selection

Metal Stamping Layout

Selections

Electro Chemical Machining


Cutting Fluid (Coolant)

Selections

Supplier Selections

Reverse Logistics Service

Providers selection


17

2.1 MADM Techniques

Because of globalization, decreasing product life cycles, increasing product variety,

changing technologies, fragmentation of supply chain and an increased focus on

sustainability companies have choices to make if they are to survive. (Hwang and

Masud 2012) explained that when there are numbers of alternative with complex criteria

(beneficial/ non-beneficial and with different units), it is very difficult to make a

transparent decision without favoritism. Some of the researchers have explained that in

general decision making contains various alternatives, various criteria (objectives) and

relative alternative performance with respect to criteria (Payoff). Where there are number

of alternatives with complex criteria and relative payoff are there at that time the ranking

of alternatives possible through multi attribute decision making (MADM). MADM is

technique to solve the multi attribute decision problems. (Rao 2007) explained that

MADM technique works with four major stages (i) list of alternatives (ii) list of attributes

(iii) calculation of the attribute weight and (iv) measurement of alternatives performance

with respect to attribute weight. A list of various MADM techniques is given below.

(1) Analytical hierarchy Process (AHP)

(2) Technique for Order Preference by Similarity to Ideal Soltuion (TOPSIS)

(3) VlseKriterijuska OptimizacijaI Komoromisno Resenje (VIKOR)

(4) ELimination and Choice Expressing Reality (ELECTRE)

(5) Preference Ranking Organization Method for Enrichment Evaluations

(PROMETHEE)

(6) Gray Relational Model (GRA)

(7) COmplex PRoportional ASsessment (COPRAS)

(8) Preference Selection Index (PSI) Method

2.1.1 Analytical Hierarchy Process (AHP)

(Saaty 1994) developed AHP, which is most highly regarded and widely used decision-

making method. AHP deals with tangible and non-tangible attributes. AHP methodology

is explained below.

2.1 MADM Techniques

18

(a) Methodology of AHP

Step 1. Find the goal and the evaluation attributes: It leads to develop a new hierarchical

structure for selection at the top level, the attribute at the second level and alternative at the

third level.

Step 2. Determination of the relative attributes weight

Make a decision matrix with relative importance of attributes and alternatives by using

base scale of AHP (Saaty 1994). The relative importance of two elements was rated using

a scale with the values 1, 3, 5, 7, and 9, where 1 denotes to ―equally important‖, 3

represents ―slightly more important‖, 5 expresses ―strongly more important‖, 7 signifies

―demonstrably more important‖, and 9 means ―absolutely more important‖. These scales

yield an n×n matrix as follows in Table 2.2.

TABLE 2.2: Decision Matrix for AHP Methodology

Alternatives …..

…..

…..

…..

…. ….. ….. ….. ….. …..

…..

Step 3. Equation (2.1) is used to calculate the geometric mean of the ith

row and

normalizing the geometric means of rows in the comparison matrix and find the attribute

weight.

[∏ ]

And [

∑

]

……………………………………… (2.1)

Step 4. Calculate matrix A3 and A4 such that and where,

[ ] .Calculate the maximum Eigen value which is the average of

matrix A4.

Step 5. Consistency Index (CI) calculated with Equation (2.2); Equation (2.3) for finding

value of Consistency Ratio (CR).

……………………………………………………………………..…… (2.2)

.…………...………….……………………………...……………………...… (2.3)


19

Here, the RI represents the average consistency index over numerous random elements of

same order reciprocal matrices. If It indicates that the matrix reached

consistency. Table 2.3 shows the Random Index (RI) which represents average of

Consistency Index (CI) over number of random elements of same order reciprocal

matrices.

TABLE 2.3: Random Index (RI) Values for AHP Technique

Attribute 3 4 5 6 7 8 9 10

RI 0.52 0.89 1.11 1.25 1.35 1.4 1.45 1.49

= 0 and complete consistency in judgment exists, since the exact values are unused in

the comparison matrices.

Step 6. Calculation of overall performance Score: The Overall performance score

determined by Equation (2.4).

∑ ……………………………………...………………………..…… (2.4)

Step 7. Alternatives Ranking Solution

The alternatives rank according to descending order. i.e. highest alternative overall

performance score is considered as first rank, while lowest alterative overall

performance score is considered as last rank.

(b) Applications of AHP methodology

Some of the applications of AHP for multi criteria selection are listed here. As per (Nirmal

and Bhatt 2019), (Kahraman and Otay 2019), (Kahraman et al. 2003) developed Fuzzy

AHP for supplier selection. (Dozic and Kalic 2014) validated AHP methodology in aircraft

selection process. (Kahraman et al. 2003), (Umadevi et al. 2012) worked on AHP for

vendor selection. (Tugrul et al. 2012) applied AHP for third party logistics provider‘s

selection. (Vinodh et al. 2011) has implemented AHP concept in manufacturing field. (Can

and Mucella 2009) tried to implement Enterprise Resource Planning (ERP) based supplier

selection with the help of AHP methodology. Flexible Manufacturing System (FMS)

selection was is carried out with Fuzzy AHP methodology by (Shamsuzzaman et al. 2003).

(Cimren et al. 2007), (Lin and Yang 1996) implemented AHP methodology in machine

tool selection area. (Sayed et al. 2017) worked on agile method selection with the help of

AHP methodology. (Kahraman and Otay 2019) explained that (Jiaqin and Huei 1997)

applied to facility location selection using AHP methodology. (Lirn et al. 2004) tried to

2.1 MADM Techniques

20

apply AHP methodology to transshipment problem selection. (Duran and Aguilo 2008)

implemented fuzzy AHP in computer aided machine tool selection for ranking. (Armillotta

2008) applied AHP in rapid prototyping layered manufacturing selection.

As per (Nirmal and Bhatt 2019) and (Kahraman and Otay 2019), (Abdullah and Najib

2016) developed AHP with interval valued intuitionistic fuzzy set.(Czekster et al. 2019)

applied AHP methodology for selection of material resource planning software to enhance

productivity. (Deshmukh and Vasudevan 2019) applied supplier selection in plastic

product manufacturing in MSME using AHP methodology. (Raut et al. 2017) applied AHP

method for selection of sustainable warehouse location selection problem. (Jain and Khan

2016) applied AHP methodology for selection of reverse logistics provider‘s selection.

Limitations of AHP methodology are listed out in section 2.4 brief conclusion of literature

review.

2.1.2 Technique for Order Preference by Similarity to Ideal Solution (TOPSIS)

Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) investigated by

(Chen and Hwang 1992a) gives preference to alternatives based on shortest distance from

positive ideal solution and farthest distance from negative ideal solution. It is a method of

compensatory aggregation that compares a set of alternatives by identifying weights for

every criterion, normalizing scores for each criterion and calculating the geometric

distance between each alternative and the ideal alternative, which is the best score in each

criterion. MADM TOPSIS method gives a PIS and NIS maximizes the benefit criteria or

attributes and minimizes the cost criteria or attributes. Mathematical steps of TOPSIS

method are explained below.

(a) Methodology of TOPSIS

Step 1. To identify the objective of MADM as, selection/ ranking/ sorting/ evaluation for

decision making.


Step 3. Preparation the decision matrix

Prepare a matrix ( ) with alternatives ( ) and attributes ( ), which is known as

decision matrix. Let consider set of alternatives as { } & set of


21

criteria as { }. Here, shows the relative performance measures

are having qualitative/ quantitative values. Table 2.4 shows the decision matrix.

TABLE 2.4: Decision Matrix for TOPSIS Methodology

…..

…..

…..

…..

…. ….. ….. ….. ….. …..

…..

Step 4. Normalization of the input matrix and convert all attributes in similar range [0,1]

Equation (2.5) applied for normalization of matrix with beneficial attributes

……………………………………………………………….…......…….. (2.5)

Equation (2.6) applied for normalization of matrix with non-beneficial attributes

…………………………………………………………….….…......…….. (2.6)

Calculate the weighted normalized decision matrix. Equation (2.6) is used to calculate

weighted normalized value . Where and and

shows the weight of the th criterion or attribute and always ∑ .

Step 5. Equation (2.7) applied for finding

………………………………………………..……….…..........…….. (2.7)

Step 6. Determination of the positive ideal solution ( ) and negative ideal ( ) solution

by Equation (2.8) and Equation (2.9) respectively

{( ) (

)} { }……………….… (2.8)

{( ) (

)} { }……….………… (2.9)

Step 7. Calculation of the separation measures using the m-dimensional Euclidean

distance. The separation measures of each alternative from the PIS and the NIS are

calculated, Equation (2.10) shows the PIS and Equation (2.11) gives the value of NIS.

√∑ (

)

, where ………………………..………..… (2.10)

√∑ (

)

, where ………………………..….…..… (2.11)

2.1 MADM Techniques

22

Step 8. Calculation of the relative closeness to the ideal solution. The relative closeness of

the alternative derived by the Equation (2.12)

Where …………….………………………..…….…. (2.12)


After calculation of alternative weight by relative closeness value of , the alternative

rank is carried out according to descending order, i.e. highest alternative relative closeness

value is considered as the first rank, while lowest alternative relative closeness value

is considered as last rank.

(b) Applications of TOPSIS methodology

Applications of TOPSIS methodology are listed here. (Qureshi et al. 2007b) implemented

TOPSIS for Third party logistics service provider selection. As per (Nirmal and Bhatt

2019) and (Kahraman and Otay 2019); (Yong 2006), (Chu 2002) validated Fuzzy

TOPSIS methodology in the plant location selection process. (Chu and Lin 2003), (Rashid

et al. 2014) worked on Fuzzy TOPSIS for robotics selection. (Byun and Lee 2005)

investigated modified TOPSIS in robotics selection. (Ic 2012) worked on computer

integrated manufacturing technology selection using TOPSIS methodology. (Sevkli et al.

2010) tried to implement F- TOPSIS in supplier selection process.

(Memari et al. 2019) applied multi criteria intuitionistic fuzzy set TOPSIS method for

finding sustainable supplier selection. (Wei et al. 2019) worked on selection of

manufacturing information system outsourcing by using TOPSIS methodology.

(Fallahpour et al. 2017) developed decision support model for sustainable supplier

selection using TOPSIS method. (Kolios et al. 2016) applied TOPSIS methodology for

decision analysis of offshore wind turbine support structure. (Dos Santos et al. 2019)

worked to select green supplier using Entropy weight Fuzzy TOPSIS methodology. (Joshi

and Kumar 2019) applied fuzzy based TOPSIS methodology under intuitionistic fuzzy

environment for selection problem.(Bianchini 2018) developed a model for third party

logistics providers by combination of AHP and TOPSIS methodology. As per (Nirmal and

Bhatt 2019) and (Kahraman and Otay 2019), (Sen et al. 2018) applied IFS- TOPSIS

method to facilitate supplier selection in sustainable supply chain. (Mittal et al. 2016)

applied fuzzy TOPSIS MADM approach for ranking of plywood industries in the India.


23

(Tewari et al. 2017) applied Fuzzy TOPSIS methodology to select quality improvement

project in manufacturing industries. (Manivannan and Kumar 2017) developed TOPSIS

methodology for selecting process parameters of cryogenically cooled micro EDM drilling

machine.

Limitations of TOPSIS methodology are listed out in section 2.4 brief conclusion of

literature review.

2.1.3 VIseKriterijuska OptimizacijaI Komoromisno Resenje (VIKOR)

VIseKriterijuska OptimizacijaI Komoromisno Resenje (VIKOR) was investigated by

(Opricovic 1998), (Rao 2008b). The multi criteria compromising ranking is developed

from the Lp-metric used in compromised method. Equation (2.13) shows the Lp-metric

initially perform VIKOR method.

{∑ [

( )

(

)]

}

……...….…..…...… (2.13)

Mathematical steps of VIKOR method are explained below.

(a) Methodology of VIKOR

Step 1. Identification of the object of MADM for selection/ ranking/ sorting/

elevation for decision making.

Step 2. Collection of various alternatives and attributes involved in selection

procedure.

Step 3. Preparation of decision matrix.





TABLE 2.5: Decision Matrix for VIKOR Methodology

…..

…..

…..

2.1 MADM Techniques

24

…..

…. ….. ….. ….. ….. …..

…..

Step 4. Determination the maximum and the minimum

values for all attribute

calculated with Equation (2.14) and Equation (2.15) respectively.

( )………………………………………..…………………....….……… (2.14)

( )……………………………………………….………….…..…..…… (2.15)

Step 5. Assign the relative importance between selection attributes (criteria)

Step 6. Calculation of the values of and

Equation (2.16) and Equation (2.17) shows the value of and respectively.

∑

( )

(

)

.………….…………………………..………………..………….. (2.16)

[

( )

(

)] . ………..…………….…..….…….… (2.17)

Step 7. Calculation of the values of Pi with Equation (2.18)

(

) (

).…………………………….………. (2.18)

Value of Normally value of K = 0.5,


Ranking is carried out with the value of in in descending order.

(b) Applications of VIKOR Methodology

Applications of VIKOR methodology are listed here. (Opricovic 2015) applied VIKOR

methodology in borrowing term selection. (Mohanty and Mahapatra 2014) also tried to

work on VIKOR technique for selection of ergonomic design product with optimum set of

design critical. Rapid prototype selection using Fuzzy VIKOR methodology was is carried

out by (Vinodh et al. 2014a). (Vinodh et al. 2014b) worked for Selection of fit concept in

modern manufacturing environment. (Devi 2011) tried to solve robot selection using fuzzy

VIKOR methodology. (Jahan and Edwards 2013) applied VIKOR methodology where


25

eleven alternatives and nine different attributes considered for material selection. As per

(Nirmal and Bhatt 2019) and (Kahraman and Otay 2019), (Geng and Liu 2015)

implemented VIKOR methodology for supplier selection problem. (Geng and Liu 2015)

also applied VIKOR methodology for Renewal energy project selection.

(Burak 2019) worked for ERP software selection using intuitionistic fuzzy VIKOR

method. (Dev et al. 2019) applied Entropy VIKOR method for automotive piston

component material selection. (Narayanamoorthy et al. 2019) applied interval valued-

intuitionistic hesitant fuzzy entropy based VIKOR methodology for robot selection. (Singh

et al. 2018) applied combination of AHP and VIKOR for selection of brake friction

materials. (Fei et al. 2019) investigated Dempster- Shafer evidence theory (DS theory)

with VIKOR method for supplier selection problem. (Zhou et al. 2018) applied fuzzy

extended VIKOR method for mobile robot selection. (Arunachalam et al. 2015) applied

AHP and VIKOR for machine tool selection problem. (Girubha et al. 2014) explained

selection of rapid prototyping technologies in an agile environment using Fuzzy VIKOR

methodology.

Limitations of VIKOR methodology are listed out in section 2.4 brief conclusion of

literature review.

2.1.4 ELimination and Choice Expressing Reality (ELECTRE):

ELECTRE-I method researched by (Roy 1968) through partial solution, however it cannot

develop the ranking of alternatives, technique not able to give ranking solution.

ELECTRE-II method implemented by (Roy and Bertier 1971) results strong and weak

outranking relations, which only work for crisp input data. ELECTRE-III method created

by (Roy 1978) works with Pseudo-criteria to calculate partial preorder alternatives with

crisp and fuzzy outranking relation. ELECTRE-IV strategy explored by (Roy and

Bouyssou 1983) with more efficient ranking solution. Mathematical steps of ELECTRE

method are explained below.

(a) Methodology of ELECTRE

Step 1. Identification of the object of MADM for selection/ ranking/ sorting/ elevation


2.1 MADM Techniques

26







TABLE 2.6: Decision Matrix for ELECTRE Methodology

…..

…..

…..

…..

…. ….. ….. ….. ….. …..

…..

Step 4. Calculation of the concordance index

For an ordered pair of alternatives( ) the concordance index is the sum of all the

weights for those criteria where the performance score of is lease as high as that of .

Equation (2.19) shows the concordance index .

∑ .……………..……………………………. (2.19)

Step 5. Calculation of the discordance index

The computation of the discordance index is more complicated when the discordance

index is zero. If performs better than on all criteria. When outperforms , the

ratio is calculated between the difference in performance level between and and the

maximum difference in score on the criteria concerned between any pair of alternatives.

The maximum of these ratios is the discordance index. Equation (2.20) shows the

discordance index .

( )

………………………………………………..……. (2.20)

Outranking relation for concordance threshold c*

discordance threshold d*

are defined such

that Then, outrank if the and . When these two

tests are completed for all the pairs of alternatives, the preferred alternatives are those


27

which outrank at least one other alternatives and are themselves and are themselves not

outranked. This set contains the promising alternatives for the considered decision problem

theory collected from source (Maniya 2012).

(b) Applications of ELECTRE

Applications of ELECTRE methodology are listed here.(Sevkli 2010) applied ELECTRE

technique supplier selection. As per (Kahraman and Otay 2019), (Vahdani et al. 2010)

implemented ELECTRE with interval weight data for supplier selection. (Stefanović-

Marinovic et al. 2015) applied ELECTRE methodology in planetary gear train

optimization problem. As per (Kahraman and Otay 2019), (Tam et al. 2003) implemented

ELECTRE-III for concrete vibrators in construction of plants selection process. (Fancello

et al. 2014) worked on ELECTRE-III and implemented in safety analysis in suburban road

network problem.

(Agrebi et al. 2017) applied ELECTRE-I for selection of location for distribution centers.

(Yanie et al. 2018) developed the web based decision support system using ELECTRE

methodology. (Aguezzoul and Pires 2016) applied ELECTRE-I methodology for third

party logistics selection. (Fahmi et al. 2016) applied ELECTRE-I supplier selection

problem. (Kumar et al. 2016) extended ELECTRE with fuzzy for optimal site selection

problem. (Gitinavard et al. 2018) applied ELECTRE method with interval valued hesitant

fuzzy set theory for green supplier selection problem. (Celik et al. 2016) worked to extend

ELECTRE method based upon interval type 2 fuzzy set for green logistics service

provider‘s evaluation.

Limitations of ELECTRE methodology are listed out in section 2.4 brief conclusion of

literature review.

2.1.5 Preference Ranking Organization Method for Enrichment Evaluations

(PROMETHEE)

PROMETHEE is one of the outranking methods which is works as MADM. It is based on

pairwise comparison method. This method was proposed by (Brans and Vincke 1985). In

PROMETHEE-I-II: Where, PROMETHEE-I is widely acceptable in outranking method

for pairwise comparison of different alternatives for each separate criteria. It gives partial

ranking solution with the help of positive and negative outranking flow. PROMETHEE-I

2.1 MADM Techniques

28

obtained only the partial solution and PROMETHEE-II obtains complete (full) ranking

solution. Mathematical steps of PROMETHEE method are explained below.

(a) Methodology of PROMETHEE









TABLE 2.7: Decision Matrix for PROMETHEE Methodology

…..

…..

…..

…..

…. ….. ….. ….. ….. …..

…..

Again pair wise comparison of alternatives and is carried out to identify preference

indicator ∑ , Where, is attribute (criteria)

weight. (Vinodh and Jeya Girubha 2012).

Step 5. Calculation of Positive Outranking Flow (POF) (Vinodh and Jeya Girubha 2012)

Equation (2.21) shows Positive Outranking Flow (POF)

∑ ……….…….………………..……………..…….......... (2.21)

Step 6. Calculation of Negative Outranking Flow (NOF) (Vinodh and Jeya Girubha 2012)

Equation (2.22) shows Negative Outranking Flow (NOF)

∑ ……….…….…………………..…..………………...… (2.22)


29

Step 7. Calculation of Net Dominance of Alternative (NDA) (Vinodh and Jeya Girubha

2012)

Equation (2.23) shows Net Dominance of Alternative (NDA)

………….…….…………………..…………………….… (2.23)


After calculation of NDA, the alternative rank according to descending order, i.e. highest

alternative Net dominance of alternative (NDA) is considered as the first rank, while

lowest alternative net dominance of alternative (NDA) is considered as last rank.

(b) Applications of PROMETHEE

Some applications of PROMETHEE methodology are listed here. As per (Dilip Kumar et

al. 2016) applied F- PROMETHEE for robot selection process. As per (Nirmal and Bhatt

2019), (Rajesh et al. 2012) applied F- PROMETHEE for selection of logistics provider in

cement industry. (Vinodh and Jeya Girubha 2012) applied PROMETHEE for sustainable

concept selection. (Dilip Kumar et al. 2015) developed model for Industrial robot selection

with the help of PROMETHEE-II technique.

(S and V M 2015) applied PROMETHEE for best metal stamping layout problem.(Curran

et al. 2014) applied PROMETHEE-II for determining the best location for US department

of defense humanitarian assistant projects. (Elevli 2014) developed Fuzzy PROMETHEE

model for choosing among potential logistics center locations. (Brans and De Smet 2016)

worked with PROMETHEE combined with outranking method. (Polat 2016) applied

integration of AHP and PROMETHEE for subcontractor selection process. (Gul et al.

2018) applied fuzzy based PROMETHEE method for material selection problem.

(Samanlioglu and Ayag 2017)applied PROMETHEE with Fuzzy AHP for evaluation of

solar power plant location in Turkey. (Borujeni and Gitinavard 2017) investigated new

extension of PROMETHEE under intuitionistic fuzzy environment for solving supplier

selection with qualitative parameters. As per (Nirmal and Bhatt 2019), (Kahraman and

Otay 2019), (Mahapatra et al. 2016) applied extension of PROMETHEE for robot

selection problem. (Bottero et al. 2019) worked with PROMETHEE for designing reuse of

abandoned railway in northern Italy. (Datta et al. 2015) applied PROMETHEE-II method

for industrial robot selection.

2.1 MADM Techniques

30

Limitations of PROMETHEE methodology are listed out in section 2.4 brief conclusion of

literature review.

2.1.6 Grey Relational Analysis (GRA)

(Ju-Long 1982) (Paramasivam et al. 2011) proposed Grey Relational Analysis (GRA)

technique for MADM. This method work to find the better ranking of multi criteria

alternatives selection. Mathematical steps of GRA method are explained below.

(a) Methodology of GRA









TABLE 2.8: Decision Matrix for GRA Methodology

…..

…..

…..

…..

…. ….. ….. ….. ….. …..

…..

Step 4. Normalization of the input matrix and convert all attributes in range [0,1]

Equation (2.24) shows the normalization rule for beneficial attributes

…………….…………………………………………..………… (2.24)

Equation (2.25) shows the normalization rule for non-beneficial attributes

…………………………………….………………………..…… (2.25)

Step 5. Identification of ideal reference sequence


31

Identification of ideal reference sequence by where and

Equation (2.26) shows the Grey correlated coefficient

Where |

|………...………..…………. (2.26)

Step 6. Calculation of the grey relation grad

Equation (2.27) shows the Grey correlated grad

∑ ……………………….………………………………....……… (2.27)

Step 7. Ranking of alternatives Preparation of the rank as per highest degree of utility .

Ranking is carried out with Grey correlated grand in descending order. i.e. highest

alterantive Grey correlated grad is considered as first rank, while lowest alternative Grey

correlated grad is considered as last rank.

(b) Applications of GRA

Some applications of GRA methodology are listed here. (Hong et al. 2012) applied GRA

with entropy weight for the location routing problem of reverse logistics service provider‘s

selection. (Rajesh and Ravi 2015) applied GRA approach for supplier selection in resilient

supply chain environment. (Wei 2011) applied GRA approach with intuitionistic fuzzy set

theory. Facility layout selection problem solved by GRA approach was implemented by

(Kuo et al. 2008). (Manikandan et al. 2017) worked on electrochemical drilling machining

of Inconel 625 using Taguchi based GRA approach for multiple performance optimization.

(Jagadish et al. 2018) applied fuzzy based GRA methodology for optimization of process

parameters for green EDM. (Kumar et al. 2018) optimized process parameters for Wire-cut

EDM of Inconel 825 material using GRA methodology. (Sen et al. 2018) applied IFS-

GRA method to facilitate supplier selection in sustainable supply chain. (Zhang and Li

2018) applied combination of TOPSIS and GRA for supplier selection problem with

interval numbers.

Limitations of GRA methodology are listed out in section 2.4 brief conclusion of literature

review.

2.1 MADM Techniques

32

2.1.7 Complex Proportional Assessment (COPRAS)

(Zavadskas et al. 1994) investigated Complex Proportional Assessment (COPRAS)

methodology for multi attribute selection. . COPRAS is one of the MADMs, which is used

to rank the alternatives where numbers of criteria are considered at the time of selection.

(Ayrim et al. 2018) investigated Novel COPRAS by using stochastic decision process

named COPRAS-S to increase the performance of COPRAS methodology. (Sahin 2019)

tried to work with Neutrosophic sets with COPRAS methodology. (Bausys et al. 2015)

applied neutrosophic set to multi criteria decision making using COPRAS methodology.

Mathematical steps of COPRAS method are explained below.

(a) Methodology of COPRAS









TABLE 2.9: Decision Matrix for COPRAS Methodology

…..

…..

…..

…..

…. ….. ….. ….. ….. …..

…..

Step 4. Normalization of the input matrix and convert all attributes in range [0,1] by using

Equation (2.28) shows the normalization rule for beneficial and non-beneficial attributes

both.

∑

……………………..………….………………………..….…..……….. (2.28)

Step 5. Determination of the attribute weight using expert opinion.

Step 6. Calculation of the weighted normalized decision matrix


33

Equation (2.29) shows the formula for weighted normalized matrix

……………………………………….………………………....…….. (2.29)

Calculation of maximizing normalized matrix indexes value of each beneficial

alternative and minimizing normalized matrix indices for each non beneficial

alternative which is to be minimized.

Step 7. Minimum value of minimum Normalized indices where

Step 8. Determination of the significance of each alternative

Equation (2.30) shows the formula for significance of each alternative

∑

∑

……………………………...………….………………… (2.30)

Step 9. Calculation of the degree of utility of each alternative

Equation (2.31) shows the formula for degree of utility of each alternative

……………………………………….………………..……… (2.31)

Step 10. Preparation of the rank as per highest degree of utility .

Ranking is carried out with degree of utility in descending order. i.e. highest alternative

degree of utility is considered as first rank, while lowest degree of utility is considered

as last rank.

(b) Applications of COPRAS

Some applications of COPRAS methodology are listed here. As per (Kahraman and Otay

2019) and (Nirmal and Bhatt 2019); (Nourianfar and Montazer 2013) applied COPRAS

methodology for Supplier selection. (Makhesana 2015) implemented improved COPRAS

which work with qualitative information for rapid prototype system selection. (Keshavarz

Ghorabaee et al. 2014) implemented COPRAS in with interval type-II fuzzy set

information with MAGDM. (Buyukozkan et al. 2018) applied interval valued intuitionistic

fuzzy set in COPRAS methodology for selection of cloud computing technology.

(Zhang et al. 2017) applied selection of emergency material supplier by combining entropy

weight method and COPRAS methodology. (Hase and Gadakh 2018) implemented

2.1 MADM Techniques

34

COPRAS methodology for selection of punch material selection. (Xia et al. 2015)

investigated improved and validated COPRAS with material selection problem. (Attri et al.

2014a) implemented cutting fluid selection using COPRAS methodology. (Bairagi et al.

2014) applied Grey COPRAS (COPRAS-G) robot selection for foundry operation.

(Liou et al. 2016) applied COPRAS- G methodology for improving and selecting supplier

in green supply chain environment. (Pancholi and Bhatt 2018) applied combined Grey

complex proportional risk management (COPRAS-G) method with preference selection

index (PSI) methodology for failure mode criticality analysis (FMECA) maintenance

planning. (Pancholi and Bhatt 2016) also developed decision making for aluminum wire

process rolling mill through grey complex proportional assessment (COPRAS-G) method.

(Roy et al. 2019) tried to extended COPRAS model for MADM and implemented the

model in web-based hotel evaluation and selection problem. As per (Nirmal and Bhatt

2019), (Wang et al. 2016) evaluated risk of failure modes with COPRAS method using

interval valued intuitionistic fuzzy set theory.

Limitations of COPRAS methodology are listed out in section 2.4 brief conclusion of

literature review.

2.1.8 Preference Selection Index (PSI) Method:

(Maniya and Bhatt 2010), (Maniya 2012) implemented and validated PSI methodology for

multi attribute selection/ ranking. (Maniya and Bhatt 2010) proved that the PSI

methodologies works with less computation, better ranking possible without calculating

attribute weight (relative weight between criteria). Mathematical steps of PSI method are

explained below.

(a) Methodology of PSI






35




are having qualitative/ quantitative values. Decision matrix for PSI methodology is shown

in Table 2.10.

TABLE 2.10: Decision Matrix for PSI Methodology

…..

…..

…..

…..

…. ….. ….. ….. …..

…..


The conversion of linguistic (qualitative) information to crisp (quantitative) information is

carried out with the help of eleven point scale proposed by (Venkatasamy and Agrawal

1996; Venkatasamy and Agrawal 1997) as shown in the Fig.2.3.

FIGURE 2.3: Fuzzy Eleventh Point Scales

[Source: Chen and Hwang (1992), Rao (2006a), (Venkatasamy and Agrawal 1996; Venkatasamy and

Agrawal 1997), (Maniya 2012)]

Table 2.11 shows the conversion rule of linguistic data to crisp score.

2.1 MADM Techniques

36

TABLE 2.11: Lingustic to Crisp Value Conversion Table

Linguistic terms of selection attributes Fuzzy number Crisp value of selection attribute

Exceptionally low M1 0.045

Extremely low M2 0.135

Very low M3 0.255

Low M4 0.335

Below average M5 0.410

Average M6 0.500

Above average M7 0.590

High M8 0.665

Very high M9 0.745

Extremely high M10 0.865

Exceptionally high M11 0.955

Collected from Source: Chen and Hwang (1992) Rao (2006a) (Venkatasamy and Agrawal 1996;

Venkatasamy and Agrawal 1997), (Maniya 2012)


Each relative attribute of alternative are having different values for that purpose

normalization is carried out. It makes the matrix (performance measure value) in a range

[0,1].

Equation (2.32) use for normalization of beneficial criteria, where higher value is desired

(i.e. quality, profit, etc.)

……………………………………….……………...…………….. (2.32)

Equation (2.33) use for normalization of non-beneficial criteria; where minor values

desirable (i.e. lead time, price, delivery time etc.)

…………………………………….…………..…………….…….. (2.33)

Table 2.12 shows normalized decision matrix for PSI technique.

TABLE 2.12: Normalized Decision Matrix for PSI Technique

…..

…..

…..

…..

…. ….. ….. ….. ….. ….

…..

Step 6. Calculation for the mean value of normalized data:

The mean (average) value of each attribute is calculated with Equation (2.34).


37

∑

…………………………………….……….…………..…….. (2.34)

Step 7. Calculation of the preference variation value

Equation (2.35) shows preference variation value

∑

………………………….……………………..…………….. (2.35)

Step 8. Calculation of the deviation preference value

Equation (2.36) shows formulate deviation preference value

| | ………………………………………….…………..……………..... (2.36)

Step 9. Calculation of the overall preference value

Equation (2.37) shows formula for calculating overall preference value

∑

…………………………………….…….…………………………...….. (2.37)

Step 10. Compute Preference selection index

Equation (2.38) shows formula for Preference selection index

∑ ( ) ……………………………….….……………….…………….. (2.38)


After calculation of alterative preference selection index the alternatives rank is

obtained according to descending order, i.e. Highest alternative preference selection index

, is considered as first rank, while lowest alternatives preference idex , is

considered as last rank.

(b) Applications of PSI Methodology

Some applications of PSI methodology are listed here. As per (Kahraman and Otay 2019)

and (Nirmal and Bhatt 2019); (Maniya and Bhatt 2010) implemented and validated PSI

methodology for material selection. (Maniya and Bhatt 2011b) applied PSI methodology

for FMS selection. As per (Kahraman and Otay 2019); (Madic et al. 2017) applied PSI

methodology for determination of laser cutting process. (Sawant et al. 2011) tried to solve

AGV selection using PSI methodology. As per (Kahraman and Otay 2019) and (Nirmal

and Bhatt 2019); (Attri and Grover 2015) implemented PSI technique for material

2.1 MADM Techniques

38

selection. (Attri et al. 2014b) tried to implement PSI model for cutting fluid selection

problem. (Madic et al. 2017) applied PSI methodology for ranking and selection of laser

cutting process conditions. (Maniya 2012) explained to show the comparative performance

with existing MADM by his investigated PSI methodology.

(Yadav et al. 2019) solved material selection problem for marine applications using hybrid

TOPSIS and PSI approach. (Jain 2018) applied combination of MOORA and PSI for

ranking of FMS. (Borujeni and Gitinavard 2017) developed a model for sustainable mining

contract selection using preference selection index (PSI) methodology. (Haddou Benderbal

et al. 2017) applied PSI methodology for machines selection in reconfigurable

manufacturing design problem.

Limitations of PSI methodology are listed out in section 2.4 brief conclusion of literature

review. As per (Maniya 2012), PSI methodology gives ranking solution with less

calculation and high accuracy as shown in Table 2.13.

TABLE 2.13: Comparative Performance of Existing MADM Techniques

Name of

MADM

CT MC SM ST CP RI RR

AHP Very High Maximum Very

critical

Poor Required Required Yes

TOPSIS High Moderate Critical Medium May be

required

Required Yes

VIKOR High Moderate Simple Medium May be

required

Required Yes

ELECTRE High Moderate Critical Medium May be

required

Required Yes

PROMETHEE High Moderate Critical Medium May be

required

Required Yes

GRA Very High Maximum Very

Critical

Medium May be

required

Required Yes

COPRAS High Moderate Critical Medium May be

required

Required Yes

PSI Very Less Minimum Very

simple

Good Do not

required

Do not

required

Yes

Adopted from source (Maniya 2012)

Where, CT: Computational time, MC: Mathematical Computations, SM: Simplicity, CP

computer programming, RI: relative importance between selection criteria (criteria

weight), RR: rank problem.


39

2.2 The Significance of Mathematical Set in MADMs

The mathematical set uses in MADMs with their individual theory, applications and their

advantages are listed below.

Crisp set

Fuzzy set (FS)

Intuitionistic fuzzy set (IFS)

Interval valued intuitionistic fuzzy set (IVIFS)

Single valued neutrosophic set (SVNS)

2.2.1 Crisp Set

(a) Crisp Set Theory

Collection of elements within a universe is called as set. It has the information in

quantitative form. The feature elements are discrete, countable integers or continuous

valued in quantitative form. In general the decision is carried out with the help of crisp/

classic set. Crisp set also known as classic set theory.

Union: The union between the two set, denoted by { } As per

(Nirmal and Bhatt 2019)and (Kahraman and Otay 2019)

Intersection: The intersection between two set { } As per


Difference: The difference between two set { } As per


(b) Applications of Crisp Set in MADM Techniques

Some applications of crisp set in MADMs techniques are listed here. Material selection:

(Rao 2007) used crisp set for material selection using AHP, TOPSIS, VIKOR method.

(Jiao et al. 2011) solved non-heat treatable cylindrical cover material selection problem

with the help of PROMETHEE, TOPSIS and ELECTRE method. They also derived that


40

material selection through PROMETHEE technique gives the better ranking solution.

Thermosetting plastic material selection calculated by (Chan 2006) using Grey relational

analysis (GRA) algorithm and found the ranking solution with the help of prioritized

performance score. (Chatterjee et al. 2010) tried to implement VIKOR, ELECTRE

methods for selection of most suitable pick and place type robot. Author solved to solve

the other example with four robots selection and compare ranking with other MADMs.

(Anojkumar et al. 2014) applied classic set for pipe material selection for sugar industry.

(Shanian and Savadogo 2006) had developed bipolar plate material selection for polymer

electrolyte fuel cell was initially solved with the help of TOPSIS. (Kumar and Garg 2010)

attempted to solve material ranking using entropy-based TOPSIS method.

(Dehghan-Manshadi et al. 2007) tried to rank material selection of cryogenic tank

for transportation of nitrogen, author also tried to solve the material selection problem for

human power aircraft spare (major element of wing used in aircraft) element by calculating

performance indices. (Chatterjee and Chakraborty 2012) solved the MADM of gear

material using PROMETHEE, COPRAS with gray relation and compared the methodology

with VIKOR, PROMETHEE. (Chatterjee et al. 2011) solved two examples of robot

selection with quantitative information wherein (i) The input matrix of MADM collected

from (Chatterjee et al. 2010) for selection most suitable pick and place type robot solved

with VIKOR and ELECTRE and (ii) ranking of industrial robots with crisp quantitative

information. (Rao and Padmanabhan 2006) tried to solve the ranking of robot using the

novel MADM approach qualitative crisp information which was developed by (Agrawal et

al. 1991) and solved by diagraph matrix solution approach. (Darji and Rao 2014b)

compared VIKOR, ELECTRE and PROMETHEE for material selection in sugar industry.

For machine tool selection problem (Paramasivam et al. 2011) calculated AHP and

ANP method for milling machine selection and compared the result with diagraph

approach. (Kumar et al. 2015) solved cited example of robot selection problem with crisp

set information and solved it with the help of VIKOR, ELECTRE-II. Other examples of

robot selection solved with the help of VIKOR and ELECTREE-II method. (Hu 2009)

worked on supplier‘s selection problem and solved the problem with hybrid approach first

attribute weight calculated with AHP methodology and in the second stage applied GRA

for supplier ranking.


41

Third party logistics providers selection was is carried out by (Zhang et al. 2004)

considering crisp data in input matrix using AHP method. (Jayant et al. 2014) solved third

partly reverse logistic providers for mobile manufacturing industry by considering crisp

value using AHP and TOPSIS methodologies.

(Tyagi et al. 2014) developed hybrid AHP and TOPSIS method and tried to analyze

the e-supply chain management performance by considering Crisp value. (Maniya and

Bhatt 2011b) implemented PSI methodology and applied for selection of FMS in industrial

applications. Authors also compare the derived ranking with Data Envelopment Analysis

(DEA), Graph Theory and Matrix Approach (GTMA) earlier derived by (Rao 2007).

(c) Advantages of Crisp Set for MADM Techniques

Crisp set is known to decision makers/ researchers/ experts

Calculations are quite easy as compare to other set theory.

The easiest way to express the decision for relative alternatives and attributes.

No need to get extra knowledge for crisp set.

Relative comparison of alternatives is made easy with the crisp set.

The limitations of crisp set for MADM techniques are listed out in section 2.4 brief

conclusion of literature review.

2.2.2 Fuzzy Set (FS) (Linguistic information)

Fuzzy set was investigated by (Zadeh 1996). Fuzzy set handles the concept of partial truth.

Fuzzy set proposed the vague and uncertain working boundary. This function maps the

elements of fuzzy set to real numbered value in interval 0 to 1, i.e. .

It can easily understand by following mathematical explanation.

{⟨ ⟩}

(a) Fuzzy Set (FS) (Linguistic information) Theory

In fuzzy set, the range [0, 1] is known as degree of membership. Fuzzy set uses to handle

uncertainty.


42

Union: The union between the two set, denoted by Intersection: The

intersection between two set (Nirmal and Bhatt 2019)and (Kahraman and Otay 2019)

{ } Difference: The difference between two set (Nirmal and

Bhatt 2019)and (Kahraman and Otay 2019) { }, Fuzzy

Arithmetic Operation is carried out as below.

Interval addition:

Interval subtraction:

Interval multiplication:

(Nirmal and Bhatt 2016a) explained that existing MADM works with crisp / lingustic sets,

while in industrial application decision maker (DMs)/ experts are having the input

information in qualitative data which is easily conveyed by crisp values. (Chen and Hwang

1992b), (Venkatasamy and Agrawal 1996; Venkatasamy and Agrawal 1997), (Nirmal and

Bhatt 2016a) identified the fuzzy (linguistic information), which is used to convert the

qualitative information to quantitative information (crisp/ classic set) is as shown in Table

2.14.

TABLE 2.14: Crisp Value of Selection Attributes

Linguistic terms of selection attributes Fuzzy number Crisp value of selection

attribute



Very low M3 0.255

Low M4 0.335


Average M6 0.500


High M8 0.665

Very high M9 0.745



Collected from Source: (Kahraman and Otay 2019), (Chen and Hwang 1992b), (Venkatasamy and Agrawal

1996), (Venkatasamy and Agrawal 1997), (Nirmal and Bhatt 2016a), (Smarandache and Pramanik 2016),

(Nirmal and Bhatt 2019).

(b) Applications of Fuzzy (Linguistic) of FS with crisp set in MADM:

Some applications of fuzzy (linguistic) set in MADMs techniques are listed here.

(Rao 2007) used crisp with linguistic information for material selection and tried to solve

the problem with the help of AHP, TOPSIS, and VIKOR method. (Dehghan-Manshadi et

al. 2007) explained material selection for the cryogenic tank with crisp (classic)


43

information. (Rao 2008b) implemented selection of material with crisp (classic) and

linguistic information and tried to convert the linguistic information (qualitative

information) in to crisp by using fuzzy conversion, which was developed by (Chen and

Hwang 1992b), (Venkatasamy and Agrawal 1996; Venkatasamy and Agrawal 1997) is as

shown in Table 2.14.

(Nirmal and Qureshi 2009) developed generalized framework of fuzzy expert

decision support system for vendor selection.(Kumar et al. 2014) attempted to solve the

material ranking for exhaust manifold with the help of TOPSIS methodology having

quantitative information. (Mayyas et al. 2016) worked with classic set and solved the eco

material selection problem for automobile load bearing panels using fuzzy TOPSIS

methodology. Authors also conclude that with dual qualitative and quantitative nature of

characteristics, fuzzy tool use to convert in to crisp and helpful for TOPSIS model.

Attention is given to convert the qualitative parameter to quantitative using fuzzy

conversion Table 2.14. (Chatterjee et al. 2011) solved that same input matrix formed by

(Rao and Padmanabhan 2006) qualitative (linguistic/fuzzy) and quantitative information

(crisp) for ranking of using novel MADM approach. (Nirmal 2011) explained the role of

fuzzy for selecting the industrial vendors. (Bahraminasab and Jahan 2011) worked on

fuzzy (linguistic) and crisp information and solved the material selection for a femoral

component which is useful for the full knee replacement. The input information given with

qualitative and quantitative information is solved with the help of VIKOR technique.

Author also concluded that the VIKOR method gives better solution in MADM selection

processes.

(Singh and Sekhon 1996) worked on diagraph and matrix approach for solving

metal stamping layout which in crisp information. (Maniya and Bhatt 2010) solve the

ranking of material with linguistic and crisp value. Ranking and selection of AGV for

industrial applications is carried out by (Maniya and Bhatt 2011a) with all linguistic

information and was solved using AHP with M-GRA, (Maniya and Bhatt 2011a) also tried

to compare the proposed methodology with AHP, TOPSIS and AHP with GRA methods.

(c) Advantages of Fuzzy (Linguistic) of FS with crisp set for MADM

Linguistic (qualitative) set is known to all decision makers/ researchers/ experts

After conversion to crisp set calculations are quite easy as compare to other set

theory.


44

It is the easiest way to express the decision for relative alternatives attributes.

No need to get extra knowledge for fuzzy set.

Relative comparison of alternatives is made easy with the crisp set.

The fuzzy set handles uncertainty.

The limitations of Linguistic/ Fuzzy set for MADM techniques are listed out in section 2.4

brief conclusion of literature review.

2.2.3 Intuitionistic Fuzzy Set (IFS)

(Smarandache and Pramanik 2016), explained that to cover-up the limitation of fuzzy set,

(Atanassov 1986) proposed the new set by adding truth membership and falsity

Membership known as Intuitionistic Fuzzy Set (IFS). As per (Nirmal and Bhatt

2016a), IFS is also known as Atanassov‘s intuitionistic fuzzy set (AIFS) . (Gorzałczany

1987) explained FS theory works only with membership function. While in IFS works

with each information in truth membership and falsity membership simultaneously. It can

easily understand by mathematical explanation as

{⟨ ⟩}.

(a) Intuitionistic Fuzzy Set (IFS) Theory

Definition: Set E is fixed. An intuitionistic fuzzy set or IFS A in E is an object

{⟨ ⟩ } where, the membership functions: and non-

membership function for the set A and .

{⟨ ⟩ }

{⟨ ⟩ }

Conversion of linguistic term set to corresponding IFV (Intuitionistic Fuzzy Value).

Initially conversion rule of linguistic set to corresponding IFV investigated by (Vahdani et

al. 2013) is as shown in Table 2.15

TABLE 2.15 Lingustic to IFV Value Conversion Investigated in 2013

Linguistic Variables Corresponding IVFs

Extremely Good/ Extremely High (1.00, 0.00)

Very Very Good/Very Very High (0.90, 0.10)

Very Good/ very High (0.80, 0.10)

Good/ High (0.70, 0.20)


45

Medium Good/ Medium High (0.60, 0.30)

Fair/ Medium (0.50, 0.40)

Medium Bad/Medium Low (0.40, 0.50)

Bad/ Low (0.25, 0.60)

Very Bad/ Very Low (0.10, 0.75)

Very Very Bad/ Very Very Low (0.10, 0.90)

Collected from Source: (Vahdani et al. 2013)

Subsequently conversion of linguistic term set to corresponding IFV was investigated by

(R et al. 2017) is as shown in Table 2.16

TABLE 2.16: Lingustic to IFV Value Conversion Investigated in 2017

Linguistic Rating (Decision Matrix) Corresponding IVFs

Extremely Good (0.95, 0.05)

Highly Preferred (0.90, 0.10)

Moderately Good (0..85, 0.10)

Moderately Preferred (0.75, 0.20)

Good (0.70, 0.20)

Neutral (0.50, 0.40)

Medium (0.50, 0.35)

Less Preferred (0.35, 0.60)

Bad (0.35, 0.55)

Highly Less Preferred (0.10, 0.90)

Moderately Bad (0.25, 0.70)

Extremely Bad (0.10, 0.90)

Collected from Source: (R et al. 2017)

(b) Applications of Intuitionistic Fuzzy Set (IFS)

Due to various limitations and difficulties listed in the research gap, no one implemented

the IFS with MADM techniques in manufacturing and supply chain field. Due to reason,

researches tried to find the applications in other area and multi attribute group decision

making (MAGDM) technique, where particular payoff (criteria with respect to alternative)

is given by more than one decision maker. (Guo et al. 2010) attempted to solve supplier

selection problem with Intuitionistic fuzzy –TOPSIS methodology where input data were

collected in Intuitionistic fuzzy set only.

(Raghunathan et al. 2017) solved the supplier selection problem with the extension

of PROMETHEE using Intuitionistic fuzzy value for MAGDM technique. (Kaur 2015)

solved supplier selection for manufacturing processes using IFS-ELETRE and IFS-

TOPSIS methodology. (Sen et al. 2018) applied IFS- TOPSIS, IFS MOORA and IFS-

GRA methods to facilitate supplier selection in sustainable supply chain. (Kumar and Garg

2018a) developed TOPSIS method with IFS method. (Keshavarz Ghorabaee 2016)

implemented extended version of VIKOR method with interval type fuzzy set for robot


46

selection problem. (Celik et al. 2016) worked to extend ELECTRE method based upon

interval type 2 fuzzy set for green logistics service provider‘s evaluation.

(c) Advantages of Intuitionistic Fuzzy Set (IFS)

Intuitionistic fuzzy set (qualitative) set is known to all decision makers/

researchers/ experts

It is more informative way to express the decision for relative alternatives attributes

using degree of truth in range, compared to crisp and lingustic set.

This set theory provides choice only for degree of truth and falsehood contains in

the range.

The limitations of Intuitionistic Fuzzy set (IFS) set for MADM techniques are listed out in

section 2.4 brief conclusion of literature review.

2.2.4 Interval Valued Intuitionstic Fuzzy Set

(Smarandache and Pramanik 2016), explained that (Atanassov and Gargov 1989) had

developed interval valued intuitionistic fuzzy set (IVIFS). This set theory contains

information in IFS (degree of troth, degree of falsehood) provided with range. It can easily

understand by following mathematical explanation.

{⟨ ⟩

⟨ ⟩}

(a) Interval Valued Intuitionistic Fuzzy Set (IVIFS) Theory

(Zhao et al. 2016) defined the operators of IVIFS as Let {⟨ ⟩ ⟨ ⟩} and

{⟨ ⟩ ⟨ ⟩} i.e.

{⟨ ⟩

⟨ ⟩}

Conversion of linguistic value to corresponding IVIFS investigated by (Afzali et al. 2016)

is as shown in Table 2.17


47

TABLE 2.17: Conversion of Linguistic Value to Corresponding IVIFS

Linguistic Variable (Decision Matrix) Corresponding IVIFS

Very Important <[0.80, 0.90], [0.05,0.10]>

Important <[0.65, 0.75],[0.10, 0.20]>

Medium <[0.45, 0.55], [0.35, 0.45]>

Un-important <[0.25,0.35], [0.55, 0.65]>

Very Important <[0.00, 0.10], [0.80, 0.90]>

Collected from Source: (Afzali et al. 2016), (Kahraman and Otay 2019), (Nirmal and Bhatt 2019).

(b) Applications of Interval Valued Intuitionistic Fuzzy Set (IVIFS)

Due to various limitations and difficulties listed in the research gap, no one implemented

the IVIFS with MADM for manufacturing and supply chain field. Due to this some other

applications of IVIFS are listed here. (Afzali et al. 2016) implemented the IVIFS in

MAGDM using Fuzzy linear programming approach for automobile supplier selection

problem. Author also attempts to convert linguistic variable to IVIFS. (Afzali et al. 2016)

also calculated the attribute weight using TOPSIS methodology and ranking of alternatives

is carried out with linear programming approach.

(Narayanamoorthy et al. 2019) applied interval valued- intuitionistic hesitant fuzzy entropy

based VIKOR method logy for robot selection. (Gitinavard et al. 2018) applied ELECTRE

method with interval valued hesitant fuzzy set theory for green supplier selection problem.

(Abdullah and Najib 2016) developed AHP with interval valued intuitionistic fuzzy set.

(Zhang and Li 2018) applied combination of TOPSIS and GRA for supplier selection

problem with interval numbers. (Abdullah and Najib 2016) developed AHP with interval

valued intuitionistic fuzzy set for supplier selection. (Kumar and Garg 2018b) worked with

TOPSIS method using interval valued IFS environment. As per (Kahraman and Otay

2019), (Nirmal and Bhatt 2019), (Wang et al. 2016) evaluated risk of failure modes with

COPRAS method using interval valued intuitionistic fuzzy set theory. (Dammak et al.

2016) carried out exhaustive study of possibility measure of IVIFS and application to multi

criteria deicision making techniquies.

The limitation of interval valued intuitionistic set (IVIFS) set for MADM techniques are

listed out in section 2.4 brief conclusion of literature review.


48

2.2.5 Single Valued Neutrosophic Set (SVNS)

(Smarandache and Pramanik 2016),(Nirmal and Bhatt 2016a) explained that, sometime

due to lack of knowledge, lack of time, pressure in public domain, decision maker may

suffer to put the decision only in degree of truth and falsity. Limitation IFS, IVIFS and all

above set are covered up with foundation of the Neutrosophic Set proposed by the

mathematics researcher (Smarandache 2005). As per (Kahraman and Otay 2019), (Nirmal

and Bhatt 2019) NS works with degree of truthness membership, indeterminacy

membership and falsehood membership, where all membership functioned independent in

the range of [0, 1] (Nirmal and Bhatt 2016a).

(Smarandache 2005) explained that in NS, the term ―Neutrosophic‖ means

―Knowledge of Neutral Thought‖. (Rivieccio 2008) worked and investigated that

neutrosophic logic is compared with other well-known logic tools for reasoning with

uncertainty and vagueness. As per (Kahraman and Otay 2019), (Nirmal and Bhatt 2019),

(Nirmal and Bhatt 2016a); (Wang et al. 2010) explained the concept of NS which is

different from the fuzzy set, IFS, IVIFS, etc. The indeterminacy is quantified explicitly.

NS contains the membership of truth, indeterminacy and falsehood, which are completely

independent. (Wang et al. 2010), (Nirmal and Bhatt 2016a) proposed subclass of SVNS the

instance part of NS and gave application to engineering and science field.

(a) Single Valued Neutrosophic Set (SVNS) Theory

(Wang et al. 2010), (Ye 2013), (Nirmal and Bhatt 2016a) define SVNS as let be a point

of a universe with unique element then SVNS is represented

by { ⟨ ⟩ }, where where,

for each point of SVNS addition and multiplication

operator investigated by (Smarandache 2016). It can easily understand by following

mathematical explanation.

{⟨ ⟩ }

SVNS addition >

SVNS multiplication >


49

Table 2.18 shows the conversion of linguistic value to corresponding SVNS investigated

by (Sahin and Yigider 2014).

TABLE 2.18: Conversion of Linguistic Value Corresponding SVNS

Linguistic Rating (Decision Matrix) Corresponding IVFs

Extremely Good/ Extremely High <1.0000, 0.0000, 0.0000>

Very Very Good/ Very Very High <0.9000, 0.1000, 0.1000>

Very Good/Very High <0.8000, 0.1500, 0.2000>

Good/ High <0.7000, 0.2500, 0.3000>

Medium Good/ Fair <0.5000, 0.5000, 0.5000>

Medium Good/Medium High <0.6000, 0.3500, 0.4000>

Medium Bad/Medium Low <0.4000, 0.6500, 0.6000>

Bad/ Low <0.3000, 0.7500, 0.7000>

Very Bad/ Very Low <0.2000, 0.8500, 0.8000>

Very Very Bed/ Very Very Low <0.1000, 0.9000, 0.9000>

Extremely Bad/ Extremely Low <0.0000, 1.0000, 1.0000>

Collected form the Source: (Sahin and Yigider 2014)

(b) Applications of Single Valued Neutrosophic Set (SVNS)

(Ye 2013) investigated MCDM method using correlation coefficient under SVNS input

matrix. (Ye 2014b) worked with input matrix with SVNS cross entropy information for

MCDM methodology. (Nirmal and Bhatt 2016a) explained that, (Liu and Wang 2014)

introduced new weighted Bonferroni mean (WBM) for MCDM approach. In

(Smarandache and Pramanik 2016) shows, (Chi and Liu 2013) extended the TOPSIS

methodology to Interval Neutrosophic Set (INS) for ranking decision. As per (Kahraman

and Otay 2019), (Nirmal and Bhatt 2019), (Nirmal and Bhatt 2016a) explained that,

(Biswas et al. 2016b) demonstrated single valued neutrosophic hesitant fuzzy set for Grey

Relational Analysis (GRA) in MADM ranking/ selection process. (Nirmal and Bhatt

2016a) implanted and validated a new single valued neutrosophic entropy weight based

MADM in selection of automated guided vehicle by showing conversion the crisp data in

to SVNS. (Boran et al. 2009) applied the intuitionistic fuzzy set with TOPSIS technique

for supplier selection with MADM.

As per (Kahraman and Otay 2019), (Nirmal and Bhatt 2019), (Nirmal and Bhatt

2016a) explained that, (Ye 2013) worked on extension theory of correlation intuitionistic

fuzzy set and investigation on correlation of SVNS for calculating weighted cosine

similarity measure between each alternative for better ranking solution. (Nirmal and Bhatt

2016a), (Smarandache and Pramanik 2016) (Biswas et al. 2014) extended grey relational

analysis (GRA) to neutrosophic environment and applied in MADM issue, which works

for calculate weight of attribute with entropy method and ranking of alterative, is carried


50

out with neutrosophic grey relational coefficient of each alternatives. (Nirmal and Bhatt

2016a) described that (Ye 2014b) again worked for single valued cross entropy for supplier

selection process. (Deli and Subas 2016) examined a trapezoidal and triangular single

valued neutrosophic set for decision making in MADM environment. (Sahin and Yigider

2014) worked on MAGDM for supplier selection using SVNS theory. As per (Kahraman

and Otay 2019), (Nirmal and Bhatt 2019), (Nirmal and Bhatt 2016a) enlightened that, (Ye

2014a) built up the streamlined neutrosophic weighted arithmetic average operator.

(Nirmal and Bhatt 2016a), (Smarandache and Pramanik 2016) explained that (Biswas et al.

2016a) extended TOPSIS methodology in Single Valued Neutrosophic Set based weighted

averaging operator for MAGDM problem.

As per (Kahraman and Otay 2019), (Nirmal and Bhatt 2019) investigated fuzzy single

valued neutrosophic MADM technique to improve performance in manufacturing and

supply chain function. In (Kahraman and Otay 2019) in which (Nirmal and Bhatt 2019)

applied the investigated methodology for selection of automated guided vehicle (AGV)

for flexible manufacturing cell for industrial applications. (Sahin and Liu 2016) worked on

SVNS with fuzzy information by considering distance and similarity measurers of multiple

attribute.

(Li et al. 2017) investigated lingustic NS and their application in multi criteria decision

making problem. As per (Kahraman and Otay 2019), (Nirmal and Bhatt 2019), (Bolturk

and Kahraman 2018) had developed novel interval valued neutrosophic AHP with Cosine

similarity measure. (Biswas et al. 2019) investigated nonlinear programming approach for

SVNS TOPSIS method.

(Liang et al. 2017) applied single valued trapezoidal neutrosophic set to evaluate e

commerce website. (Biswas et al. 2015) investigated Cosine similarity measure based

MADM with trapezoidal fuzzy neutrosophic set. As per (Kahraman and Otay 2019), (Garg

and Nancy 2018) investigated new logarithmic operational laws and their application to

MADM for single valued neutrosophic numbers. As per (Kahraman and Otay 2019) and

(Nirmal and Bhatt 2019), (Pramanik et al. 2017) had tried to extend TOPSIS for MADM

with neutrosophic cubic information.


51

(c) Advantages of Single Valued Neutrosophic Set (SVNS)

As per (Smarandache and Pramanik 2016), Single valued neutrosophic set (SVNS)

is the result NS, which can deal with indeterminate, uncertain, inconsistent and

imprecise data (Nirmal and Bhatt 2016a), (Wang et al. 2010), (Majumdar 2015).

SVNS can deal with uncertainty, indeterminate, imprecise and inconsistent data

(Wang et al. 2010), (Nirmal and Bhatt 2016a).

After investigation of SVNS, Interval valued SVNS, where each has been identified with

by following mathematical explanation.

{

}

But this work is published limited to the initial mathematical operators for IVSVNS by the

various mathematicians and there is no certain application based approach carried out by

the mathematician as well as in the field of manufacturing and supply chain management.

From the different mathematical set theories with their application in MADM shows the

newer techniques gifted to give more accurate solution it also add some new features in

decision makers/ decision making to improve the solution.

2.3 Selection Processes for Improving Performance in Manufacturing

and Supply Chain Areas:

(Alomar and Pasek 2014) defined that performance measurement is a tool to support

decision makers for launching, selection action and redefining objectives. Here, the

research area is considered only as the selection process enhancement. Related to selection

methodology, (Parkan and Wu 1999) explains that MADM technique is one of the tool for

performance measurement. Here identify some random cases of choice in listed

production and supply chain environment are, where work with existing MADM is carried

out. They are as follows.

(1) Material selection

(2) Machine tool selection

(3) Rapid prototype selection

(4) Non-traditional machining process selection

2.3 Selection Processes for Improving Performance in Manufacturing and Supply Chain Areas:

52

(5) Automated guided vehicle selection

(6) Robot selection

(7) Metal stamping layout selection

(8) Electro chemical machining process selection

(9) Cutting fluid (coolant) selection

(10) Supplier selection

(11) Third party reverse logistic providers selection

2.3.1 Material Selection

Material selection is an essential aspect of engineering processes of both products and

production system and it is often crucial for the success of the resulting product

performance (Kaspar et al. 2016). The proper selection of material for a given application

involves numbers of various attributes (criteria). Selection of material is an important role

in the manufacturing industries (Darji and Rao 2014a). Material selection is not only based

on single criteria.

―Improper equipment selection leads to negatively affect the overall performance

and productivity of a manufacturing system, while accurate selection can enhance the

manufacturing process, provide effective utilization of manpower, increase the production

and improve flexibility‖, (Paramasivam et al. 2011) tried to prove that the selection process

is one of the activities which enhance the overall performance, productivity of

manufacturing system for smoothly running supply chain.

Applications of existing MADM techniques for Material Selection:

Applications of existing MADM techniques for material selection are tried to collect from

peer reviewed journal and international books are enlisted here. (Dehghan-Manshadi et al.

2007) tried to rank for material selection for manufacturing of cryogenic tank for

transportation of nitrogen, they also solved the material selection problem for human

power aircraft spare (major element of wing used in aircraft) element with twelve

alternatives and six attributes by calculating performance indices method after the same

material selection problem was solved by (Chatterjee et al. 2011) developed hybrid

COPRAS and EVAMIX methodology. (Chatterjee and Chakraborty 2012) solved the

MADM for gear material selection using PROMETHEE, COPRAS with gray relation by


53

and compared the methodology with VIKOR, PROMETHEE. (Bhowmik et al. 2018)

implemented selection of energy efficient material with the help of entropy based TOPSIS

methodology. (Rao 2007) applied GTMA, SAW, WPM, AHP, TOPSIS and VIKOR for

three case examples of material selection. (Jahan and Edwards 2013) applied VIKOR

methodology for material selection. (Nirmal and Bhatt 2015a) implemented TOPSIS

methodology material selection for an electroplating process.

(Dev et al. 2019) applied Entropy VIKOR method for automotive piston component

material selection. (Singh et al. 2018) applied combination of AHP and VIKOR for

selection of brake friction materials. (Gul et al. 2018) applied fuzzy based PROMETHEE

method for material selection problem. (Yadav et al. 2019) solved material selection

problem for marine applications using hybrid TOPSIS and PSI approach.

2.3.2 Machine Tool Selection

The selection of appropriate machine tool is one of the most crucial decisions for

manufacturing industries to make an efficient and effective production environment,

whereas wrong selection of machine tool negatively affects the overall performance of

production system (Ertugrul and Gunes 2007).

(Paramasivam et al. 2011) explained that machine tool (equipment) selection is not easy

task because due to the availability of large numbers of machine tools in the market and

the features are many and vary from each manufacturer.

Applications of existing MADM techniques for Machine Tool Selection:

Applications of existing MADM techniques for machine tool selection are tried to collect

from peer reviewed journal and international books are enlisted here.(Paramasivam et al.

2011) explained milling machine equipment selection using Diagraph and Matrix

approach, AHP and ANP in manufacturing industry. (Yurdakul 2004) implemented AHP

and ANP for machine tool selection problem. (Wang et al. 2000) developed fuzzy MADM

model for machine tool selection for flexible manufacturing cells. As per (Kahraman and

Otay 2019), (Sahu et al. 2014) applied AHP methodology for CNC machine tool selection.

(Ozceylan et al. 2016) applied PROMETHEE methodology for selection of CNC router

machine tool. (Ozgen et al. 2011) applied Delphi method, AHP and PROMETHEE

approach with fuzzy set and compered with Fuzzy TOPSIS methodology for machine tool


54

selection. (Taha and Rostam 2012) implemented Fuzzy AHP and PROMETHEE

methodology for selection of turning center CNC machine tool for flexible manufacturing

AHP and ANP cell.

As per (Kahraman and Otay 2019), (Nirmal and Bhatt 2019); (Haddou Benderbal et al.

2017) applied PSI methodology for machines selection in reconfigurable manufacturing

design problem. (Arunachalam et al. 2015) applied AHP and VIKOR for machine tool

selection problem. (Samvedi et al. 2012) applied Fuzzy AHP and GRA for machine tool

selection problem. (Nguyen et al. 2014) developed hybrid approach for fuzzy MADM in

machine tool selection problem. (Ilangkumaran et al. 2012) explained AHP and VIKOR

methodologies for machine tool selection problem in fuzzy environment. (Nguyen et al.

2015) calculated machine tool selection problem using AHP and Fuzzy COPRAS

methodology with fuzzy linguistic information.

2.3.3 Rapid Prototype Selection

Rapid prototype processes are carried out with three steps. In first stage sub active means

imply, second stage additive (material removal from a work piece) and third is virtual.

(Byun and Lee 2005) explains rapid prototype as the production of physical model from

computer aided design (CAD) data layer by layer deposition without using cutting tool.

(Byun and Lee 2005) explained Rapid prototype has been established to reduce cost and

product development. Recently new emerging techniques of RP makes it commercialized

worldwide i.e. aerospace, automobile, home appliances, etc.

Applications of existing MADM techniques for Rapid Prototype Selection:

Applications of existing MADM techniques for rapid prototype tool selection are tried to

collect from peer reviewed journal and international books are enlisted here. (Liao et al.

2014) explained rapid prototyping selection for three dimensional printer service provider

selection using DEMATEL and VIKOR. (Byun and Lee 2005) attempted to solve rapid

prototype problem with the help of modified TOPSIS methodology. (Rao and

Padmanabhan 2007) attempted to solve the same problem of rapid prototype proposed by

(Byun and Lee 2005) with the help of GTMA methodology. (Mahapatra and Panda 2013)

solved the selection of rapid prototype problem with the help of GRA and Fuzzy TOPSIS

methodology. (Kek and Kek 2016) applied ANP and TOPSIS methodology for rapid


55

prototype selection process. (Mahapatra and Panda 2013) implemented fuzzy TOPSIS with

GRA method for rapid prototype selection.

As per (Kahraman and Otay 2019), (Nirmal and Bhatt 2019); (Grote et al. 2010) applied

decision methods to select rapid prototyping technologies. (Girubha et al. 2014) explained

selection of rapid prototyping technologies in an agile environment using Fuzzy VIKOR

methodology.

2.3.4 Non-Traditional Machining Process (NTMP) Selection

(Temucin et al. 2014) explained that due to various beneficial and non-beneficial criteria,

MCDM (MADM) approaches are tremendously used for the selection process. Proper

selection of NTMP process is one of the key factors to improve the manufacturing

performance.

Applications of existing MADM techniques for NTMP Selection:

Applications of existing MADM techniques for NTMP selection are tried to collect from

peer reviewed journal and international books are enlisted here.(Shivakoti et al. 2017)

worked to find the optimum ranking for NTMP selection of laser beam micro machining

process with the help of fuzzy TOPSIS methodology. (Yurdakul and Ccogun 2003)

worked on NTMP selection for automotive manufacturing industry using AHP and

TOPSIS methodologies. (Das and Chakraborty 2011) implemented Analytical Network

Process (ANP) to solve the NTMP selection. (Sivapirakasam et al. 2011) developed

Taguchi and fuzzy TOPSIS methodology for process parameter optimization in green

manufacturing electrical discharge machining process. Here Taguchi orthogonal array was

used to evaluate the sensitivity of the attributes while, F-TOPSIS was used for ranking of

alternatives. (Temucin et al. 2014) solved the NTMP using different MADMs like,

TOPSIS, ELECTRE, PROMETHE-II, Fuzzy TOPSIS and Fuzzy ELECTRE-I technique.

(Manivannan and Kumar 2017) developed TOPSIS methodology for selecting process

parameters of cryogenically cooled micro EDM drilling machine. (Choudhury et al. 2013)

implemented TOPSIS methodology for NTMP selection.


56

2.3.5 Automated Guided Vehicle (AGV) Selection

(Kulak 2005) explained proper material handling system selection in the organization

which may lead to effective use of the labor, make the system more flexible, productivity

improvement, reduce the lead time and relative cost. Author also explained material

handling equipment classified in to cranes, industrial trucks, automated storage and

retrieval system (AS/RS), conveyer and AGV‘s.

Applications of existing MADM techniques for AGV Selection:

Applications of existing MADM techniques for AGV selection are tried to collect from

peer reviewed journal and international books are enlisted here. Selection and ranking of

AGV for engineering application is carried out by (Rao 2008b). where outranking method

for different AGV having eight alternatives and six attributes with all linguistic

information and the same case example was solved by (Maniya and Bhatt 2011a) using

AHP with M-GRA. Authors also tried to compare the proposed methodology with other

MADM: AHP with TOPSIS and AHP with GRA. (Nirmal and Bhatt 2016a),

(Smarandache and Pramanik 2016) described that, (Sawant et al. 2011) applied preference

selection index methodology for ranking of AGV. (Nirmal and Bhatt 2016a) implemented

entropy based fuzzy SVNS Novel MADM method for selection of AGV. (Sawant and

Mohite 2009) applied fuzzy TOPSIS methodology for selection of AGV. As per

(Kahraman and Otay 2019), (Nirmal and Bhatt 2019), (Nirmal and Bhatt 2019) applied the

F-SVNS N-MADM methodology for selection of automated guided vehicle (AGV) for

flexible manufacturing cell for industrial application.

2.3.6 Robot Selection

Robots are used in many industrial applications like welding, painting, material handling,

finishing, machining, loading/unloading and assembly where repetitive, hazardous,

difficult and precise work is carried out. The robot selection decision is more complex

because robot performance is specified by large number of attributes. (Karsak et al. 2012)

explained robot selection key aspect to find robot performance by considering various

conflicting attributes (criteria). (Nirmal et al. 2015a) explained that, the right selection of

robots for manufacturing environment form large set of alternatives which make difficulty


57

for decision makers. (Nirmal et al. 2015a) also explained there are various criteria for

selection robots are availability of material, configuration, cost space requirement, load

capacity, human interface, degree of freedom, type of controls, programming methods,

volume of work, velocity, movement, quality, etc.

Applications of existing MADM techniques for Robot Selection:

Applications of existing MADM techniques for robot selection are tried to collect from

peer reviewed journal and international books are enlisted here. As per (Kahraman and

Otay 2019), (Nirmal and Bhatt 2019); (Agrawal et al. 1991) worked to select the welding

robots using TOPSIS for manufacturing industry. (Rao and Padmanabhan 2006) applied

Diagraph and matrix approach for robot selection for industrial application. (Chatterjee et

al. 2011) solved that same input matrix formed by (Rao and Padmanabhan 2006) with

qualitative (linguistic/fuzzy) and quantitative information (crisp) for ranking of Robots

using novel MADM approach. (Devi 2011) applied intuitionistic fuzzy set theory with

VIKOR methodology for selection of robots. (Nirmal et al. 2015a) implemented and

validated COPRAS methodology for industrial robot selection problem.

In (Kahraman and Otay 2019); (Nirmal and Bhatt 2019) applied the F-SVNS N-MADM

methodology for selection of automated guided vehicle (AGV) for flexible manufacturing

cell for industrial application. (Narayanamoorthy et al. 2019) applied interval valued-

intuitionistic hesitant fuzzy entropy based VIKOR method logy for robot selection. (Zhou

et al. 2018) applied fuzzy extended VIKOR method for mobile robot selection. As per

(Kahraman and Otay 2019); (Mahapatra et al. 2016) applied extension of PROMETHEE

for robot selection problem.(Datta et al. 2015) applied PROMETHEE-II method for

industrial robot selection. (Keshavarz Ghorabaee 2016) implemented extended version of

VIKOR method with interval type fuzzy set for robot selection problem.

(Narayanamoorthy et al. 2019) applied interval valued- intuitionistic hesitant fuzzy entropy

based VIKOR method logy for robot selection. In (Kahraman and Otay 2019); (Nirmal and

Bhatt 2019) applied the investigated methodology for selection of automated guided

vehicle (AGV) for flexible manufacturing cell for industrial application.


58

2.3.7 Metal Stamping Layout Selection

(Nye 2000) explained 75% or more of total costs occur in stamping facilities due to only

materials. Stamping dies are needed for manufacturing of large number of products from

metallic sheet. In mass production from sheet metal cutting, even small errors in utilization

of part can lead to wastage of large amount from a blank profile; strip layout design is an

important step planning stage. Metal stamping layout depends on knowledge and skill of

designer, on the other hand complexity in the strip layout with manual judgment makes it

time consuming and impossible to judge the efficient way (Das and Srinivas 2013).

Applications of existing MADM techniques for Metal Stamping Layout Selection:

Applications of existing MADM techniques for metal stamping layout selection are tried to

collect from peer reviewed journal and international books are enlisted here.(Singh and

Sekhon 1996) solved metal stamping layout selection using diagraph and matrix approach.

The same case example further was calculated by RAO with GTMA, SAW, WPM, AHP,

TOPSIS and modified TOPSIS. (Das and Srinivas 2013) demonstrated the same problem

with TOPSIS and AHP methodology. (V M 2015) applied PROMETHEE methodology to

solve the metal stamping layout. (S and V M 2015) applied PROMETHEE for best metal

stamping layout problem.

2.3.8 Electro Chemical Machining (ECM) Program Selection

Electro chemical machining processes is an advanced machining technology, with some

unique advantages over other traditional and non-traditional machining processes. In ECM

process work piece with highest strength, hardness with lower strength and harder tool

material are used. No tool wear (theoretically, infinite tool life), zero thermal damage,

good surface finish, dimensional tolerances and burr free and stress free machined surfaces

can be produced (Jain 2002). Optimization of ECM process parameters, because

optimization in process parameters significantly lead to improve manufacturing process

performance (Bhattacharyya and Munda 2003), (Bhattacharyya et al. 2001), (De Silva et

al. 2000).


59

Applications of existing MADM techniques for ECM Program Selection:

Applications of existing MADM techniques for ECM program selection are tried to collect

from peer reviewed journal and international books are enlisted here.(Rao 2008c) solved

the ECM programming selection using AHP, TOPSIS and modified TOPSIS

methodologies. (Venkata Rao and Patel 2010) attempted to solve the ECM programming

selection using PROMETHEE methodology. (Venkata Rao 2009) implemented improved

compromising ranking method for ECM program selection. (Choudhury et al. 2013)

implemented TOPSIS methodology for NTMP selection. (Chauhan and Pradhan 2014)

tried to combine TOPSIS and AHP approach for selection of NTMP.

2.3.9 Cutting Fluid (Coolant) Selection

Cutting fluids are used in machining process to cool the work piece, reduce friction and

tool wear, increase cutting tool life, reduce surface roughness and flush away the chips, it

also protects from corrosion and provide lubrication (Johnson et al. 2014). So, the use of

cutting fluid (coolant) is very essential during machining operations. The Cutting fluids are

widely used in industries for machining processes and coolant may negatively effects on

the health, environment, legislation, public and environmental concerns. (Rao 2007) was

explained the cutting fluid selection is more an art, than a science, because there is almost

no standardized method available for given application.

Applications of existing MADM techniques for Cutting Fluid (coolant) Selection:

Applications of existing MADM techniques for cutting fluid selection are tried to collect

from peer reviewed journal and international books are enlisted here.(Attri et al. 2014a)

applied COPRAS for cutting fluid selection. (Jagadish and Ray 2014) applied AHP

methodology for cutting fluid criteria selection and VIKOR methodology for cutting fluid

(alternatives) ranking. (Bai et al. 2018) developed a method based on MADM for selecting

cutting fluid for granite sawing process.

2.3.10 Supplier Selection

(Helmold and Terry 2017) clearly defined Supplier, who provides process, product or

services to the organization to add the value., in which author also tried to identify


60

hierarchy of supplier network by type of suppliers like ram material supplier, component/

parts supplier, systems supplier, module supplier and integrated supplier. In today‘s highly

competitive and consistent manufacturing surroundings, the effective selection of supplier

is very important to the success of a manufacturing firm. Outsourcing (buy decision) is one

of the key decision making strategies carried for smoothly running of supply chain.

Outsourcing decision is the strategic decision which leads to influence several performance

across the entire business (Aron and Singh 2005), (Ronan et al. 2009), (Tyagi et al. 2015).

(Vonderembse and Tracey 1999) derived that performance improvement is as important as

the evaluation which is used to select the supplier. The authors also tried to convey that

selection of the right supplier may lead to improvement and enhance the performance

using various MADM techniques. (Nirmal and Qureshi 2009) developed generalized

framework of fuzzy expert decision support system for vendor (Supplier) selection.

(Nirmal et al. 2015b) explained selecting right supplier significantly reduces purchasing

cost, improve competitiveness in the market and enhances user satisfaction level. (Nirmal

et al. 2015b) also identified the cause and effect diagram for supplier selection.

(Chaharsooghi and Ashrafi 2014) explained that the supplier selection plays an important

role in SCM. (Nirmal et al. 2015c) implemented and validated MADM technique for

supplier selection for smoothly running SCM.

Applications of existing MADM techniques for Supplier Selection:

Applications of existing MADM techniques for supplier selection are tried to collect from

peer reviewed journal and international books are enlisted here.(Chaharsooghi and Ashrafi

2014) also explained that any MADM model can be used for evaluation performance of

suppliers. (Senvar et al. 2014) implemented supplier selection using F-PROMETHEE for

manufacturing industry. (Nirmal and Bhatt 2015b) developed Integrated MCDM model of

supplier selection for sustainable manufacturing environment. (Nirmal et al. 2014)

developed hierarchical structure and conceptual model of supplier selection with Fuzzy

AHP, Fuzzy Delphi, and F-TOPSIS.

(Deshmukh and Vasudevan 2019) applied supplier selection in plastic product

manufacturing in MSME using AHP methodology. (Memari et al. 2019) applied multi

criteria IFS TOPSIS method for finding sustainable supplier selection. (Fallahpour et al.

2017) developed decision support model for sustainable supplier selection using TOPSIS

method. (Dos Santos et al. 2019) worked to select green supplier using Entropy weight


61

Fuzzy TOPSIS methodology. (Sen et al. 2018) applied IFS- TOPSIS method to facilitate

supplier selection in sustainable supply chain. (Fei et al. 2019) investigated Dempster-

Shafer evidence theory (DS theory) with VIKOR method for supplier selection problem.

(Fahmi et al. 2016) applied ELECTRE-I supplier selection problem. (Gitinavard et al.

2018) applied ELECTRE method with interval valued hesitant fuzzy set theory for green

supplier selection problem. (Borujeni and Gitinavard 2017) investigated new extension of

PROMETHEE under intuitionistic fuzzy environment for solving supplier selection with

qualitative parameters. (Sen et al. 2018) applied IFS- GRA method to facilitate supplier

selection in sustainable supply chain. (Zhang and Li 2018) applied combination of TOPSIS

and GRA for supplier selection problem with interval numbers. (Liou et al. 2016) applied

COPRAS- G methodology for improving and selecting supplier in green supply chain

environment. (Sen et al. 2018) applied IFS- TOPSIS, IFS MOORA and IFS- GRA

methods to facilitate supplier selection in sustainable supply chain. (Gitinavard et al. 2018)

applied ELECTRE method with interval valued hesitant fuzzy set theory for green supplier

selection problem. (Zhang and Li 2018) applied combination of TOPSIS and GRA for

supplier selection problem with interval numbers.

2.3.11 Third Party Reverse Logistic Providers (TPRLP) Selection

(Kannan 2009) first applied AHP and Fuzzy AHP for reverse logistics provider‘s selection.

(Kumar et al. 2007) explained that proper selection of logistic provider which leads to

improve the supply chain performance. (Nirmal and Bhatt 2016b) explained the role of

third party logistic service providers for healthcare waste management and healthcare

assessment with MADM approach.

Applications of existing MADM techniques for TPRLP Selection:

Applications of existing MADM techniques for TPRLP selection are tried to collect from

peer reviewed journal and international books are enlisted here. (Kumar et al. 2007) solved

the third party logistic provider‘s selection so that potential service providers can be

selected with the help of AHP and TOPSIS methodology. (Qureshi et al. 2007a)

implemented TOPSIS methodology with interval data to select the potential third party

logistic provider. (Kannan et al. 2009) implemented fuzzy TOPSIS to select the reverse

logistic providers. (Qureshi et al. 2007a) attempted to solve the reverse logistics service

2.4 Brief Conclusion of Literature Review

62

provider selection using AHP methodology. (Rajesh et al. 2012) worked on logistic service

provider by using F-PROMETHEE for cement manufacturing industry.

(Jain and Khan 2016) applied AHP methodology for selection of reverse logistics

provider‘s selection. (Aguezzoul and Pires 2016) applied ELECTRE-I methodology for

third party logistics selection. (Celik et al. 2016) worked to extend ELECTRE method

based upon interval type 2 fuzzy set for green logistics service provider‘s evaluation.

(Elevli 2014) developed Fuzzy PROMETHEE model for choosing among potential

logistics center locations. (Celik et al. 2016) worked to extend ELECTRE method based

upon interval type 2 fuzzy set for green logistics service provider‘s evaluation.


At the end of literature survey, one can able to understand that there are several existing

MADM techniques present. They are having their own advantages, and applications. Some

individual weaknesses of the existing MADM methods which are reported in the literature

are as under.

AHP Methodology

When there are large number of alternatives and attributes, it is very difficult to

decide relative importance between attribute as well as alternatives. To achieve

perfect consistency, it becomes difficult for calculating relative importance

between alternatives as well as attributes. It needs to conduct the consistency test

for the judgment while assigning the relative importance. It needs the expert

decision/ research scholar‘s decision for finding weight of attribute, which leads to

different ranking solution.

TOPSIS Methodology

As per (Kahraman and Otay 2019) and (Nirmal and Bhatt 2019) explained that, the

same type of normalization formula is used for beneficial and non-beneficial

attributes. It uses the Euclidean distance principle, but it does not consider the

correlation of attributes.


63

VIKOR Methodology

It only worked with weight strategy for calculating the rank. The value in the range

[0, 1]; hence, different attribute weight leads to different ranking solution.

ELECTRE Methodology

ELECTRE work is only preferred for large set of alternatives and few attributes.

ELECTRE parameter is not easily understood by practitioners, it also takes more

calculation time for determination of net concordance and net discordance values.

The major drawback of ELECTRE methodology might lead to incomparability if

both alternatives are quite similar. For such situation it is required to choose

between the two alternatives.

PROMETHEE Methodology

It is difficult to decide the preference functions used in PROMETHEE and it may

be inaccurate in real life selection problems. It is very difficult to explain the

preference information to non-specialists. Loss of input information; while

performing calculation of positive and negative difference of outranking flows.

GRA Methodology

It is very difficult to decide the Grey relation among the attributes. During

normalization some of the attribute measure becomes zero, this may lead to loss of

data or information during further calculation. Distinguish coefficient has critical

effect on ranking which will make to lead the different ranking and selection of

alternatives for the same weight of attributes.

COPRAS Methodology

Here also the same normalization technique used for beneficial and non-beneficial

criteria. It needs the decision maker/ expert/ researcher for attribute weight, it may

vary the ranking solutions. During normalization some of the value becomes zero

which may lead to change the overall ranking solution.


64

PSI Methodology

During normalization through other techniques found extra variation in the ranking

solution. So far the research has been done in PSI methodology; as per (Kahraman

and Otay 2019); (Nirmal and Bhatt 2019) explained that, it can handle only the

fuzzy and crisp data. During calculation degree of truthness, degree of

indeterminacy and degree of falsity are not considered.

The second phase insights, there are several mathematical sets through which MADMs and

other decision making are possible. Mathematical set theories are having their individual

advantages and applications. Some individual limitations of existing mathematical set

theory for functioning with MADMs are as under.

Drawback of Crisp Set for MADM Techniques

In crisp set decision maker/ researchers/ experts not allowed to give the information

in qualitative i.e. quality of product, customer satisfaction, accuracy, range, etc.

Crisp set can‘t handle degree of falsehood and indeterminacy at same time.

Crisp set can‘t handle the decision in range solution.

Drawbacks of Fuzzy (Linguistic) of FS with crisp set for MADM

Decision maker can express in degree of truthness only. Cannot express decision

for the falsehood ness for relative attributes.

Gives decision in only the degree of truth membership with range [0, 1]

Drawbacks of Intuitionistic Fuzzy Set (IFS)

Does not provide the space to handle the degree of indeterminate solution.

(Smarandache and Pramanik 2016) explained IFS cannot handle indeterminate and

inconsistent information. In real world applications, the information of input data is

often incomplete, indeterminate and inconsistent.

Drawbacks of Interval Valued Intuitionistic Fuzzy Set (IVIFS)

As per (Smarandache and Pramanik 2016), IVIFS cannot handle the inconsistent

and indeterminate information. In real application, information of input data‘s is

often incomplete, indeterminate and inconsistent.


65

This set theory provides only choice for degree of truth and falsehood contains the

range, it does not provide the space to handle the degree indeterminate solution.

This chapter is also insight various applications of existing MADM techniques which are

proposed by various researchers in eleven random selection process which are affecting

manufacturing and supply chain environment in the decision making.

Chapter 3: Proposed MADM Techniques


67

CHAPTER: 3

Proposed MADM Techniques

The previous chapter presented the information regarding several existing MADMs

and different types of Mathematical set theories. From the literature review we found that,

there are various limitations of existing MADMs. Existing MADMs work with calculating/

predefine values of attribute weight, except PSI methodology. It is also found that the

change in the attribute weight leads to change in the ranking order of alternatives. To solve

limitations of existing MADMs and more accurate result, in this chapter three new

approaches for MADMs are tried to investigate. They are as under.

(i) Fuzzy Single Valued Neutrosophic Set Novel MADM(F-SVNS N- MADM),

(ii) Fuzzy Single Valued Neutrosophic Set Entropy Weight based MADM (F-

SVNS EW-MADM) and

(iii) Fuzzy Single Valued Neutrosophic Set Advanced Correlation Coefficient

MADM (F-SVNS ACC-MADM);

In (Smarandache and Pramanik 2016), (Nirmal and Bhatt 2016a), (Nirmal and Bhatt

2019) explained, proposed SVNS MADM which works with conversion on crisp/ fuzzy set

into single valued neutrosophic set. The positive impact of two methodologies (i) F-SVNS

N-MADM and (ii) F-SVNS ACC-MADM, gives the solution without calculating attributes

weight. The same SVNS set theory is applied to F-SVNS EW-MADM methodology and it

also shows the better ranking solution by considering attribute weight criteria. In

(Smarandache and Pramanik 2016), (Nirmal and Bhatt 2016a) explained that, SVNS

MADM give the enhanced solution with imprecise, indeterminate, inconsistent and

uncertainty information by considering degree of truth, degree of indeterminacy and

degree of falsehood.

The proposed MADMs are gifted with conversations of crisp/ Lingustic information to

F-SVNS. This leads to improve the ranking solution. These conversions have the following

hidden benefits (to identify the human decision behavior) as follows.

3.1 Proposed Methodology-1: Fuzzy-Single Valued Neutrosophic Set Novel Multi Attribute Decision

Making Technique (F-SVNS-N-MADM):

68

(i) Able to identify value of the degree of truthness

(ii) Able to identify value of the degree of indeterminacy

(iii) Able to identify value of the degree of falsity

At the end the proposed methods are implemented in two random examples collected

from the industry. (i) Supplier selection and (ii) Material provider‘s selection; the results of

the each selection problem shows the similarity of ranking order and soundness of ranking

solution of proposed methodologies.

3.1 Proposed Methodology-1: Fuzzy-Single Valued Neutrosophic Set

Novel Multi Attribute Decision Making Technique (F-SVNS-N-

MADM):

(Nirmal and Bhatt 2019) investigated Fuzzy Single Valued Neutrosophic Set Novel Multi

Attribute Decision Making (F-SVNS N-MADM) methodological steps are as below.

Step 1. Identify the objective of MADM for selection/ ranking/ sorting/ evaluation for

decision making.


Step 3. Preparation the decision matrix




are having qualitative/ quantitative values. Table 3.1 shows the decision matrix

TABLE 3.1: Decision Matrix for F-SVNS N-MADM

…..

…..

…..

…..

…. ….. ….. ….. ….. …..

…..


Convert qualitative (linguistic) information in to quantitative (crisp) value with the help of

Table 3.2.


69

TABLE 3.2: Conversion of Linguistic Terms in to Classic (Crisp) Set

Linguistic terms of selection attributes Fuzzy number Crisp value of selection

attribute



Very low M3 0.255

Low M4 0.335


Average M6 0.500


High M8 0.665

Very high M9 0.745



Collected from Source: (Chen and Hwang 1992b) (Venkatasamy and Agrawal 1996; Venkatasamy and

Agrawal 1997), In (Smarandache and Pramanik 2016), (Nirmal and Bhatt 2016a)

If the input matrix contains only quantitative information, than skip this step.

Step 5. Generalization/ Normalization of matrix

In (Smarandache and Pramanik 2016), As per (Nirmal and Bhatt 2016a), Each relative

attributes of alternatives are having different values. Normalization is a calculation is

carried out for making the value in the comparable scale. Here the calculation is carried

with Vector Normalization Method (VNM) normalization method.

For beneficial criteria, where higher values are desirable (i.e. quality, profit, etc.)

normalization is carried out with Equation (3.1)

√∑

…………………………………………………………..……… (3.1)

For non- beneficial criteria, where higher values are desirable (i.e. price, lead time etc.)

normalization is carried out with Equation (3.2)

√∑

…………………………..……………………. ………… (3.2)

Normalized decision matrix is shown in Table 3.3

3.1 Proposed Methodology-1: Fuzzy-Single Valued Neutrosophic Set Novel Multi Attribute Decision

Making Technique (F-SVNS-N-MADM):

70

TABLE 3.3: Normalized Decision Matrix for F-SVNS N-MADM

…..

…..

…..

…..

…. ….. ….. ….. ….. …..

…..

Step 6. Conversion of classic set/ fuzzy set to Single Valued Neutrosophic Set (SVNS):

SVNS normalized decision matrix is shown in Table 3.4

TABLE 3.4: SVNS Normalized Decision Matrix for F-SVNS N-MADM

…..

…..

…..

…..

…. ….. ….. ….. …..

…..

In (Smarandache and Pramanik 2016), as per (Nirmal and Bhatt 2016a), the conversion

rules for classic or fuzzy set to SVNS for beneficial and non-beneficial criteria (Nirmal and

Bhatt 2016a) are as follow.

In (Smarandache and Pramanik 2016), as per (Nirmal and Bhatt 2016a), Beneficial

criteria: (higher value of performance measures of selection criteria is desirable i.e.,

profit, quality, etc.): Considering positive ideal solution (PIS)

as

; normalized input matrix beneficial criteria are

considered as degree of truthness , while degree of indeterminacy and degree

of falsehood as respectively. SVNS conversion is

carried out with Equation (3.3).

⟨ ⟩ = ⟨ ( ) ( )⟩.…..................… (3.3)

In (Smarandache and Pramanik 2016), as per (Nirmal and Bhatt 2016a), Non-

beneficial criteria: (Lower value of performance measure of selection criteria is

desirable i.e. cost) Considering with negative ideal solution(NIS) as

; normalized input matrix non-beneficial criteria are

considered as degree of indeterminacy and falsehood as while

degrees of truthness is considered as .SVNS

conversion is carried out with Equation (3.4).

⟨ ⟩ = ⟨( ) ⟩………………….....…… (3.4)


71

Step 7. Find the ideal solution for beneficial and non-beneficial attributes

Beneficial attributes ideal solution ⟨

⟩ ⟨ ⟩

Non beneficial attributes ideal solution ⟨

⟩ ⟨ ⟩

Step 8. Calculation of the alternative weight

Equation (3.5) shows weight of the alternative

∑ (( ) (

) ( )*

…….…. (3.5)

Where beneficial attributes ⟨

⟩ ⟨ ⟩ and non-

beneficial attributes ⟨

⟩ ⟨ ⟩


After calculation of alternative weight , the alternatives are ranked according to

descending order. i.e. highest alternative Correlation Coefficient is considered as first

rank, while lowest alternative score is considered as last rank.

3.2 Proposed Methodology- 2: Fuzzy-Single Valued Neutrosophic Set

Entropy Weight Based Multi Attribute Decision Making

Technique (F-SVNS-EW-MADM)

Fuzzy Single Valued Neutrosophic Set Entropy Weight based Multi Attribute Decision

Making (F-SVNS EW-MADM) method is explained in (Smarandache and Pramanik

2016), with chapter (Nirmal and Bhatt 2016a). F-SVNS EW-MADM methodological steps

are as below.

Step 1. To identify the objective of selection.

Step 2. Identification of various alternatives and relative attributes (criteria) involved in

selection problem.

Step 3. Preparation of the decision matrix

3.2 Proposed Methodology- 2: Fuzzy-Single Valued Neutrosophic Set Entropy Weight Based Multi

Attribute Decision Making Technique (F-SVNS-EW-MADM)

72

All alternatives and attributes (criteria) in matrix form with comparative performance are

known as decision matrix. Let us consider set of alternatives as { }

& set of criteria as { }, is the performance of alternatives for

relative criteria . are having qualitative/ quantitative values. Table 3.5 shows the

decision matrix.

TABLE 3.5: Decision Matrix for F-SVNS EW-MADM

…..

…..

…..

…..

…. ….. ….. ….. ….. …..

…..

Step 4. Conversion of qualitative data in the quantitative data


Table 3.2. If the input matrix contains only quantitative information, than skip this step.


In (Smarandache and Pramanik 2016), As per (Nirmal and Bhatt 2016a), each relative

attributes of alternatives are having different values. Normalization is carried out to make

the information in range [0, 1]. Here, the normalization is carried out with Vector

Normalization Method (VNM).

For beneficial criteria; where maximum values are desirable (i. e. profit, quality etc.)

normalization is carried out with Equation (3.1) and for non-beneficial criteria where lower

values are desirable (i.e. lead time price etc.) normalization is carried out with Equation

(3.2). Normalized decision matrix is shown in Table 3.6

TABLE 3.6: Normalized Decision Matrix for F-SVNS EW-MADM

…..

…..

…..

…..

…. ….. ….. ….. ….. …..

…..

Step 6. Conversion of classic set/ fuzzy set to single value neutrosophic set (SVNS) SVNS

normalized decision matrix for F-SVNS EW-MADM is as shown in Table 3.7


73

TABLE 3.7: SVNS Normalized Decision Matrix for F-SVNS EW-MADM

…..

…..

…..

…..

…. ….. ….. ….. …..

…..

As per (Nirmal and Bhatt 2016a), the conversion rule for classic or fuzzy set to SVNS for

beneficial and non-beneficial criteria (Nirmal and Bhatt 2016a) is explained below.

In (Smarandache and Pramanik 2016), as per (Nirmal and Bhatt 2016a),

Beneficial criteria: (higher value of performance measures of selection criteria

is desirable. i.e. quality, profit etc.) considering positive ideal solution (PIS)

as

; normalized input matrix beneficial criteria

are considered as degree of truthness , while degree of indeterminacy,

degree of falsity as respectively. SVNS conversion

is carried out with Equation (3.3).

In (Smarandache and Pramanik 2016), as per (Nirmal and Bhatt 2016a), Non-

beneficial criteria: (lower value of performance measure of selection criteria is

desirable i.e. cost, lead time etc.): Considering negative ideal solution (NIS) as

; normalized input matrix non-beneficial

criteria are considered as degree of indeterminacy and falsehood as

while degrees of truthness is considered as

.SVNS conversion is carried out with Equation (3.4).


In (Smarandache and Pramanik 2016), As per (Nirmal and Bhatt 2016a),


⟩ ⟨ ⟩

Non beneficial attributes ideal solution ⟨

⟩ ⟨ ⟩

Step 8. Calculation of the entropy value of attribute

Find the entropy value for attribute with Equation (3.6).

⁄ ∑ ( ) | ( ) |

………………………….…. (3.6)

Step 9. Calculation of the entropy weight of attribute

3.3 Proposed Methodology-3: Fuzzy Single Valued Neutrosophic Set SVNS Advance Correlation

Coefficient Multi Attribute Decision Making Technique (F-SNVS-ACC-MADM)

74

Find the entropy weight of attribute by Equation (3.7)

∑

……………………………….……………………………… (3.7)

Where, we get weight vector of attributes,

{ } With and∑

.

Step 10. Calculate the entropy weight of alterative

Find the alternative weight by Equation (3.10)

∑ (

)

(3.8)

Where, for beneficial attributes ⟨

⟩ ⟨ ⟩ and for non-

beneficial attributes ⟨

⟩ ⟨ ⟩.


After calculation of alternative weight , the alternatives are ranked according to

descending order. i.e. highest alternatives correlation coefficient is considered as first

rank, while lowest alternative score .

3.3 Proposed Methodology-3: Fuzzy Single Valued Neutrosophic Set

SVNS Advance Correlation Coefficient Multi Attribute Decision

Making Technique (F-SNVS-ACC-MADM)

Fuzzy Single Valued Neutrosophic Set Advance Correlation Coefficient Multi Attribute

Decision Making (F-SVNS ACC-MADM) methodological steps are as below.

Step 1. Define the objective of MADM i.e. ranking/ sorting/ evaluation/ selection in

decision making.

Step 2. Identification of various alternatives and relative attributes (criteria) involved in

selection problem.

Step 3. Preparation of the decision matrix

All alternatives and attributes (criteria) in matrix form with relative performance are

known as decision matrix. Let us consider set of alternatives as { }

& set of criteria as { }, is the performance of alternatives for


75

relative criteria . are having qualitative/ quantitative values. Table 3.8 shows the

decision matrix.

TABLE 3.8: Decision Matrix for F-SVNS ACC-MADM

…..

…..

…..

…..

…. ….. ….. ….. ….. …..

…..

Step 4. Conversion of qualitative data in the quantitative data


Table 3.2. If the input matrix contains only quantitative information, than skip this step.


In (Smarandache and Pramanik 2016), As per (Nirmal and Bhatt 2016a), each relative

attributes of alternatives are having different values. Normalization is carried out to make

the information in range [0, 1]. Here, the normalization is carried out with Vector

Normalization Method (VNM).

For beneficial criteria; where highest values are desirable (i. e. quality, profit, etc.)

normalization is carried out with Equation (3.1) and for non-beneficial criteria where lower

values are desirable (i.e. price, lead time etc.) normalization is carried out with Equation

(3.2)

Normalized decision matrix is shown in Table 3.9

TABLE 3.9: Normalized Decision Matrix for F-SVNS ACC- MADM

…..

…..

…..

…..

…. ….. ….. ….. ….. …..

…..

Step 6. Conversion of classic set/ fuzzy set to Single valued neutrosophic (SVNS)

SVNS normalized decision matrix for F-SVNS ACC-MADM is as shown in Table 3.10

3.3 Proposed Methodology-3: Fuzzy Single Valued Neutrosophic Set SVNS Advance Correlation

Coefficient Multi Attribute Decision Making Technique (F-SNVS-ACC-MADM)

76

TABLE 3.10: SVNS Normalized Decision Matrix for F-SVNS ACC-MADM

…..

…..

…..

…..

…. ….. ….. ….. …..

…..

In (Smarandache and Pramanik 2016), as per (Nirmal and Bhatt 2016a), the conversion

rule for classic or fuzzy set to SVNS for beneficial and non-beneficial criteria (Nirmal and

Bhatt 2016a) is explained below.

In (Smarandache and Pramanik 2016), as per (Nirmal and Bhatt 2016a), beneficial

criteria: (higher value of performance measures of selection criteria is desirable. i.e.

quality, profit, etc.) considering positive ideal solution (PIS)

as

; normalized input matrix beneficial criteria are

considered as degree of truthness , while degree of indeterminacy, degree of

falsity as respectively. SVNS conversion is carried out

with Equation (3.3).

In (Smarandache and Pramanik 2016), as per (Nirmal and Bhatt 2016a), non-

beneficial criteria: (lower value of performance measure of selection criteria is

desirable i.e. cost, lead time, etc.): Considering negative ideal solution (NIS) as

; normalized input matrix non-beneficial criteria

are considered as degree of indeterminacy and falsehood as while

degrees of truthness is considered as .SVNS

conversion is carried out with Equation (3.4).



⟩ ⟨ ⟩

Non-beneficial attributes ideal solution ⟨

⟩ ⟨ ⟩

Step 8. Calculation of the Advance Correlation Coefficient function of Alternatives

Find the Advance Correlation Coefficient function for each alternative with Equation (3.9)

∑

,∑

∑

- ……………….……..….. (3.9)



77

After calculation of alternative weight the alternatives are ranked according to

descending order. i.e. highest alternatives correlation coefficient is considered as

leading rank, while lowest alternative score .

3.4 Demonstration of Proposed Methodologies

Here, two industrial case examples are collected and demonstrated in (i) and (ii) as under.

3.4.1 Industrial Case Example 1 Supplier’s selection:

The proposed methodology is demonstrated using an example. The considered example is

related to selection of vendor for Sidhdhapura machine tool manufacturing industry

situated at GIDC, Bhavnagar. The solution is demonstrated step by step using all three

methodologies.

Step 1 to Step 7 is similar in proposed methodologies. Here, step 1 to step 7 is carried out

initially.

Step: 1 The objective of MADM problem is to select/ rank/ evaluate an appropriate

supplier for a Sidhdhapura machine tool manufacturing industry application.

Step: 2 Here seven Supplier‘s alternatives with seven attributes (criteria) and their

attributes measures are C1: Product quality from [0,1] in range, C2: Product price as per

last invoice in Rs., C3: Price fluctuations from [0, 5] in range, C4: Geographical location

[0, 100] in range, C5: Technical level [0, 1] in range, C6: Supply ability [0, 1] in range,

C7: Delivery [0, 100] in range, Here beneficial attributes are C1, C5, C6, C7; whereas C2,

C3 C4 are considered as non-beneficial attributes.

Step: 3 Decision matrix collected from the experts of the Sidhdhapura machine tool

manufacturing industry is as shown in Table 3.11.

TABLE 3.11: Decision Matrix for F-SVNS MADM for Industrial Case Example-I

Sr. No. Alternatives C1 (+) C2 (-) C3 (-) C4 (-) C5 (+) C6 (+) C7 (+)

A1 0.4 52000 3 1 2 0.1 10

A2 0.8 5000 1 38 7 0.5 15

A3 0.7 37800 3 75 5 0.2 35

A4 0.8 5300 2 80 5 0.6 70

A5 0.9 8579 2 15 8 0.9 98

A6 0.6 48620 5 35 6 0.8 30

A7 0.9 168695 2 60 9 0.9 45


78

Step: 4 Conversion of qualitative data in to quantitative data

All given data are in quantitative information. Hence, skip this step to convert the

qualitative data in to quantitative data.

Step: 5 Normalization is carried out with the Equation (3.1)/ Equation (3.2). Supplier

selection normalized matrix is shown in Table 3.12.

TABLE 3.12: Normalized Decision Matrix for F-SVNS MADM

Sr. No.

Alternatives C1 (+) C2 (-) C3 (-) C4 (-) C5 (+) C6 (+) C7 (+)

A1 0.2023 0.7224 0.5991 0.9927 0.1187 0.0585 0.0726

A2 0.4046 0.9733 0.8664 0.7208 0.4154 0.2926 0.1089

A3 0.3540 0.7982 0.5991 0.4489 0.2967 0.1170 0.2541

A4 0.4046 0.9717 0.7327 0.4121 0.2967 0.3511 0.5081

A5 0.4551 0.9542 0.7327 0.8898 0.4747 0.5267 0.7114

A6 0.3034 0.7404 0.3318 0.7428 0.3560 0.4682 0.2178

A7 0.4551 0.0993 0.7327 0.5591 0.5341 0.5267 0.3266

Step 6. Convert crisp normalized matrix into SVNS decision matrix: Crisp data is

converted in SVNS degree of truthness, indeterminate and

falsehood form.

Beneficial attributes i.e. Alternative A1 and attribute C1 is having value 0. 5513

converted in SVNS gives the value ⟨ ⟩

⟨ ⟩. The same calculation is also is carried out for attributes

C2 and C4.

Non-beneficial attributes i.e. Alternative A 1 and attribute C3 having value

converted in SVNS gives the value⟨ ⟩

⟨ ⟩.

Step 7. Find the beneficial attribute ideal solution and non-beneficial attribute ideal

solution.

Beneficial attribute ideal solution and non-beneficial attribute ideal solution is discovered

with Equation (3.3)/ Equation (3.4), where ⟨

⟩

⟨ ⟩ and ⟨

⟩ ⟨ ⟩. The following

conversions are carried out to prepare Table 3.13.


79

TABLE 3.13: SVNS Normalized Decision Matrix for Industrial Case Example-I

Sr. No.

Alternatives C1 (+) C2 (-) C3 (-) C4 (-) C5 (+) C6 (+)

A1

<0.2023,

0.7977,

0.7977>

<0.2776,

0.7224,

0.7224>

<0.4009,

0.5991,

0.5991>

<0.0073,

0.9927,

0.9927>

<0.1187,

0.8813,

0.8813>

<0.0585,

0.9415,

0.9415>

A2

<0.4046,

0.5954,

0.5954>

<0.0267,

0.9733,

0.9733>

<0.1336,

0.8664,

0.8664>

<0.2792,

0.7208,

0.7208>

<0.4154,

0.5846,

0.5846>

<0.2926,

0.7074,

0.7074>

A3

<0.3540,

0.6460,

0.9460>

<0.2018,

0.7982,

0.7982>

<0.4009,

0.5991,

0.5991>

<0.5511,

0.4489,

0.4489>

<0.2967,

0.7033,

0.7033>

<0.1170,

0.8830,

0.8830>

A4

<0.4046,

0.5954,

0.5954>

<0.0283,

0.9717,

0.9717>

<0.2673,

0.7327,

0.7327>

<0.5879,

0.4121,

0.4121>

<0.2967,

0.7033,

0.7033>

<0.3511,

0.6489,

0.6489>

A5

<0.4551,

0.5449,

0.5449>

<0.0458,

0.9542,

0.9542>

<0.2673,

0.7327,

0.7327>

<0.1102,

0.8898,

0.8898>

<0.4747,

0.5253,

0.5253>

<0.5267,

0.4733,

0.4733>

A6

<0.3034,

0.6966,

0.6966>

<0.2596,

0.7404,

0.7404>

<0.6682,

0.3318,

0.3318>

<0.2572,

0.7428,

0.7428>

<0.3560,

0.6440,

0.6440>

<0.4682,

0.4733,

0.4733>

A7

<0.4551,

0.5449,

0.5449>

<0.9007,

0.0993,

0.0993>

<0.2673,

0.7327,

0.7327>

<0.4409,

0.5591,

0.5591>

<0.5341,

0.4659,

0.4659>

<0.5267,

0.5318,

0.5318>

<1.000,

0.0000,

0.0000>

<0.0000,

1.0000,

1.0000>

<0.0000,

1.0000,

1.0000>

<0.0000,

1.0000,

1.0000>

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>

(i) Proposed Method 1: F-SVNS N-MADM for Supplier Selection

Step 1 to step 7 are described earlier in point 3.4 (i)

Step 8. Calculation of the alternative weight

Calculate the alternative weight with the Equation (3.5) is as shown in Table 3.14. i.e.

consider the alternative weight of first alternatives calculated as {

} { }

{ } {

} { } {

} { }

The same calculation is also is carried out for remaining alternatives.


80

TABLE 3.14: F-SVNS N-MADM Ranking for Industrial Case Example-I

Sr. No.


Rank

A1

<0.2023,

0.7977,

0.7977>

<0.2776,

0.7224,

0.7224>

<0.4009,

0.5991,

0.5991>

<0.0073,

0.9927,

0.9927>

<0.1187,

0.8813,

0.8813>

<0.0585,

0.9415,

0.9415>

<0.0726,

0.9274,

0.9274>

5.0803 4

A2

<0.4046,

0.5954,

0.5954>

<0.0267,

0.9733,

0.9733>

<0.1336,

0.8664,

0.8664>

<0.2792,

0.7208,

0.7208>

<0.4154,

0.5846,

0.5846>

<0.2926,

0.7074,

0.7074>

<0.1089,

0.8911,

0.8911>

6.3423 2

A3

<0.3540,

0.6460,

0.9460>

<0.2018,

0.7982,

0.7982>

<0.4009,

0.5991,

0.5991>

<0.5511,

0.4489,

0.4489>

<0.2967,

0.7033,

0.7033>

<0.1170,

0.8830,

0.8830>

<0.2541,

0.7459,

0.7459>

4.7142 6

A4

<0.4046,

0.5954,

0.5954>

<0.0283,

0.9717,

0.9717>

<0.2673,

0.7327,

0.7327>

<0.5879,

0.4121,

0.4121>

<0.2967,

0.7033,

0.7033>

<0.3511,

0.6489,

0.6489>

<0.5081,

0.4919,

0.4919>

5.7937 3

A5

<0.4551,

0.5449,

0.5449>

<0.0458,

0.9542,

0.9542>

<0.2673,

0.7327,

0.7327>

<0.1102,

0.8898,

0.8898>

<0.4747,

0.5253,

0.5253>

<0.5267,

0.4733,

0.4733>

<0.7114,

0.2886,

0.2886>

7.3213 1

A6

<0.3034,

0.6966,

0.6966>

<0.2596,

0.7404,

0.7404>

<0.6682,

0.3318,

0.3318>

<0.2572,

0.7428,

0.7428>

<0.3560,

0.6440,

0.6440>

<0.4682,

0.4733,

0.4733>

<0.2178,

0.7822,

0.7822>

4.9756 5

A7

<0.4551,

0.5449,

0.5449>

<0.9007,

0.0993,

0.0993>

<0.2673,

0.7327,

0.7327>

<0.4409,

0.5591,

0.5591>

<0.5341,

0.4659,

0.4659>

<0.5267,

0.5318,

0.5318>

<0.3266,

0.6734,

0.6734>

4.6249 7

<1.000,

0.0000,

0.0000>

<0.0000,

1.0000,

1.0000>

<0.0000,

1.0000,

1.0000>

<0.0000,

1.0000,

1.0000>

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>


The alternatives rank according to alternative weight in descending order, i.e. highest

alternative weight is considered as first rank, while lowest alternative weight is

considered as last rank; is as shown in Table 3.14. The in descending order ranking is

with alternatives

ranking orders as The rank is calculated with

F-SVNS-N-MADM is as shown in Table 3.14.

(ii) Proposed Method 2: F-SVNS EW-MADM for Supplier Selection

Step 1 to step 7 was is carried out in 3.4 (i)

Step 8. Calculation of the entropy value for attribute

Calculate the attribute value with the Equation (3.6) is as shown in Table 3.15. i.e. consider

calculation of the entropy value for attribute C1.

{ } {

} { } {


81

} { } {

} { }

The same calculation is also is carried out for remaining attributes.


Calculate the attribute value with the Equation (3.7) is as shown in Table 3.15.

i.e. consider calculation of the alternative entropy value for attributes.

*

+

*

+

*

+

*

+

*

+

*

+


82

*

+

Where,

∑

Step 10. Calculation of the entropy weight of alterative

Find the alternative weight by Equation (3.8) is as shown in Table 3.15.

{ }

{ }

{ }

{ }

{ }

{ }

{ }





considered as last rank; is as shown in Table 3.15.

The in descending order ranking is

with alternatives ranking orders as

The rank is calculated with F-SVNS-EW-MADM is as shown in Table 3.15.

TABLE 3.15: F-SVNS EW-MADM Ranking for Industrial Case Example-I

Sr. No.


Rank

A1

<0.2023,

0.7977,

0.7977>

<0.2776,

0.7224,

0.7224>

<0.4009,

0.5991,

0.5991>

<0.0073,

0.9927,

0.9927>

<0.1187,

0.8813,

0.8813>

<0.0585,

0.9415,

0.9415>

<0.0726,

0.9274,

0.9274>

0.8535 4


83

A2

<0.4046,

0.5954,

0.5954>

<0.0267,

0.9733,

0.9733>

<0.1336,

0.8664,

0.8664>

<0.2792,

0.7208,

0.7208>

<0.4154,

0.5846,

0.5846>

<0.2926,

0.7074,

0.7074>

<0.1089,

0.8911,

0.8911>

1.0504 2

A3

<0.3540,

0.6460,

0.9460>

<0.2018,

0.7982,

0.7982>

<0.4009,

0.5991,

0.5991>

<0.5511,

0.4489,

0.4489>

<0.2967,

0.7033,

0.7033>

<0.1170,

0.8830,

0.8830>

<0.2541,

0.7459,

0.7459>

0.7994 6

A4

<0.4046,

0.5954,

0.5954>

<0.0283,

0.9717,

0.9717>

<0.2673,

0.7327,

0.7327>

<0.5879,

0.4121,

0.4121>

<0.2967,

0.7033,

0.7033>

<0.3511,

0.6489,

0.6489>

<0.5081,

0.4919,

0.4919>

0.9837 3

A5

<0.4551,

0.5449,

0.5449>

<0.0458,

0.9542,

0.9542>

<0.2673,

0.7327,

0.7327>

<0.1102,

0.8898,

0.8898>

<0.4747,

0.5253,

0.5253>

<0.5267,

0.4733,

0.4733>

<0.7114,

0.2886,

0.2886>

1.1924 1

A6

<0.3034,

0.6966,

0.6966>

<0.2596,

0.7404,

0.7404>

<0.6682,

0.3318,

0.3318>

<0.2572,

0.7428,

0.7428>

<0.3560,

0.6440,

0.6440>

<0.4682,

0.4733,

0.4733>

<0.2178,

0.7822,

0.7822>

0.8227 5

A7

<0.4551,

0.5449,

0.5449>

<0.9007,

0.0993,

0.0993>

<0.2673,

0.7327,

0.7327>

<0.4409,

0.5591,

0.5591>

<0.5341,

0.4659,

0.4659>

<0.5267,

0.5318,

0.5318>

<0.3266,

0.6734,

0.6734>

0.6226 7

<1.000,

0.0000,

0.0000>

<0.0000,

1.0000,

1.0000>

<0.0000,

1.0000,

1.0000>

<0.0000,

1.0000,

1.0000>

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>

0.7369 0.2683 0.5912 0.5588 0.6926 0.6383 0.5030

0.0874 0.2430 0.1358 0.1465 0.1021 0.1201 0.1651 1.0000

(iii) Proposed Method 3: F-SVNS ACC-MADM for Supplier Selection

Step 1 to step 7 was is carried out in 3.4 (i)

Step 8. Calculation of the Advance Correlation Coefficient function of Alternatives

Calculate the Advance Correlation Coefficient function for each alternative with Equation

(3.9) is as shown in Table 3.16.

W (Aj)

[

{

{ } { } { } { } { } { } { } }

{

(

{ } { } { } { } { } { } { } )

(

)

}

]

W (Aj)


84

The same is calculation is carried out for remaining alternatives.

TABLE 3.16: F-SVNS ACC-MADM Ranking for Industrial Case Example-I

Sr. No.


Rank

A1

<0.2023,

0.7977,

0.7977>

<0.2776,

0.7224,

0.7224>

<0.4009,

0.5991,

0.5991>

<0.0073,

0.9927,

0.9927>

<0.1187,

0.8813,

0.8813>

<0.0585,

0.9415,

0.9415>

<0.0726,

0.9274,

0.9274>

0.5080 4

A2

<0.4046,

0.5954,

0.5954>

<0.0267,

0.9733,

0.9733>

<0.1336,

0.8664,

0.8664>

<0.2792,

0.7208,

0.7208>

<0.4154,

0.5846,

0.5846>

<0.2926,

0.7074,

0.7074>

<0.1089,

0.8911,

0.8911>

0.6342 2

A3

<0.3540,

0.6460,

0.9460>

<0.2018,

0.7982,

0.7982>

<0.4009,

0.5991,

0.5991>

<0.5511,

0.4489,

0.4489>

<0.2967,

0.7033,

0.7033>

<0.1170,

0.8830,

0.8830>

<0.2541,

0.7459,

0.7459>

0.4714 6

A4

<0.4046,

0.5954,

0.5954>

<0.0283,

0.9717,

0.9717>

<0.2673,

0.7327,

0.7327>

<0.5879,

0.4121,

0.4121>

<0.2967,

0.7033,

0.7033>

<0.3511,

0.6489,

0.6489>

<0.5081,

0.4919,

0.4919>

0.5794 3

A5

<0.4551,

0.5449,

0.5449>

<0.0458,

0.9542,

0.9542>

<0.2673,

0.7327,

0.7327>

<0.1102,

0.8898,

0.8898>

<0.4747,

0.5253,

0.5253>

<0.5267,

0.4733,

0.4733>

<0.7114,

0.2886,

0.2886>

0.7321 1

A6

<0.3034,

0.6966,

0.6966>

<0.2596,

0.7404,

0.7404>

<0.6682,

0.3318,

0.3318>

<0.2572,

0.7428,

0.7428>

<0.3560,

0.6440,

0.6440>

<0.4682,

0.4733,

0.4733>

<0.2178,

0.7822,

0.7822>

0.4976 5

A7

<0.4551,

0.5449,

0.5449>

<0.9007,

0.0993,

0.0993>

<0.2673,

0.7327,

0.7327>

<0.4409,

0.5591,

0.5591>

<0.5341,

0.4659,

0.4659>

<0.5267,

0.5318,

0.5318>

<0.3266,

0.6734,

0.6734>

0.4625 7

<1.000,

0.0000,

0.0000>

<0.0000,

1.0000,

1.0000>

<0.0000,

1.0000,

1.0000>

<0.0000,

1.0000,

1.0000>

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>




considered as last rank; is as shown in Table 3.16.



The rank is calculated with F-SVNS-ACC-MADM is as shown in Table 3.16

(iv) Industrial Case Example 1 Result of Ranking Solutions:

The ranking solutions of the proposed methodologies for supplier selection are shown in

Table: 3.17.


85

TABLE 3.17: F-SVNS MADMs Ranking for Industrial Case Example-I

Sr. No. Alternatives F-SVNS-N-MADM F-SVNS-EW-MADM F-SVNS-ACC-MADM

A1 4 4 4

A2 2 2 2

A3 6 6 6

A4 3 3 3

A5 1 1 1

A6 5 5 5

A7 7 7 7

The result shows that the proposed methodologies give likewise solution.

3.4.2 Industrial Case Example 2: Material Provider’s Selection:

Another industrial case example for material provider selection collected from the Forbes

marshal industry, which is leading boiler manufacturer located at Pune, Maharashtra. The

solution is demonstrated step by step using all three methodologies.

Step 1 to Step 7 is similar in proposed methodologies. Step 1 to step 7 is carried out

initially.

Step: 1 The objective of MADM problem is to select/ rank/ evaluate an appropriate

material provider‘s selection for boiler manufacturing industry for Forbes marshal industry

located at Pune.

Step 2. Here seven material providers‘ alternatives are considered with seven

attributes and their attributes measures C1: Weight in Kg, C2: Process time in week, C3:

Price in Rs., C4: Quality in percentage, C5: Safety level, C6: Product capacity in

percentage, C7: Supply continuity capacity. Here, beneficial attributes are C4, C5, C6 and

C7: whereas non-beneficial attributes are C1, C2 and C3.

Step: 3 Decision matrix is collected from the experts of the Forbes Marshal Industry is as


TABLE 3.18: Decision Matrix for F-SVNS MADM for Industrial Case Example-II

Sr. No. Alternatives C1 (-) C2 (-) C3 (-) C4 (+) C5 (+) C6 (+) C7 (+)

A1 12 1.7 1800 93 1.2 71 51

A2 10.7 1.6 1900 91 2 66 30

A3 9.80 2.1 2100 77 2.3 81 35

A4 10.32 2 1500 78 1.7 75 60

A5 9.67 2.4 1950 88 1.8 71 40


86

A6 9.18 3 2500 81 2.2 82 35

A7 9.02 2.08 1900 76 1.91 72 35

Step: 4 Conversion of qualitative data in to quantitative data

All given data are in quantitative information. Hence, step to convert the qualitative data in

to quantitative data.

Step: 5 Normalization of Table 3.18 is carried out with the Equation (3.1)/ Equation

(3.2). Material provider‘s selection normalized matrix is shown in Table 3.19.

TABLE 3.19: Normalized Decision Matrix of F-SVNS MADM for Industrial Case Example-II

Sr. No.

Alternatives C1 (-) C2 (-) C3 (-) C4 (+) C5 (+) C6 (+) C7 (+)

A1 0.5528 0.7038 0.6547 0.4200 0.2383 0.3617 0.4584

A2 0.6013 0.7212 0.6355 0.4110 0.3972 0.3362 0.2697

A3 0.6348 0.6341 0.5971 0.3478 0.4568 0.4126 0.3146

A4 0.6154 0.6516 0.7122 0.3523 0.3377 0.3821 0.5393

A5 0.6397 0.5819 0.6259 0.3974 0.3575 0.3617 0.3596

A6 0.6579 0.4773 0.5204 0.3658 0.4370 0.4177 0.3146

A7 0.6639 0.6376 0.6355 0.3432 0.3794 0.3668 0.3146



falsehood form.

Beneficial attributes i.e. Alternative A1 and attribute C4 with value 0. 4200

converted in SVNS as

⟨ ⟩ ⟨ ⟩. The same

calculation is also carried out for attribute C5, C6, C7.

Non-beneficial attributes i.e. Alternative A1 and attribute C1 is 0.5528 converted in

SVNS gives value⟨ ⟩ ⟨ ⟩.

The same calculation is also carried out for attribute C2 and C3.

Step 6. Find the beneficial attribute ideal solution and non-beneficial attributes ideal

solution.

Beneficial attribute ideal solution and non-beneficial attribute ideal solution is

discovered with Equation (3.3)/ Equation (3.4), where

⟨

⟩ ⟨ ⟩ and

⟨

⟩ ⟨ ⟩.


87

SVNS normalized decision matrix is shown in Table 3.20.

TABLE 3.20: SVNS Normalized Decision Matrix for Industrial Case Example-II

Sr. No.


A1

<0.4472,

0.5528,

0.5528>

<0.2962,

0.7038,

0.7038>

<0.3453,

0.6547,

0.6547>

<0.4200,

0.5800,

0.5800>

<0.2383,

0.7617,

0.7617>

<0.3617,

0.6383,

0.6383>

<0.4584,

0.5416,

0.5416>

A2

<0.3987,

0.6013,

0.6013>

<0.2788,

0.7212,

0.7212>

<0.3645,

0.6355,

0.6355>

<0.4110,

0.5890,

0.5890>

<0.3972,

0.6028,

0.6028>

<0.3362,

0.6638,

0.6638>

<0.2697,

0.7303,

0.7303>

A3

<0.3652,

0.6348,

0.6348>

<0.3659,

0.6341,

0.6341>

<0.4029,

0.5971,

0.5971>

<0.3478,

0.6522,

0.6522>

<0.4568,

0.5432,

0.5432>

<0.4126,

0.5874,

0.5874>

<0.3146,

0.6854,

0.6854>

A4

<0.3846,

0.6154,

0.6154>

<0.3484,

0.6516,

0.6516>

<0.2878,

0.7122,

0.7122>

<0.3523,

0.6477,

0.6477>

<0.3377,

0.6623,

0.6623>

<0.3821,

0.6179,

0.6179>

<0.5393,

0.4607,

0.4607>

A5

<0.3603,

0.6397,

0.6397>

<0.4181,

0.5819,

0.5819>

<0.3741,

0.6259,

0.6259>

<0.3974,

0.6026,

0.6026>

<0.3575,

0.6425,

0.6425>

<0.3617,

0.6383,

0.6383>

<0.3596,

0.6404,

0.6404>

A6

<0.3421,

0.6579,

0.6579>

<0.5227,

0.4773,

0.4773>

<0.4796,

0.5204,

0.5204>

<0.3658,

0.6342,

0.6342>

<0.4370,

0.5630,

0.5630>

<0.4177,

0.5823,

0.5823>

<0.3146,

0.6854,

0.6854>

A7

<0.3361,

0.6639,

0.6639>

<0.3624,

0.6376,

0.6376>

<0.3645,

0.6355,

0.6355>

<0.3432,

0.6568,

0.6568>

<0.3794,

0.6206,

0.6206>

<0.3668,

0.6332,

0.6332>

<0.3146,

0.6854,

0.6854>

<0.0000,

1.0000,

1.0000>

<0.0000,

1.0000,

1.0000>

<0.0000,

1.0000,

1.0000>

<1.0000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>

(i) Proposed Method 1: F-SVNS N-MADM Material Provider’s Selection

Step 1 to step 7 are described earlier in point 3.4 (ii)

Step 7. Calculate the alternative Weight

Calculate the alternative weight with the Equation (3.5) is as shown in Table 3.21. i.e.


} { }

{ } {

} { } {

} { }




88


alternative weight is consider as first rank, while lowest alternative weight is

consider as last rank; is as shown in Table 3.21. .The in descending order ranking is

with alternatives

ranking orders as .The rank is calculated with F-

SVNS-N-MADM is as shown in Table 3.21

TABLE 3.21: F-SVNS N-MADM Ranking for Industrial Case Example-II

Sr. No.


Rank

A1

<0.4472,

0.5528,

0.5528>

<0.2962,

0.7038,

0.7038>

<0.3453,

0.6547,

0.6547>

<0.4200,

0.5800,

0.5800>

<0.2383,

0.7617,

0.7617>

<0.3617,

0.6383,

0.6383>

<0.4584,

0.5416,

0.5416>

5.3012 3

A2

<0.3987,

0.6013,

0.6013>

<0.2788,

0.7212,

0.7212>

<0.3645,

0.6355,

0.6355>

<0.4110,

0.5890,

0.5890>

<0.3972,

0.6028,

0.6028>

<0.3362,

0.6638,

0.6638>

<0.2697,

0.7303,

0.7303>

5.3302 2

A3

<0.3652,

0.6348,

0.6348>

<0.3659,

0.6341,

0.6341>

<0.4029,

0.5971,

0.5971>

<0.3478,

0.6522,

0.6522>

<0.4568,

0.5432,

0.5432>

<0.4126,

0.5874,

0.5874>

<0.3146,

0.6854,

0.6854>

5.2641 5

A4

<0.3846,

0.6154,

0.6154>

<0.3484,

0.6516,

0.6516>

<0.2878,

0.7122,

0.7122>

<0.3523,

0.6477,

0.6477>

<0.3377,

0.6623,

0.6623>

<0.3821,

0.6179,

0.6179>

<0.5393,

0.4607,

0.4607>

5.5698 1

A5

<0.3603,

0.6397,

0.6397>

<0.4181,

0.5819,

0.5819>

<0.3741,

0.6259,

0.6259>

<0.3974,

0.6026,

0.6026>

<0.3575,

0.6425,

0.6425>

<0.3617,

0.6383,

0.6383>

<0.3596,

0.6404,

0.6404>

5.1711 6

A6

<0.3421,

0.6579,

0.6579>

<0.5227,

0.4773,

0.4773>

<0.4796,

0.5204,

0.5204>

<0.3658,

0.6342,

0.6342>

<0.4370,

0.5630,

0.5630>

<0.4177,

0.5823,

0.5823>

<0.3146,

0.6854,

0.6854>

4.8465 7

A7

<0.3361,

0.6639,

0.6639>

<0.3624,

0.6376,

0.6376>

<0.3645,

0.6355,

0.6355>

<0.3432,

0.6568,

0.6568>

<0.3794,

0.6206,

0.6206>

<0.3668,

0.6332,

0.6332>

<0.3146,

0.6854,

0.6854>

5.2781 4

<0.0000,

1.0000,

1.0000>

<0.0000,

1.0000,

1.0000>

<0.0000,

1.0000,

1.0000>

<1.0000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>

(ii) Proposed Method 2: F-SVNS EW-MADM Material Supplier Selection

Step 1 to Step 7 was is carried out in 3.4 (ii)

Step 8. Calculation of the entropy value for attribute

Calculate the attribute (criteria) entropy value with the Equation (3.6). i.e. consider

calculation of the entropy value for attribute C1.


89

{ } {

} { } {

} { } {

} { }

The same calculation is also is carried out for remaining attributes is as shown in Table

3.22.


Calculate the attribute value with the Equation (3.7)is as shown in Table 3.22.

i.e. consider calculation of the alternative entropy value for attribute C1.

*

+

0.1368

*

+

0.

*

+

*

+

*

+

*

+


90

*

+

Where,

∑

Step 10. Calculation of the entropy weight of alterative

Find the alternative weight by Equation (3.8) is as shown in Table 3.22

{ }

{ }

{ }

{ }

{ }

{ }

{ }





consider as last rank; is as shown in Table 3.22.



The rank is calculated with F-SVNS-EW-MADM is as shown in Table 3.22

TABLE 3.22: F-SVNS EW-MADM Ranking for Industrial Case Example-II

Sr. No.

Alternatives C1 (-) C2 (-) C3 (-) C4 (+) C5 (+) C6 (+) C7 (+) Rank

A1

<0.4472,

0.5528,

0.5528>

<0.2962,

0.7038,

0.7038>

<0.3453,

0.6547,

0.6547>

<0.4200,

0.5800,

0.5800>

<0.2383,

0.7617,

0.7617>

<0.3617,

0.6383,

0.6383>

<0.4584,

0.5416,

0.5416>

0.7589 3


91

A2

<0.3987,

0.6013,

0.6013>

<0.2788,

0.7212,

0.7212>

<0.3645,

0.6355,

0.6355>

<0.4110,

0.5890,

0.5890>

<0.3972,

0.6028,

0.6028>

<0.3362,

0.6638,

0.6638>

<0.2697,

0.7303,

0.7303>

0.7598 2

A3

<0.3652,

0.6348,

0.6348>

<0.3659,

0.6341,

0.6341>

<0.4029,

0.5971,

0.5971>

<0.3478,

0.6522,

0.6522>

<0.4568,

0.5432,

0.5432>

<0.4126,

0.5874,

0.5874>

<0.3146,

0.6854,

0.6854>

0.7495 5

A4

<0.3846,

0.6154,

0.6154>

<0.3484,

0.6516,

0.6516>

<0.2878,

0.7122,

0.7122>

<0.3523,

0.6477,

0.6477>

<0.3377,

0.6623,

0.6623>

<0.3821,

0.6179,

0.6179>

<0.5393,

0.4607,

0.4607>

0.7968 1

A5

<0.3603,

0.6397,

0.6397>

<0.4181,

0.5819,

0.5819>

<0.3741,

0.6259,

0.6259>

<0.3974,

0.6026,

0.6026>

<0.3575,

0.6425,

0.6425>

<0.3617,

0.6383,

0.6383>

<0.3596,

0.6404,

0.6404>

0.7360 6

A6

<0.3421,

0.6579,

0.6579>

<0.5227,

0.4773,

0.4773>

<0.4796,

0.5204,

0.5204>

<0.3658,

0.6342,

0.6342>

<0.4370,

0.5630,

0.5630>

<0.4177,

0.5823,

0.5823>

<0.3146,

0.6854,

0.6854>

0.6875 7

A7

<0.3361,

0.6639,

0.6639>

<0.3624,

0.6376,

0.6376>

<0.3645,

0.6355,

0.6355>

<0.3432,

0.6568,

0.6568>

<0.3794,

0.6206,

0.6206>

<0.3668,

0.6332,

0.6332>

<0.3146,

0.6854,

0.6854>

0.7513 4

<1.000,

0.0000,

0.0000>

<0.0000,

1.0000,

1.0000>

<0.0000,

1.0000,

1.0000>

<0.0000,

1.0000,

1.0000>

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>

0.7526 0.7277 0.7482 0.7536 0.7440 0.7540 0.7120

0.1368 0.1506 0.1393 0.1363 0.1416 0.1361 0.1593 1.0000

(iii)Proposed Method 3: F-SVNS ACC-MADM for Material Provider’s Selection

Step 1 to step 7 was is carried out in 3.4 (ii)

Step 8. Calculation of the Advance Correlation Coefficient function of alternatives

Find the advance correlation coefficient function for each alternative with Equation (3.9) is

as shown in Table 3.23.

W (Aj)

[

{

{ } { } { } { } { } { } { } }

{

(

{ } { } { } { } { } { } { } )

(

)

}

]

W (Aj)


92

The same calculation is also is carried out for remaining alternatives is as shown in Table

3.23.




consider as last rank; is as shown in Table 3.23.



The rank is calculated with F-SVNS-ACC-MADM is as shown in Table 3.23.

TABLE 3.23 F-SVNS ACC-MADM Ranking for Industrial Case example-II

Sr. No.


Rank

A1

<0.4472,

0.5528,

0.5528>

<0.2962,

0.7038,

0.7038>

<0.3453,

0.6547,

0.6547>

<0.4200,

0.5800,

0.5800>

<0.2383,

0.7617,

0.7617>

<0.3617,

0.6383,

0.6383>

<0.4584,

0.5416,

0.5416>

0.5301 3

A2

<0.3987,

0.6013,

0.6013>

<0.2788,

0.7212,

0.7212>

<0.3645,

0.6355,

0.6355>

<0.4110,

0.5890,

0.5890>

<0.3972,

0.6028,

0.6028>

<0.3362,

0.6638,

0.6638>

<0.2697,

0.7303,

0.7303>

0.5330 2

A3

<0.3652,

0.6348,

0.6348>

<0.3659,

0.6341,

0.6341>

<0.4029,

0.5971,

0.5971>

<0.3478,

0.6522,

0.6522>

<0.4568,

0.5432,

0.5432>

<0.4126,

0.5874,

0.5874>

<0.3146,

0.6854,

0.6854>

0.5264 5

A4

<0.3846,

0.6154,

0.6154>

<0.3484,

0.6516,

0.6516>

<0.2878,

0.7122,

0.7122>

<0.3523,

0.6477,

0.6477>

<0.3377,

0.6623,

0.6623>

<0.3821,

0.6179,

0.6179>

<0.5393,

0.4607,

0.4607>

0.5570 1

A5

<0.3603,

0.6397,

0.6397>

<0.4181,

0.5819,

0.5819>

<0.3741,

0.6259,

0.6259>

<0.3974,

0.6026,

0.6026>

<0.3575,

0.6425,

0.6425>

<0.3617,

0.6383,

0.6383>

<0.3596,

0.6404,

0.6404>

0.5171 6

A6

<0.3421,

0.6579,

0.6579>

<0.5227,

0.4773,

0.4773>

<0.4796,

0.5204,

0.5204>

<0.3658,

0.6342,

0.6342>

<0.4370,

0.5630,

0.5630>

<0.4177,

0.5823,

0.5823>

<0.3146,

0.6854,

0.6854>

0.4846 7

A7

<0.3361,

0.6639,

0.6639>

<0.3624,

0.6376,

0.6376>

<0.3645,

0.6355,

0.6355>

<0.3432,

0.6568,

0.6568>

<0.3794,

0.6206,

0.6206>

<0.3668,

0.6332,

0.6332>

<0.3146,

0.6854,

0.6854>

0.5278 4

<1.000,

0.0000,

0.0000>

<0.0000,

1.0000,

1.0000>

<0.0000,

1.0000,

1.0000>

<0.0000,

1.0000,

1.0000>

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>

(iv) Industrial Case Example 1 Result of Ranking Solutions:

The ranking solutions of the proposed methodologies for material provider‘s selection are

shown in Table: 3.24.


93

TABLE 3.24: –F-SVNS MADMs Ranking for Industrial Case Example-II

Sr. No. Alternatives F-SVNS-N-MADM F-SVNS-EW-MADM F-SVNS-ACC-MADM

A1 3 3 3

A2 2 2 2

A3 5 5 5

A4 1 1 1

A5 6 6 6

A6 7 7 7

A7 4 4 4

The result shows that the proposed methodologies give likewise solution. The comparative

ranking solution proves the relative accuracy in result of proposed methodologies. These

methodologies prove their best ranking solution. For further research in the next chapter

work is carried out to check the accuracy by implementing proposed methodologies in

eleven domains through random case example, which are collected in each domain from

peer reviewed journal/ book. Random eleven domains are identified where, best selection

process one of the keys to improve performance of manufacturing and supply chain. The

names of random domains which are related to manufacturing and supply chain multi

criteria decision making are as under.






o Robot selection





o Third Party Reverse Logistics Providers (TPRLP) selection.

94

Chapter 4: Implementation and Validation


95

CHAPTER: 4

Implementation and Validation

In this chapter, the proposed methods are initially implemented and validated with some

published random case examples collected form the literature and solved by the proposed

methodologies; validation is carried out by comparing the result obtained by proposed

MADM with published result. These initial row data are collected from the literature for

manufacturing and supply chain environment to validate the proposed methodologies

realistically. Some important area of selection which leads to improve performance in

manufacturing and supply chain functions are listed as Table 4.1.

TABLE 4.1: Collected Random Samples from the Peer Reviewed Journal/ Book

Sr.

No Name of Selection Reference

Publisher of Journal/

Book

Citation as on

14.01.2018

1. Material Selection (Maniya and Bhatt 2010) Science direct 119

(Rao 2008b) Elsevier 149

2. Machine Tool Selection (Paramasivam et al. 2011) Springer 29

3. Rapid Prototyping

Selection

(Byun and Lee 2005) Springer 183

(Rao 2007) Springer Book 562

(Rao and Padmanabhan 2007) T & F 13

4. NTMP Selection (Rao 2007) Springer Book 562

5. AGV Selection (Maniya and Bhatt 2011a) Elsevier 47


6. Robot Selection

(Khouja and Booth 1991) Wiley Online Library 20

(Karsak et al. 2012), T & F 18

(Parkan and Wu 1999) Elsevier 223

(David et al. 1992) Emerald insight 37

(Dilip Kumar et al. 2015) Emerald insight 16

7 Metal Stamping Layout

Selection

(Singh and Sekhon 1996) Elsevier 22


(Das and Srinivas 2013) Elsevier 56

8 ECM Program

Selection

(Sarkis 1999) Elsevier 199


(Rao 2008c) Sage 49

9 Cutting Fluid (Coolant)

Selection (Rao 2007) Springer Book 562

10 Supplier Selection

(Liu et al. 2000) Emerald Insight 544

(Ng 2008) Elsevier 396

(Kuo et al. 2008) Elsevier 548


11

Third Party Reverse

Logistic Provider‘s

Selection

(Kannan et al. 2009) Elsevier 325

4.1 Collected Case Example 1: Material Selection

96

The ranking is carried out to identify the best alternative. Here, the main reference of

comparison is the final selection of best alternative which is ranked on the first position by

proposed methods and existing published result.


Step 1. The goal of with the help of F-SVNS N-MADM Material Selection is to solve

the collected case example of material selection considered to demonstrate the PSI method

(Maniya and Bhatt 2010). The same case example illustrated by (Rao 2008b) using

compromise ranking method.

Step 2. Here five material alternatives are considered with four attributes and their

attributes measures are C1: tensile strength in MPa, C2: Young‘s modulus in GPA, C3:

Density in gm/cm3 and C4: corrosion resistance. Here, beneficial attributes are C1 and C2:

whereas non-beneficial attributes are C3 and C4.

Step 3. Decision matrix was collected from (Maniya and Bhatt 2010), (Rao 2008b) is


TABLE 4.2: Material Selection Input Matrix (Collected Case Example)

Material Alternatives

(Sr. No.) C1 (+) C2 (+) C3 (-) C4 (+)

A1 1650 58.5 2.3 Average

A2 1000 45.4 2.1 Low

A3 350 21.7 2.6 Low

A4 2150 64.3 2.4 Average

A5 700 23 1.71 Above Average

Collected from Source: (Maniya and Bhatt 2010), (Rao 2008b)


Qualitative information to quantitative value conversion is carried out for Attribute C4

with the help of Table 3.2. Table 4.3 shows the conversion of qualitative linguistic data in

to crisp numbers.

TABLE 4.3: Material Selection Converted Input Matrix (Qualitative to Quantitative form)

Material Alternatives

(Sr. No.) C1 (+) C2 (+) C3 (-) C4 (+)

A1 1650 58.5 2.3 0.5

A2 1000 45.4 2.1 0.335

A3 350 21.7 2.6 0.335

A4 2150 64.3 2.4 0.5

A5 700 23 1.71 0.59


97

Step 5. Normalization is carried out with the Equation (3.1)/ Equation (3.2). Material

selection normalized matrix is shown in Table 4.4.

TABLE 4.4: Material Selection Normalized Matrix using VNM

Material Alternatives C1 (+) C2 (+) C3 (-) C4 (+)

A1 0.5513 0.5677 0.5413 0.4828

A2 0.3341 0.4406 0.5812 0.3235

A3 0.1169 0.2106 0.4815 0.3235

A4 0.7184 0.6240 0.5214 0.4828

A5 0.2339 0.2232 0.6590 0.5697



falsehood form.

Beneficial attributes i.e. Alternative A1 and attribute C1 is having value 0. 5513



C2 and C4.

Non-beneficial attributes i.e. Alternative A1 and attribute C3 having value


⟨ ⟩.


solution.



⟩

⟨ ⟩ and ⟨

⟩ ⟨ ⟩.

4.1.1 Proposed Method 1: F-SVNS N-MADM for Material Selection

Step 1 to step 7 are described earlier in point 4.1.

The calculations of step 8 and step 9 are shown briefly in the Annexure A[1]. The rank is

calculated with F-SVNS-N-MADM is as shown in Table 4.5.


98

TABLE 4.5: F-SVNS N-MADM Ranking for Material Selection

Alternative

Sr. No. C1 (+) C2 (+) C3 (-) C4 (+) Rank

A1

<0.5513,

0.4487,

0.4487>

<0.5677,

0.4323,

0.4323>

<0.4587,

0.5413,

0.5413>

<0.4828,

0.5172,

0. 5172>

2.6845 2

A2

<0.3341,

0.6659,

0.6659>

<0.4406,

0.5594,

0.5594>

<0.4188,

0.5812,

0. 5812>

<0.3235,

0.6765,

0. 6765>

2.2606 4

A3

<0.1169,

0.8831,

0.8831>

<0.2106,

0.7894,

0.7894>

<0.5185,

0.4815,

0. 4815>

<0.3235,

0.6765,

0. 6765>

1.6140 5

A4

<0.7184,

0.2816,

0.2816>

<0.6240,

0.3760,

0.3760>

<0.4786,

0.5214,

0.5214>

<0.4828,

0.5172,

0.5172>

2.8679 1

A5

<0.2339,

0.7661,

0.7661>

<0.2232,

0.7768,

0.7768>

<0.3410,

0.6590,

0.6590>

<0.5697,

0.4303,

0.4303>

2.3448 3

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>

<0.0000,

1.0000,

1.0000>

<1.000,

0.0000,

0.0000>

4.1.2 Proposed Method 2: F-SVNS EW-MADM for Material Selection


The calculations of step 8 to step 11 are shown briefly in the Annexure-B [1]. The rank is

calculated with F-SVNS-EW-MADM is as shown in Table 4.6

TABLE 4.6: F-SVNS EW-MADM Ranking for Material Selection

Sr. No. C1 (+) C2 (+) C3 (-) C4 (+) Rank

A1

<0.5513,

0.4487,

0.4487>

<0.5677,

0.4323,

0.4323>

<0.4587,

0.5413,

0.5413>

<0.4828,

0.5172,

0. 5172>

0.6083 2

A2

<0.3341,

0.6659,

0.6659>

<0.4406,

0.5594,

0.5594>

<0.4188,

0.5812,

0. 5812>

<0.3235,

0.6765,

0. 6765>

0.4641 3

A3

<0.1169,

0.8831,

0.8831>

<0.2106,

0.7894,

0.7894>

<0.5185,

0.4815,

0. 4815>

<0.3235,

0.6765,

0. 6765>

0.2822 5

A4

<0.7184,

0.2816,

0.2816>

<0.6240,

0.3760,

0.3760>

<0.4786,

0.5214,

0.5214>

<0.4828,

0.5172,

0.5172>

0.6883 1

A5

<0.2339,

0.7661,

0.7661>

<0.2232,

0.7768,

0.7768>

<0.3410,

0.6590,

0.6590>

<0.5697,

0.4303,

0.4303>

0.4179 4

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>

<0.0000,

1.0000,

1.0000>

<1.000,

0.0000,

0.0000>

0.5661 0.6731 0.8714 0.8171

0.4047 0.3049 0.1199 0.1705 1.0000


99

4.1.3 Proposed Method 3: F-SVNS ACC-MADM for Material Selection


The calculations of step 8 and step 9 are shown briefly in the Annexure-C[1]. The rank is


TABLE: 4.7 F-SVNS ACC-MADM Ranking for Material Selection

Sr. No. C1 (+) C2 (+) C3 (-) C4 (+) Rank

A1

<0.5513,

0.4487,

0.4487>

<0.5677,

0.4323,

0.4323>

<0.4587,

0.5413,

0.5413>

<0.4828,

0.5172,

0. 5172>

0.5369 2

A2

<0.3341,

0.6659,

0.6659>

<0.4406,

0.5594,

0.5594>

<0.4188,

0.5812,

0. 5812>

<0.3235,

0.6765,

0. 6765>

0.4521 4

A3

<0.1169,

0.8831,

0.8831>

<0.2106,

0.7894,

0.7894>

<0.5185,

0.4815,

0. 4815>

<0.3235,

0.6765,

0. 6765>

0.3228 5

A4

<0.7184,

0.2816,

0.2816>

<0.6240,

0.3760,

0.3760>

<0.4786,

0.5214,

0.5214>

<0.4828,

0.5172,

0.5172>

0.5736 1

A5

<0.2339,

0.7661,

0.7661>

<0.2232,

0.7768,

0.7768>

<0.3410,

0.6590,

0.6590>

<0.5697,

0.4303,

0.4303>

0.4690 3

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>

<0.0000,

1.0000,

1.0000>

<1.000,

0.0000,

0.0000>

4.1.4 Performance Measures Comparison: Material Ranking

The result of the three proposed methodologies is compared with the published results to

validate the proposed methods for material selection. To compare the result, all material

alternatives are ranked according to alternatives weight values is as shown in Table 4.8.

The material alternatives are ranked first whose alternative weight value is highest;

material alternative is ranked second whose alternatives weight values is second highest.

Finally the ranking orders obtained by the proposed three different methodologies are

compared with the ranking order published in the literature and result comparisons are

shown in Table 4.8.


100

TABLE 4.8: Material Selection Performance Measures Comparison

Alternatives

F-SVNS MADMs

PSI* # Improved Compromise

Ranking Method (CRM) Novel Entropy

Weight ACC

A1 2 2 2 2 2

A2 4 3 4 4 4

A3 5 5 5 5 5

A4 1 1 1 1 1

A5 3 4 3 3 3

Ranking Solution Collected from Source *(Maniya and Bhatt 2010)

, # (Rao 2008b)

The result comparisons presented in Table 4.8 shows that the results obtained from

the proposed methodologies almost match with the result reported in the literature. All

methods suggested alternative A4 and alternative A1 as the first and second optimal choice

of material selection respectively. While all methods show that alternative A3 is the

poorest choice in the ranking solution. (Rao 2008b) used improved Compromise ranking

method (CRM) for solving material selection problem. Alternative A4 as the first choice

and alternative A1 as second choice with calculating attribute weight by using AHP

method to assign relative importance between attributes. For a given material selection

problem the same ranking was suggested by (Maniya and Bhatt 2010) using PSI

methodology. PSI methods flow though the calculations like preference variation value,

deviation variation value, overall variation value and then preference value of alternatives

to be found for ranking of alternative. By considering first ranking solution, the proposed

methodologies also work with minimum calculations, not need to resize the assignment

matrix and it is gifted to convert simple set or lingustic set to F-SVNS.

In this chapter explained that comparison is carried out only with the first rank.

Coincidently in this case example the second and last rank is matched with published result

so it is explained for similarity. Further, 4th

rank is calculated by F-SVNS N-MADM and

F-SVNS ACC-MADM matched with published results. While F- SVNS EW-MADM 4th

Rank shows for alternative A5 which is not match with published result. It shows that, the

weight criteria make change in rank position, but it hold well for the first ranking purpose.

Further, First ranking similarity of proposed MADMs is briefly discussed in point 4.12.

Two methodologies (i) F-SVNS N-MADM and (ii) F-SVNS ACC-MADM , work without

calculating attribute weight among three proposed methodology, Whereas F-SVNS EW-

MADM works with calculating attribute weight. With comparison with other published

results show that proposed methods prove the validity, applicability and reliability for the


101

material selection for manufacturing environment which leads to improve manufacturing

function.

4.2 Collected Case Example 2: Machine Tool Selection

Step 1. The case example of milling machine selection was solved initially by

(Dagdeviren 2008) using PROMETHEE, AHP, TOPSIS and ELECTRE methodologies.

The same case example solved by (Paramasivam et al. 2011). The problem was solved by

them with GTMA, AHP and Analytic Network Process (ANP) methods.

Step 2. The attributes are C1: Prices with unit Dollar, C2: Weight with unit Kg, C3:

Power with unit Watt, C4: Spindle Speed with unit rpm, C5: diameter with unit mm and

C6: stroke with unit mm. Here beneficial attributes are C3, C4, C5 and C6. Whereas Non-

beneficial attributes are C1 and C2.

Step 3. Decision matrix was collected from (Paramasivam et al. 2011) is as shown in

Table 4.9.

TABLE 4.9: Machine Tool Selection Input Matrix (Collected Case Example)

Alternatives

(Sr. No.) C1 (-) C2 (-) C3 (+) C4 (+) C5 (+) C6 (+)

A1 936 4.8 1300 24000 12.7 58

A2 1265 6 2000 21000 12.7 65

A3 680 3.5 900 24000 8 50

A4 650 5.2 1600 22000 12 62

A5 580 3.5 1050 25000 12 62

Collected from the source (Paramasivam et al. 2011), (Dağdeviren 2008)

Step: 4 Conversion of qualitative data in to quantitative data:

Here, the input information contains quantitative information only, so there is no need to

convert qualitative value in to quantitative value. So, this step is eliminated in the current

case example.

Step: 5 Normalization of Table 4.9 is carried out with the Equation 3.1/ Equation

3.2. Machine selection normalized matrix is shown in Table 4.10.

TABLE 4.10: Machine Tool Selection Normalized Matrix using VNM

Sr. No. C1 (-) C2 (-) C3 (+) C4 (+) C5 (+) C6 (+)

A1 0.5132 0.54354 0.4078 0.4617 0.4890 0.4350

A2 0.3421 0.4294 0.6274 0.4040 0.4890 0.4875

A3 0.6464 0.6672 0.2823 0.4617 0.3080 0.3750

A4 0.6620 0.5055 0.5019 0.4232 0.4620 0.4650

A5 0.6984 0.6672 0.3294 0.4809 0.46202 0.4650


102



falsehood form.




C2.

Beneficial attributes i.e. Alternative A1 and attribute C3 having value 0. 4078



C4, C5, C6.


solution.



⟩

⟨ ⟩ and ⟨

⟩ ⟨ ⟩.

4.2.1 Proposed Method 1: F-SVNS N-MADM for Machine Tool Selection


The calculations of step 8 and step 9 are shown briefly in the Annexure A [2]. The rank is

calculated with F-SVNS-N-MADM is as shown in Table 4.11

TABLE 4.11: F-SVNS N-MADM Ranking for Machine Tool Selection

Sr. No. C1 (-) C2 (-) C3 (+) C4 (+) C5 (+) C6 (+) Rank

A1

<0.4868,

0.5132,

0.5132>

<0.4565,

0.5435,

0. 5435>

<0.4078,

0.5922,

0.5922>

<0.4617,

0.5383,

0. 5383>

<0.4890,

0.5110,

0.5110>

<0.4350,

0.5650,

0.5650>

3.9071 4

A2

<0.6579,

0.3421,

0.3421>

<0.5706,

0.4294,

0.4294>

<0.6274,

0.3726,

0. 3726>

<0.4040,

0.5960,

0.5960>

<0.4890,

0.5110,

0.5110>

<0.4875,

0.5125,

0.5125>

3.5510 5

A3

<0.3536,

0.6464,

0.6464>

<0.3328,

0.6672,

0.6672>

<0.2823,

0.7177,

0. 7177>

<0.4617,

0.5383,

0.5383>

<0.3080,

0.6920,

0.6920>

<0.3750,

0.6250,

0.6250>

4.0541 3

A4

<0.3380,

0.6620,

0.6620>

<0.4945,

0.5055,

0.5055>

<0.5019,

0.4981,

0.4981>

<0.4232,

0.5768,

0.5768>

<0.4620,

0.5380,

0.5380>

<0.4650,

0.5350,

0.5350>

4.1871 2

A5

<0.3016,

0.6984,

0.6984>

<0.3328,

0.6672,

0.6672>

<0.3294,

0.6706,

0.6706>

<0.4809,

0.5191,

0.5191>

<0.4620,

0.5380,

0.5380>

<0.4650,

0.5350,

0.5350>

4.4684 1


103

<0.0000,

1.0000,

1.0000>

<0.0000,

1.0000,

1.0000>

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>

4.2.2 Proposed Method 2: F-SVNS EW-MADM for Machine Tool Selection


The calculations of step 8 and step 9 are shown briefly in the Annexure –B[2]. The rank is


TABLE 4.12: F-SVNS EW-MADM Ranking for Machine Tool Selection

Sr. No. C1 (-) C2 (-) C3 (+) C4 (+) C5 (+) C6 (+) Rank

A1

<0.4868,

0.5132,

0.5132>

<0.4565,

0.5435,

0. 5435>

<0.4078,

0.5922,

0.5922>

<0.4617,

0.5383,

0. 5383>

<0.4890,

0.5110,

0.5110>

<0.4350,

0.5650,

0.5650>

0.7083 4

A2

<0.6579,

0.3421,

0.3421>

<0.5706,

0.4294,

0.4294>

<0.6274,

0.3726,

0. 3726>

<0.4040,

0.5960,

0.5960>

<0.4890,

0.5110,

0.5110>

<0.4875,

0.5125,

0.5125>

0.6295 5

A3

<0.3536,

0.6464,

0.6464>

<0.3328,

0.6672,

0.6672>

<0.2823,

0.7177,

0. 7177>

<0.4617,

0.5383,

0.5383>

<0.3080,

0.6920,

0.6920>

<0.3750,

0.6250,

0.6250>

0.7656 3

A4

<0.3380,

0.6620,

0.6620>

<0.4945,

0.5055,

0.5055>

<0.5019,

0.4981,

0.4981>

<0.4232,

0.5768,

0.5768>

<0.4620,

0.5380,

0.5380>

<0.4650,

0.5350,

0.5350>

0.7917 2

A5

<0.3016,

0.6984,

0.6984>

<0.3328,

0.6672,

0.6672>

<0.3294,

0.6706,

0.6706>

<0.4809,

0.5191,

0.5191>

<0.4620,

0.5380,

0.5380>

<0.4650,

0.5350,

0.5350>

0.8331 1

<0.0000,

1.0000,

1.0000>

<0.0000,

1.0000,

1.0000>

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>

0.7289 0.8184 0.7561 0.8926 0.8840 0.8910

0.2635 0.1765 0.2371 0.1043 0.1127 0.1059 1.0000

4.2.3 Proposed Method 3: F-SVNS ACC-MADM for Machine Tool Selection

Step 1 to step 7 are described earlier in point 4.2

The calculations of step 8 to step 11 are shown briefly in the Annexure –C[2]. The rank is


TABLE 4.13: F-SVNS ACC-MADM Ranking for Machine Tool Selection

Sr. No. C1 (-) C2 (-) C3 (+) C4 (+) C5 (+) C6 (+) Rank

A1

<0.4868,

0.5132,

0.5132>

<0.4565,

0.5435,

0. 5435>

<0.4078,

0.5922,

0.5922>

<0.4617,

0.5383,

0. 5383>

<0.4890,

0.5110,

0.5110>

<0.4350,

0.5650,

0.5650>

0.4884 4

A2 <0.6579, <0.5706, <0.6274, <0.4040, <0.4890, <0.4875, 0.4439 5


104

0.3421,

0.3421>

0.4294,

0.4294>

0.3726,

0. 3726>

0.5960,

0.5960>

0.5110,

0.5110>

0.5125,

0.5125>

A3

<0.3536,

0.6464,

0.6464>

<0.3328,

0.6672,

0.6672>

<0.2823,

0.7177,

0. 7177>

<0.4617,

0.5383,

0.5383>

<0.3080,

0.6920,

0.6920>

<0.3750,

0.6250,

0.6250>

0.5068 3

A4

<0.3380,

0.6620,

0.6620>

<0.4945,

0.5055,

0.5055>

<0.5019,

0.4981,

0.4981>

<0.4232,

0.5768,

0.5768>

<0.4620,

0.5380,

0.5380>

<0.4650,

0.5350,

0.5350>

0.5234 2

A5

<0.3016,

0.6984,

0.6984>

<0.3328,

0.6672,

0.6672>

<0.3294,

0.6706,

0.6706>

<0.4809,

0.5191,

0.5191>

<0.4620,

0.5380,

0.5380>

<0.4650,

0.5350,

0.5350>

0.5586 1

<0.0000,

1.0000,

1.0000>

<0.0000,

1.0000,

1.0000>

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>

4.2.4 Performance Measures Comparison: Machine Tool Ranking

The result of proposed three methodologies is compared with the published results to

validate them for machine tool selection. To compare the results, all machine tool

alternatives are ranked according to alternatives weight values is as shown in Table 4.14.

The machine tool alternative is ranked first whose alternative weight value is highest;

machine tool alternative is ranked second whose alternatives weight values is second

highest. Finally the ranking order obtained by the proposed three different methodologies

is compared with the ranking order published in the literature and result comparisons are


TABLE 4.14: Machine Tool Selection Performance Measures Comparison

Alternatives

(Reno.)

F-SVNS MADMs

PSI@

AHP@

PROMETHEE* TOPSIS

* ELECTRE

* GTMA

#

Novel Entropy

Weight ACC

A1 4 4 4 4 2 4 3 2 4

A2 5 5 5 3 5 3 5 5 5

A3 3 3 3 5 4 5 2 4 2

A4 2 2 2 2 3 2 4 3 3

A5 1 1 1 1 1 1 1 1 1

[*Source of ranking result (Dagdeviren 2008), # source of ranking result from (Paramasivam et al. 2011),

@

source of ranking result from (Maniya 2012)]

The result comparisons presented in Table 4.14 shows that the result obtained from

the proposed methodologies are quite similar to the result reported in the literature. All

methods suggested alternative A5 as the first and best choice of machine also.

(Dagdeviren 2008) applied AHP, PROMETHEE, TOPSIS and ELECTRE method

and recommended alternative A5 is optimal choice (Dagdeviren 2008) suggested machine

tool alternative 2 is the last choice using AHP, PROMETHEE, TOPSIS and ELECTRE.


105

Ranking result of AHP with (Maniya 2012), result shows that first rank is similar with all

other methods. (Dagdeviren 2008) proved that PROMETHEE in conjunction with AHP

method is more appropriate for selection of machine tool for the given machine tool

selection problem. Furthermore, (Maniya 2012) also recommended the machine tool

alternative A5 as most suitable for the choice using PSI methodology. (Paramasivam et al.

2011) suggested alternative A5 as most suitable by GTMA, while AHP method suggests

A2 as the best choice. Through the comparison with the input matrix information between

the A2 and alternative A5, one can easily identify that the best alternative option is only

with A5. Proposed methodologies works with minimum calculations, without calculating

any kind of relative importance of attributes, not need to resize the assignment matrix and

it is gifted to convert simple set or lingustic set to F-SVNS.

Further, 2nd

rank is calculated by all proposed methods matched with PSI, PROMETHEE

results. While other MADM like AHP, TOPSIS, ELECTRE and GTMA published result

of 2nd

Rank their selves not match among each other, due to different weight criteria

calculation/ assumption/ expert opinion. While 4th

Rank is calculated by proposed

methods matched with PSI, PROMETHEE and GTMA While other MADM like AHP,

TOPSIS and ELECTRE published result of 4th

Rank their selves not match among each

other, due to different weight criteria calculation/ assumption/ expert opinion. It shows that

the weight criteria make change in rank position in further ranking result, but it hold well

for the first ranking purpose. Further, First ranking similarity of proposed MADMs is

briefly discussed in point 4.12.

In addition, individual weaknesses of PROMETHEE, TOPSIS, ELECTRE, GTMA, AHP

and PSI are already described in chapter 2.

Two methodologies (i) F-SVNS N-MADM and (ii) F-SVNS ACC-MADM , work

without calculating attribute weight among three proposed methodology, Whereas F-

SVNS EW-MADM works with calculating attribute weight. With comparison with other

published results show that proposed methods prove the validity, applicability and

reliability for the machine tool selection for manufacturing environment which leads to

improve manufacturing function.

4.3 Collected Case Example 3: Rapid Prototype Program Selection

106


Step 1. One case example of Rapid prototype program selection for industrial

application was demonstrated by (Byun and Lee 2005) with modified TOPSIS

methodology. Table 4.15 gives the quantitative information on how each rapid prototype

(alternatives) is expected to perform with respective process parameters (attributes). The

same case example was further calculated by (Rao 2007), (Rao 2008a) with GTMA, SAW,

WPM, AHP, TOPSIS and modified TOPSIS

Step 2. The matrix consists of six rapid prototype systems as alternatives and six

attributes measures are C1: accuracy, C2: surface roughness, C3: tensile strength, C4:

elongation, C5: cost of part and C6: build time. Here, the published input data shows that

beneficial attributes are C3 and C4, whereas Non-beneficial attributes are C1, C2, C5 and

C6. Actually accuracy of rapid prototype must be considered as positive attribute but, for

comparison with other published ranking and as per assumption from section 1.6 with 2nd

point, data collected from the source is not changed.

Step 3. Decision matrix was collected from (Byun and Lee 2005), (Rao 2007) is as

shown in Table 4.15

TABLE 4.15: Rapid Prototype Selection Input Matrix (Collected Case Example)

Sr. No. Alternative C1 (-) C2 (-) C3 (+) C4 (+) C5 (-) C6 (-)

A1 120 6.5 65 5 0.745 0.5

A2 150 12.5 40 8.5 0.745 0.5

A3 125 21 30 10 0.665 0.745

A4 185 20 25 10 0.59 0.41

A5 95 3.5 30 6 0.745 0.41

A6 600 15.5 5 1 0.135 0.255

Collected from Source: (Byun and Lee 2005), (Rao 2007) , (Rao and Padmanabhan 2007)




case example.

Step 5. Normalization of Table 4.15 is carried out with the Equation 3.1/ Equation 3.2.

Rapid prototype selection normalized matrix is shown in Table 4.16

TABLE 4.16: Rapid Prototype Selection Normalized Matrix using VNM

Sr. No. C1 (-) C2 (-) C3 (+) C4 (+) C5 (-) C6 (-)

A1 0.8223 0.8192 0.7145 0.2735 0.5263 0.5857

A2 0.7778 0.6522 0.4397 0.4649 0.5263 0.5857


107

A3 0.8148 0.4158 0.3298 0.5470 0.5772 0.3826

A4 0.7260 0.4436 0.2748 0.5470 0.6249 0.6602

A5 0.8593 0.9026 0.3298 0.3282 0.5263 0.6602

A6 0.1113 0.5688 0.0550 0.0547 0.9142 0.7887



falsehood form.




C2, C5 and C6.

Beneficial attributes i.e. Alternative A1 and attribute C3 having value 0. 7145


⟨ ⟩. The same calculation is also carried out for attribute

C4.


solution.



⟩

⟨ ⟩ and ⟨

⟩ ⟨ ⟩.

4.3.1 Proposed Method 1: F-SVNS N-MADM for Rapid Prototype Selection




TABLE 4.17: F-SVNS N-MADM Ranking for Rapid Prototype Selection

Sr. No. C1 (-) C2 (-) C3 (+) C4 (+) C5 (-) C6 (-) Rank

A1

<0.1777,

0.8223,

0.8223>

<0.1808,

0.8192,

0.8192>

<0.7145,

0.2855,

0.2855>

<0.2735,

0.7265,

0.7265>

<0.4737,

0.5263,

0.5263>

<0.4143,

0.5857,

0.5857>

6.4948 2

A2

<0.2222,

0.7778,

0.7778>

<0.3478,

0.6522,

0.6522>

<0.4397,

0.5603,

0. 5603>

<0.4649,

0.5351,

0.5351>

<0.4737,

0.5263,

0.5263>

<0.4143,

0.5857,

0.5857>

5.9887 3

A3

<0.1852,

0.8148,

0.8148>

<0.5842,

0.4158,

0.4158>

<0.3298,

0.6702,

0. 6702>

<0.5470,

0.4530,

0.4530>

<0.4228,

0.5772,

0.5772>

<0.6174,

0.3826,

0.3826>

5.2576 5


108

A4

<0.2740,

0.7260,

0.7260>

<0.5564,

0.4436,

0.4436>

<0.2748,

0.7252,

0.7252>

<0.5470,

0.4530,

0.4530>

<0.3751,

0.6249,

0.6249>

<0.3398,

0.6602,

0.6602>

5.7311 4

A5

<0.1407,

0.8593,

0.8593>

<0.0974,

0.9026,

0.9026>

<0.3298,

0.6702,

0.6702>

<0.3282,

0.6718,

0.6718>

<0.4737,

0.5263,

0.5263>

<0.3398,

0.6602,

0.6602>

6.5549 1

A6

<0.8887,

0.1113,

0.1113>

<0.4312,

0.5688,

0.5688>

<0.0550,

0.9450,

0.9450>

<0.0547,

0.9453,

0.9453>

<0.0858,

0.9142,

0.9142>

<0.2113,

0.7887,

0.7887>

4.8754 6

<0.0000,

1.0000,

1.0000>

<0.0000,

1.0000,

1.0000>

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>

<0.0000,

1.0000,

1.0000>

<0.0000,

1.0000,

1.0000>

4.3.2 Proposed Method 2: F-SVNS-EW-MADM for Rapid Prototype Selection


The calculations of step 8 to step 11 are shown briefly in the Annexure -B [3]. The rank is


TABLE 4.18: F-SVNS-EW-MADM Ranking for Rapid Prototype Selection

Sr. No. C1 (-) C2 (-) C3 (+) C4 (+) C5 (-) C6 (-) Rank

A1

<0.1777,

0.8223,

0.8223>

<0.1808,

0.8192,

0.8192>

<0.7145,

0.2855,

0.2855>

<0.2735,

0.7265,

0.7265>

<0.4737,

0.5263,

0.5263>

<0.4143,

0.5857,

0.5857>

1.1503 2

A2

<0.2222,

0.7778,

0.7778>

<0.3478,

0.6522,

0.6522>

<0.4397,

0.5603,

0. 5603>

<0.4649,

0.5351,

0.5351>

<0.4737,

0.5263,

0.5263>

<0.4143,

0.5857,

0.5857>

1.0482 3

A3

<0.1852,

0.8148,

0.8148>

<0.5842,

0.4158,

0.4158>

<0.3298,

0.6702,

0. 6702>

<0.5470,

0.4530,

0.4530>

<0.4228,

0.5772,

0.5772>

<0.6174,

0.3826,

0.3826>

0.9416 5

A4

<0.2740,

0.7260,

0.7260>

<0.5564,

0.4436,

0.4436>

<0.2748,

0.7252,

0.7252>

<0.5470,

0.4530,

0.4530>

<0.3751,

0.6249,

0.6249>

<0.3398,

0.6602,

0.6602>

0.9736 4

A5

<0.1407,

0.8593,

0.8593>

<0.0974,

0.9026,

0.9026>

<0.3298,

0.6702,

0.6702>

<0.3282,

0.6718,

0.6718>

<0.4737,

0.5263,

0.5263>

<0.3398,

0.6602,

0.6602>

1.1523 1

A6

<0.8887,

0.1113,

0.1113>

<0.4312,

0.5688,

0.5688>

<0.0550,

0.9450,

0.9450>

<0.0547,

0.9453,

0.9453>

<0.0858,

0.9142,

0.9142>

<0.2113,

0.7887,

0.7887>

0.6542 6

<0.0000,

1.0000,

1.0000>

<0.0000,

1.0000,

1.0000>

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>

<0.0000,

1.0000,

1.0000>

<0.0000,

1.0000,

1.0000>

0.3704 0.6388 0.5715 0.6758 0.7683 0.7007

0.2768 0.1588 0.1884 0.1425 0.1019 0.1316 1

4.3.3 Proposed Method 3: F-SVNS-ACC-MADM for Rapid Prototype Selection



109

The calculations of step 8 to step 11 are shown briefly in the Annexure -C [3]. The rank is

calculated with F-SVNS-EW-MADM is as shown in Table 4.19.

TABLE 4.19: F-SVNS ACC-MADM Ranking for Rapid Prototype Selection

Sr.

No. C1 (-) C2 (-) C3 (+) C4 (+) C5 (-) C6 (-) Rank

A1

<0.1777,

0.8223,

0.8223>

<0.1808,

0.8192,

0.8192>

<0.7145,

0.2855,

0.2855>

<0.2735,

0.7265,

0.7265>

<0.4737,

0.5263,

0.5263>

<0.4143,

0.5857,

0.5857>

0.6495 2

A2

<0.2222,

0.7778,

0.7778>

<0.3478,

0.6522,

0.6522>

<0.4397,

0.5603,

0. 5603>

<0.4649,

0.5351,

0.5351>

<0.4737,

0.5263,

0.5263>

<0.4143,

0.5857,

0.5857>

0.5989 3

A3

<0.1852,

0.8148,

0.8148>

<0.5842,

0.4158,

0.4158>

<0.3298,

0.6702,

0. 6702>

<0.5470,

0.4530,

0.4530>

<0.4228,

0.5772,

0.5772>

<0.6174,

0.3826,

0.3826>

0.5258 5

A4

<0.2740,

0.7260,

0.7260>

<0.5564,

0.4436,

0.4436>

<0.2748,

0.7252,

0.7252>

<0.5470,

0.4530,

0.4530>

<0.3751,

0.6249,

0.6249>

<0.3398,

0.6602,

0.6602>

0.5731 4

A5

<0.1407,

0.8593,

0.8593>

<0.0974,

0.9026,

0.9026>

<0.3298,

0.6702,

0.6702>

<0.3282,

0.6718,

0.6718>

<0.4737,

0.5263,

0.5263>

<0.3398,

0.6602,

0.6602>

0.6555 1

A6

<0.8887,

0.1113,

0.1113>

<0.4312,

0.5688,

0.5688>

<0.0550,

0.9450,

0.9450>

<0.0547,

0.9453,

0.9453>

<0.0858,

0.9142,

0.9142>

<0.2113,

0.7887,

0.7887>

0.4875 6

<0.0000,1.0

000,

1.0000>

<0.0000,1.

0000,

1.0000>

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>

<0.0000,1

.0000,

1.0000>

<0.0000,1

.0000,

1.0000>

4.3.4 Performance Measures Comparison: Rapid Prototype Ranking


validate the proposed methods for rapid prototype selection. To compare the result, all

rapid prototype alternatives are ranked according to alternatives weight values is as shown

in Table 4.20. The rapid prototype alternatives are ranked first whose alternative weight

value is highest; rapid prototype alternative is ranked second whose alternatives weight

values is second highest. Finally the ranking order obtained by the proposed three different

methodologies are compared with the ranking order published in the literature and result

comparisons are shown in Table 4.20

TABLE 4.20: Rapid Prototype Selection Performance Measures Comparison

Alternatives

(Sr. No.)

F-SVNS MADMs Collected from the source (Rao 2007)

Novel Entropy

Weight ACC GTMA SAW WPM AHP TOPSIS

Modified

TOPSIS VIKOR

A1 2 2 2 2 2 2 2 1 1 2

A2 3 3 3 3 3 3 3 3 3 3

A3 5 5 5 5 4 4 4 4 4 5


110

A4 4 4 4 4 5 5 5 5 5 4

A5 1 1 1 1 1 1 1 2 2 1

A6 6 6 6 6 6 6 6 6 6 6

The result comparisons presented in Table 4.20 shows that results obtained from the

proposed methodologies are relatively similar to the results reported in the literature. The

same rapid prototype problem was solved by (Rao 2007) using GTMA, SAW, WPM, AHP

and VIKOR methodologies. All the methods give the same 1st choice which is alternative

A5 except TOPSIS and modified TOPSIS methodology. These methodologies considered

attribute weight and depend upon decision maker to identify attribute weight, which leads

to change ranking solution.

Further, 2nd

rank is calculated by all proposed methods matched with all published results

except TOPSIS and Modified TOPSIS methodologies due to their different weight criteria

calculation. While 4th

rank is calculated by proposed methods matched with VIKOR and

GTMA While other MADM like SAW, AHP, TOPSIS and modified TOPSIS

methodologies published result of 4th

Rank match among each other with minor ranking

change 5th

rank due to different weight criteria calculation/ assumption/ expert opinion.

The 6th

ranking is calculated by the proposed methods shows that alternative A6 match

with published results. It shows that the weight criteria make change in rank position in

further ranking result, but it hold well for the first ranking purpose. Further, First ranking

similarity of proposed MADMs is briefly discussed in point 4.12.

Proposed methodologies work with minimum calculations and without calculating relative

importance of attributes, there is no need to resize the assignment matrix and it is gifted to

convert simple set or lingustic set to F-SVNS. In addition, weakness of the GTMA, SAW,

WPM, AHP, TOPSIS, Modified TOPSIS and VIKOR methods are described in Chapter 2.





reliability for the rapid prototyping selection for manufacturing environment which leads

to improve manufacturing function.


111

4.4 Collected Case Example 4: Non-Traditional Machining Processes

(NTMP) Selection

Step 1. Non-traditional machining processes ranking calculations were adopted and

illustrated with GTMA, TOPSIS and modified TOPSIS by (Rao 2007). (Maniya 2012) was

adopted same example and solved it with PSI methodology. This same case example was

adopted and demonstrated by (Roy et al. 2014) with AHP and TOPSIS hybrid

methodology in automotive industries for nontraditional machining processes was carried

out.

Step 2. Here four non-traditional machining processes four alternatives with six

attributes and their attributes measures are C1: surface finish in μm, C2: surface damage in

μm, C3: taper material in mm/mm and C4: material removal rate in mm3/mm, C5: work

material (WM) here units assigned on a scale of 1, 2 and 3 where 1 for poor, 2 for medium

and 3 for good application, C6: Cost (c) also scale of 1 to 9, here 1shows low, 5 medium

and 9 very high. Here, beneficial attributes are C4, C5; whereas Non-beneficial attributes

are C1, C2, C3 and C6.

Step 3. Decision matrix collected from (Rao 2007) is shown in Table 4.21

TABLE 4.21: NTMP Selection Input Matrix (Collected Case Example)

Sr. No. Alternatives C1 (-) C2 (-) C3 (-) C4 (+) C5 (+) C6 (-)

A1 0.5 25 0.005 500 2 5

A2 2 20 0.001 800 3 7

A3 3 100 0.02 2 2 1

A4 1 100 0.05 2 2 1

Collected from the Source: (Rao 2007) , (Maniya 2012)




case example.


NTMP selection normalized matrix is shown in Table 4.22

TABLE 4.22: NTMP Selection Normalized Matrix using VNM

Sr. No. C1 (-) C2 (-) C3 (-) C4 (+) C5 (+) C6 (-)

A1 0.8675 0.8276 0.9076 0.5300 0.4364 0.4265

A2 0.4702 0.8621 0.9815 0.8480 0.6547 0.1970

4.4 Collected Case Example 4: Non-Traditional Machining Processes (NTMP) Selection

112

A3 0.2053 0.3103 0.6303 0.0021 0.4364 0.8853

A4 0.7351 0.3103 0.0757 0.0021 0.4364 0.8853



falsehood form.




C2, C3 and C6.

Beneficial attributes i.e. Alternative A1 and attribute C4 having value 0.5300



C5.


solution.



⟩

⟨ ⟩ and ⟨

⟩ ⟨ ⟩.

4.4.1 Proposed Method 1: F-SVNS N-MADM for NTMP Selection




TABLE 4.23: F-SVNS N-MADM Ranking of NTMP Selection

Sr. No. C1 (-) C2 (-) C3 (-) C4 (+) C5 (+) C6 (-) Rank

A1

<0.1325,

0.8675,

0.8675>

<0.1724,

0.8276,

0.8276>

<0.0924,

0.9076,

0.9076>

<0.5300,

0.4700,

0.4700>

<0.4364,

0.5636,

0.5636>

<0.5735,

0.4265,

0.4265>

7.0248 1

A2

<0.5298,

0.4702,

0.4702>

<0.1379,

0.8621,

0.8621>

<0.0185,

0.9815,

0. 9815>

<0.8480,

0.1520,

0.1520>

<0.6547,

0.3453,

0.3453>

<0.8030,

0.1970,

0.1970>

6.5243 2

A3

<0.7947,

0.2053,

0.2053>

<0.6897,

0.3103,

0.3103>

<0.3697,

0.6303,

0. 6303>

<0.0021,

0.9979,

0.9979>

<0.4364,

0.5636,

0.5636>

<0.1147,

0.8853,

0.8853>

4.5009 3

A4 <0.2649,

0.7351,

<0.6897,

0.3103,

<0.9243,

0.0757,

<0.0021,

0.9979,

<0.4364,

0.5636,

<0.1147,

0.8853, 4.4513 4


113

0.7351> 0.3103> 0.0757> 0.9979> 0.5636> 0.8853>

<0.0000,1.

0000,

1.0000>

<0.0000,1.

0000,

1.0000>

<0.0000,1.

0000,

1.0000>

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>

<0.0000,1.

0000,

1.0000>

4.4.2 Proposed Method 2: F-SVNS-EW-MADM for NTMP Selection




TABLE 4.24: F-SVNS EW-MADM Ranking for NTMP Selection

Sr. No. C1 (-) C2 (-) C3 (-) C4 (+) C5 (+) C6 (-) Rank

A1

<0.1325,

0.8675,

0.8675>

<0.1724,

0.8276,

0.8276>

<0.0924,

0.9076,

0.9076>

<0.5300,

0.4700,

0.4700>

<0.4364,

0.5636,

0.5636>

<0.5735,

0.4265,

0.4265>

1.2644 1

A2

<0.5298,

0.4702,

0.4702>

<0.1379,

0.8621,

0.8621>

<0.0185,

0.9815,

0. 9815>

<0.8480,

0.1520,

0.1520>

<0.6547,

0.3453,

0.3453>

<0.8030,

0.1970,

0.1970>

1.1755 2

A3

<0.7947,

0.2053,

0.2053>

<0.6897,

0.3103,

0.3103>

<0.3697,

0.6303,

0. 6303>

<0.0021,

0.9979,

0.9979>

<0.4364,

0.5636,

0.5636>

<0.1147,

0.8853,

0.8853>

0.8398 3

A4

<0.2649,

0.7351,

0.7351>

<0.6897,

0.3103,

0.3103>

<0.9243,

0.0757,

0.0757>

<0.0021,

0.9979,

0.9979>

<0.4364,

0.5636,

0.5636>

<0.1147,

0.8853,

0.8853>

0.7387 4

<0.0000,

1.0000,

1.0000>

<0.0000,

1.0000,

1.0000>

<0.0000,

1.0000,

1.0000>

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>

<0.0000,

1.0000,

1.0000>

0.5364 0.4655 0.2782 0.5113 0.7225 0.4265

0.1515 0.1747 0.2359 0.1597 0.0907 0.1874 1

4.4.3 Proposed method: 3 F-SVNS-ACC-MADM for NTMP Selection


The calculations of step 8 and step 9 are shown briefly in the Annexure -C [4]. The rank is

calculated with F-SVNS-ACC-MADM is as shown in Table 4.25

TABLE 4.25: F-SVNS ACC-MADM Ranking for NTMP Selection

Sr.

No. C1 (-) C2 (-) C3 (-) C4 (+) C5 (+) C6 (-) Rank

A1

<0.1325,

0.8675,

0.8675>

<0.1724,

0.8276,

0.8276>

<0.0924,

0.9076,

0.9076>

<0.5300,

0.4700,

0.4700>

<0.4364,

0.5636,

0.5636>

<0.5735,

0.4265,

0.4265>

0.7025 1

4.4 Collected Case Example 4: Non-Traditional Machining Processes (NTMP) Selection

114

A2

<0.5298,

0.4702,

0.4702>

<0.1379,

0.8621,

0.8621>

<0.0185,

0.9815,

0. 9815>

<0.8480,

0.1520,

0.1520>

<0.6547,

0.3453,

0.3453>

<0.8030,

0.1970,

0.1970>

0.6524 2

A3

<0.7947,

0.2053,

0.2053>

<0.6897,

0.3103,

0.3103>

<0.3697,

0.6303,

0. 6303>

<0.0021,

0.9979,

0.9979>

<0.4364,

0.5636,

0.5636>

<0.1147,

0.8853,

0.8853>

0.4501 3

A4

<0.2649,

0.7351,

0.7351>

<0.6897,

0.3103,

0.3103>

<0.9243,

0.0757,

0.0757>

<0.0021,

0.9979,

0.9979>

<0.4364,

0.5636,

0.5636>

<0.1147,

0.8853,

0.8853>

0.4451 4

<0.0000,

1.0000,

1.0000>

<0.0000,

1.0000,

1.0000>

<0.0000,

1.0000,

1.0000>

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>

<0.0000,

1.0000,

1.0000>

4.4.4 Performance Measures Comparison: NTMP Ranking

The results of proposed three methodologies are compared with the published results to

validate them for NTMP selection. To compare the result, all NTMP‘s alternatives are

ranked according to alternatives weight values is as shown in Table 4.26. The NTMP

alternatives are ranked first whose alternative weight value is highest; NTMP alternative is

ranked second whose alternatives weight values is second highest. Finally the ranking

orders obtained by the proposed three different methodologies are compared with the

ranking order published in the literature and result comparisons are shown in Table 4.26.

TABLE 4.26: NTMP Selection Performance Measures Comparison

Alternatives

(Sr. No.)

F-SVNS MADMs

GTMA* TOPSIS* Modified

TOPSIS* Novel Entropy

Weight ACC

A1 1 1 1 2 2 1

A2 2 2 2 1 1 2

A3 3 3 3 4 3 3

A4 4 4 4 3 4 4

* Source of ranking result from (Rao 2007), (Maniya 2012)

The result comparisons presented in Table 4.26 shows that the results obtained from the

proposed methodologies are quite similar to the result of reported in the literature. The

same NTMP problem was initially solved by (Rao 2007) using GTMA which shows that

the alternative A2 is the first choice by calculating digraph approach. (Rao 2007) also

solved the same problem using TOPSIS with calculated attribute weight using AHP

methodology and obtained the 2nd

alternative A2 as first choice.

From the comparison with the published result shows that proposed methods gives the

similar ranking solution with Modified TOPSIS methodology. While, in GTMA and

TOPSIS methods published 1st, 2

nd rank and 3

rd, 4

th ranks are changed due to different

weight criteria calculation/ assumption/ expert opinion. Further, First ranking similarity of


115

proposed MADMs is briefly discussed in point 4.12. The same problem was solved by

(Rao 2007) using modified TOPSIS methodology with positive and negative ideal solution

and identified weighted Euclidean distance and relative closeness of particular alternatives

and obtained find the 1st alternatives A1 as the first choice. Proposed methodologies work

with minimum calculations and without calculating any kind of relative weight of

attributes. There is no need to resize the assignment matrix and it is gifted to convert

simple set or lingustic set to F-SVNS.





reliability for the NTMP selection for manufacturing environment which leads to improve

manufacturing function.

4.5 Collected Case Example 5: Automated Guided Vehicle (AGV)

Selection

Step 1. The case example is taken from (Maniya and Bhatt 2011a), who have considered

8 different AGV‘s as alternatives, while 6 attributes for decision criteria.

Step 2. (Maniya and Bhatt 2011a) was presented an illustrative problem for evaluation

and ranking of AGV using PSI methodology, (Maniya and Bhatt 2011a) have considered 8

different AGV‘s as alternatives, while 6 attributes for decision criteria. The attributes are

C1: controllability, C2: accuracy, C3: cost, C4: range, C5: reliability and C6: flexibility.

Here, beneficial attributes are C1, C2, C4, C5, C6; whereas Non-beneficial attribute is C3.

Step 3. Decision matrix was collected from In (Kahraman and Otay 2019); (Nirmal and

Bhatt 2019), (Maniya and Bhatt 2011a) is as shown in Table 4.27.

TABLE 4.27: AGV Selection Input Matrix (Collected Case Example)

Alternatives (Sr. No.) C1 (+) C2 (+) C3 (-) C4 (+) C5 (+) C6 (+)

A1 0.895 0.495 0.695 0.495 0.895 0.295

A2 0.115 0.895 0.895 0.895 0.495 0.495

A3 0.115 0.115 0.895 0.115 0.695 0.895

A4 0.295 0.895 0.115 0.495 0.495 0.895

A5 0.895 0.495 0.115 0.695 0.295 0.495

A6 0.495 0.495 0.895 0.115 0.695 0.695

A7 0.115 0.295 0.895 0.115 0.895 0.895

A8 0.115 0.495 0.695 0.495 0.495 0.695

4.5 Collected Case Example 5: Automated Guided Vehicle (AGV) Selection

116

Collected from Source collected from (Maniya and Bhatt 2011a), (Smarandache and Pramanik 2016),

(Nirmal and Bhatt 2016a), (Nirmal and Bhatt 2019),(Kahraman and Otay 2019)


As per (Kahraman and Otay 2019); (Nirmal and Bhatt 2019) Here, the input information

contains quantitative information only, so there is no need to convert qualitative value into

quantitative value. So, this step is eliminated in the current case example.


AGV selection normalized matrix is shown in Table 4.28

TABLE 4.28: AGV Selection Normalized Matrix using VNM

Sr. No. C1 (+) C2 (+) C3 (-) C4 (+) C5 (+) C6 (+)

A1 0.6349 0.3022 0.6607 0.3450 0.4861 0.1485

A2 0.0816 0.5465 0.5631 0.6238 0.2688 0.2492

A3 0.0816 0.0702 0.5631 0.0801 0.3775 0.4505

A4 0.2093 0.5465 0.9439 0.3450 0.2688 0.4505

A5 0.6349 0.3022 0.9439 0.4844 0.1602 0.2492

A6 0.3512 0.3022 0.5631 0.0801 0.3775 0.3499

A7 0.0816 0.1801 0.5631 0.0801 0.4861 0.4505

A8 0.0816 0.3022 0.6607 0.3450 0.2688 0.3499

Collected from Source (Smarandache and Pramanik 2016), (Nirmal and Bhatt 2016a), (Nirmal and Bhatt

2019), (Kahraman and Otay 2019)

Step 6. As per (Nirmal and Bhatt 2019),(Kahraman and Otay 2019), Convert crisp

normalized matrix into SVNS decision matrix: Crisp data is converted in SVNS

degree of truthness, indeterminate and falsehood form.

As per (Nirmal and Bhatt 2019),(Kahraman and Otay 2019), Beneficial attributes

i.e. Alternative A1 and attribute C1 having value 0.6349 converted in SVNS gives

the value ⟨ ⟩ ⟨ ⟩. The

same calculation is also is carried out for attributes C2, C4, C5, C6 for each

alternative.

As per (Nirmal and Bhatt 2019),(Kahraman and Otay 2019), Non-beneficial

attributes i.e. Alternative A1 and attribute C3 having value converted in

SVNS gives the value

⟨ ⟩ ⟨ ⟩.


solution.


117



⟩

⟨ ⟩ and ⟨

⟩ ⟨ ⟩.

4.5.1 Proposed Method 1: F-SVNS N-MADM for AGV Selection




TABLE 4.29: F-SVNS N-MADM Ranking for AGV Selection

Sr. No. C1 (+) C2 (+) C3 (-) C4 (+) C5 (+) C6 (+) Rank

A1

<0.6349,

0.3651,

0.3651>

<0.3022,

0.6978,

0.6978>

<0.3393,

0.6607,

0.6607>

<0.3450,

0.6550,

0.6550>

<0.4861,

0.5139,

0.5139>

<0.1485,

0.8515,

0.8515>

3.2382 3

A2

<0.0816,

0.9184,

0.9184>

<0.5465,

0.4535,

0.4535>

<0.4369,

0.5631,

0. 5631>

<0.6238,

0.3762,

0.3762>

<0.2688,

0.7312,

0.7312>

<0.2492,

0.7508,

0.7508>

2.8960 4

A3

<0.0816,

0.9184,

0.9184>

<0.0702,

0.9298,

0.9298>

<0.4369,

0.5631,

0. 5631>

<0.0801,

0.9199,

0.9199>

<0.3775,

0.6225,

0.6225>

<0.4505,

0.5495,

0.5495>

2.1862 8

A4

<0.2093,

0.7907,

0.7907>

<0.5465,

0.4535,

0.4535>

<0.0561,

0.9439,

0.9439>

<0.3450,

0.6550,

0.6550>

<0.2688,

0.7312,

0.7312>

<0.4505,

0.5495,

0.5495>

3.7078 2

A5

<0.6349,

0.3651,

0.3651>

<0.3022,

0.6978,

0.6978>

<0.0561,

0.9439,

0.9439>

<0.4844,

0.5156,

0.5156>

<0.1602,

0.8398,

0.8398>

<0.2492,

0.7508,

0.7508>

3.7187 1

A6

<0.3512,

0.6488,

0.6488>

<0.3022,

0.6978,

0.6978>

<0.4369,

0.5631,

0.5631>

<0.0801,

0.9199,

0.9199>

<0.3775,

0.6225,

0.6225>

<0.3499,

0.6501,

0.6501>

2.5871 6

A7

<0.0816,

0.9184,

0.9184>

<0.1801,

0.8199,

0.8199>

<0.4369,

0.5631,

0.5631>

<0.0801,

0.9199,

0.9199>

<0.4861,

0.5139,

0.5139>

<0.4505,

0.5495,

0.5495>

2.4047 7

A8

<0.0816,

0.9184,

0.9184 >

<0.3022,

0.6978,

0.6978>

<0.3393,

0.6607,

0.6607>

<0.3450,

0.6550,

0.6550>

<0.2688,

0.7312,

0.7312>

<0.3499,

0.6501,

0.6501>

2.6690 5

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>

<0.0000,

1.0000,

1.0000>

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>

4.5.2 Proposed Method 2: F-SVNS-EW-MADM for AGV Selection



118



TABLE 4.30: F-SVNS EW-MADM Ranking for AGV Selection

Sr. No. C1 (+) C2 (+) C3 (-) C4 (+) C5 (+) C6 (+) Rank

A1

<0.6349,

0.3651,

0.3651>

<0.3022,

0.6978,

0.6978>

<0.3393,

0.6607,

0.6607>

<0.3450,

0.6550,

0.6550>

<0.4861,

0.5139,

0.5139>

<0.1485,

0.8515,

0.8515>

0.5437 3

A2

<0.0816,

0.9184,

0.9184>

<0.5465,

0.4535,

0.4535>

<0.4369,

0.5631,

0. 5631>

<0.6238,

0.3762,

0.3762>

<0.2688,

0.7312,

0.7312>

<0.2492,

0.7508,

0.7508>

0.4594 4

A3

<0.0816,

0.9184,

0.9184>

<0.0702,

0.9298,

0.9298>

<0.4369,

0.5631,

0. 5631>

<0.0801,

0.9199,

0.9199>

<0.3775,

0.6225,

0.6225>

<0.4505,

0.5495,

0.5495>

0.3200 8

A4

<0.2093,

0.7907,

0.7907>

<0.5465,

0.4535,

0.4535>

<0.0561,

0.9439,

0.9439>

<0.3450,

0.6550,

0.6550>

<0.2688,

0.7312,

0.7312>

<0.4505,

0.5495,

0.5495>

0.5760 2

A5

<0.6349,

0.3651,

0.3651>

<0.3022,

0.6978,

0.6978>

<0.0561,

0.9439,

0.9439>

<0.4844,

0.5156,

0.5156>

<0.1602,

0.8398,

0.8398>

<0.2492,

0.7508,

0.7508>

0.6233 1

A6

<0.3512,

0.6488,

0.6488>

<0.3022,

0.6978,

0.6978>

<0.4369,

0.5631,

0.5631>

<0.0801,

0.9199,

0.9199>

<0.3775,

0.6225,

0.6225>

<0.3499,

0.6501,

0.6501>

0.4095 5

A7

<0.0816,

0.9184,

0.9184>

<0.1801,

0.8199,

0.8199>

<0.4369,

0.5631,

0.5631>

<0.0801,

0.9199,

0.9199>

<0.4861,

0.5139,

0.5139>

<0.4505,

0.5495,

0.5495>

0.3523 7

A8

<0.0816,

0.9184,

0.9184 >

<0.3022,

0.6978,

0.6978>

<0.3393,

0.6607,

0.6607>

<0.3450,

0.6550,

0.6550>

<0.2688,

0.7312,

0.7312>

<0.3499,

0.6501,

0.6501>

0.4090 6

<1.0000,

0.0000,

0.0000>

<1.0000,

0.0000,

0.0000>

<0.0000,

1.0000,

1.0000>

<1.0000,

0.0000,

0.0000>

<1.0000,

0.0000,

0.0000>

<1.0000,

0.0000,

0.0000>

0.4042 0.5916 0.6346 0.5340 0.6735 0.6746

0.2395 0.1642 0.1469 0.1873 0.1313 0.1308 ∑ =1

4.5.3 Proposed method: 3 F-SVNS-ACC-MADM for AGV Selection


The calculations of step 8 and step 9 are shown briefly in the Annexure –C[5]. The rank is


TABLE 4.31: F-SVNS ACC-MADM Ranking for AGV Selection

Sr. No. C1 (+) C2 (+) C3 (-) C4 (+) C5 (+) C6 (+) Rank

A1

<0.6349,

0.3651,

0.3651>

<0.3022,

0.6978,

0.6978>

<0.3393,

0.6607,

0.6607>

<0.3450,

0.6550,

0.6550>

<0.4861,

0.5139,

0.5139>

<0.1485,

0.8515,

0.8515>

0.4626 3

A2 <0.0816,

0.9184,

<0.5465,

0.4535,

<0.4369,

0.5631,

<0.6238,

0.3762,

<0.2688,

0.7312,

<0.2492,

0.7508, 0.4137 4


119

0.9184> 0.4535> 0. 5631> 0.3762> 0.7312> 0.7508>

A3

<0.0816,

0.9184,

0.9184>

<0.0702,

0.9298,

0.9298>

<0.4369,

0.5631,

0. 5631>

<0.0801,

0.9199,

0.9199>

<0.3775,

0.6225,

0.6225>

<0.4505,

0.5495,

0.5495>

0.3123 8

A4

<0.2093,

0.7907,

0.7907>

<0.5465,

0.4535,

0.4535>

<0.0561,

0.9439,

0.9439>

<0.3450,

0.6550,

0.6550>

<0.2688,

0.7312,

0.7312>

<0.4505,

0.5495,

0.5495>

0.5297 2

A5

<0.6349,

0.3651,

0.3651>

<0.3022,

0.6978,

0.6978>

<0.0561,

0.9439,

0.9439>

<0.4844,

0.5156,

0.5156>

<0.1602,

0.8398,

0.8398>

<0.2492,

0.7508,

0.7508>

0.5312 1

A6

<0.3512,

0.6488,

0.6488>

<0.3022,

0.6978,

0.6978>

<0.4369,

0.5631,

0.5631>

<0.0801,

0.9199,

0.9199>

<0.3775,

0.6225,

0.6225>

<0.3499,

0.6501,

0.6501>

0.3696 6

A7

<0.0816,

0.9184,

0.9184>

<0.1801,

0.8199,

0.8199>

<0.4369,

0.5631,

0.5631>

<0.0801,

0.9199,

0.9199>

<0.4861,

0.5139,

0.5139>

<0.4505,

0.5495,

0.5495>

0.3435 7

A8

<0.0816,

0.9184,

0.9184 >

<0.3022,

0.6978,

0.6978>

<0.3393,

0.6607,

0.6607>

<0.3450,

0.6550,

0.6550>

<0.2688,

0.7312,

0.7312>

<0.3499,

0.6501,

0.6501>

0.3813 5

<1.0000,

0.0000,

0.0000>

<1.0000,

0.0000,

0.0000>

<0.0000,

1.0000,

1.0000>

<1.0000,

0.0000,

0.0000>

<1.0000,

0.0000,

0.0000>

<1.0000,

0.0000,

0.0000>

4.5.4 Performance Measures Comparison: AGV Ranking


validate them for AGV selection. To compare the result, all AGV alternatives are ranked

according to alternatives weight values is as shown in Table 4.32. The AGV alternatives

are ranked first whose alternative weight value is highest; AGV alternative is ranked

second whose alternatives weight values is second highest. Finally the ranking order

obtained by the proposed three different methodologies is compared with the ranking order

published in the literature and result comparisons are shown in Table 4.32

TABLE 4.32: AGV Selection Performance Measures Comparison

Alternatives

(Sr. No.)

F-SVNS MADMs (Maniya and Bhatt 2011a), As per (Nirmal

and Bhatt 2019),(Kahraman and Otay 2019)

Novel Entropy

Weight ACC

AHP/M-

GRA AHP/GRA AHP/TOPSIS

A1 3 3 3 4 5 3

A2 4 4 4 6 7 5

A3 8 8 8 8 8 7

A4 2 2 2 3 3 4

A5 1 1 1 1 4 1

A6 6 5 6 2 1 2

A7 7 7 7 7 6 6

A8 5 6 5 5 2 8

The result comparisons presented in Table 4.32 shows that the result obtained from the

proposed methodologies are quite similar to the result reported in the literature. While


120

comparison with other MADM methodology it is really tough to find which method gives

better and more accurate solution.

After calculation by PSI method, result shows that the A7 is on second highest rank

while as per novel approach gives result alternative A4 on the first rank. Now to find better

and accurate solution, the data from input matrix can be referred. Here, alternative A4 and

A7 are compared and result shows A4 with four criteria among six give better solution

than A7. It automatically proves that A4 is better solution than A7. Again in PSI method,

results show that A5 is on 6th rank which is quite far away from accurate solution.

(Maniya and Bhatt 2011a) proves that their methodology AHP/M-GRA gives better

solution than AHP/ GRA and AHP/ TOPSIS. For comparison, with proposed

methodologies only AHP/ M-GRA method is considered. In AHP/M- GRA result shows

A5 is the best solution, while proposed MADM gives best solution as A4. Proposed

MADMs the alternatives A4 and A5 are compared among six criteria. From the input

matrix shows that alternative A4 is better than A5, which shows that these methods give

more accurate result. . The same comparisons among AHP/M-GRA and other MADM

proposed methodology for ranking shows investigated methodology gives better solution

with no need to find attribute weight.

Further, 2nd

and 4th

rank is calculated by all proposed methods are not match

published MADM like AHP/ M-GRA, AHP/ GRA, AHP/TOPSIS because published

results their selves not match among each other, due to different weight criteria

calculation/ assumption/ expert opinion. While, the lowest 8th

ranking is calculated by the

proposed methods shows that alternative A3 match with published except AHP/TOPSIS

due to criteria weight consideration. It shows that the weight criteria make change in rank

position in further ranking result, but it hold well for the first ranking purpose. Further,

First ranking similarity of proposed MADMs is briefly discussed in point 4.12.

Proposed methodologies works with minimum calculations, without calculating any kind

of relative importance of attributes, not need to resize the assignment matrix and it is gifted

to convert simple set or lingustic set to F-SVNS.





121


AGV selection for manufacturing environment which leads to improve manufacturing

function.

4.6 Collected Case Example 6: Robot Selection

Step 1: One case example of robot selection was adopted and demonstrate by (Khouja

and Booth 1991) with regression analysis. The case example was implemented further and

illustrated by (Karsak et al. 2012) with fuzzy regression model by (David et al. 1992) with

multivariate procedure, (Parkan and Wu 1999) was worked on the same problem with

TOPSIS methodology,, (Dilip Kumar et al. 2015) were worked on the same case example

with PROMETHEE-II.

Step 2: Here twenty seven robot alternatives with four attributes and their attributes

measures are C1: velocity (m/s), C2: load capacity (Kg), C3: cost (Dollar) and C4:

Repeatability (mm). Here, beneficial attributes are C1 and C2; whereas Non-beneficial

attributes are C3 and C4. Actually repeatability of robot must be considered as positive

attribute but, for comparison with other published ranking and as per assumption from

section 1.6 with 2nd

point, data collected from the source is not changed.

Step: 3 Decision matrix was collected from (Khouja and Booth 1991), (Karsak et al.

2012), (David et al. 1992) , (Dilip Kumar et al. 2015) and (Parkan and Wu 1999) is as

shown in Table 4.33

TABLE 4.33: Robot Selection Input Matrix (Collected Case Example)

Sr. No. Alternatives C1 (+) C2 (+) C3(-) C4 (-)

A1 1.35 60 7.2 0.15

A2 1.1 6 4.8 0.05

A3 1.27 45 5 1.27

A4 0.66 1.5 7.2 0.025

A5 0.05 50 9.6 0.25

A6 0.3 1 1.07 0.1

A7 1 5 1.76 0.1

A8 1 15 3.2 0.1

A9 1.1 10 6.72 0.2

A10 1 6 2.4 0.05

A11 0.9 30 2.88 0.5

A12 0.15 13.6 6.9 1

A13 1.2 10 3.2 0.05

A14 1.2 30 4 0.05


122

A15 1.2 47 3.68 1

A16 1 80 6.88 1

A17 2 15 8 2

A18 1 10 6.3 0.2

A19 0.3 10 0.94 0.05

A20 0.8 1.5 0.16 2

A21 1.7 27 2.81 2

A22 1 0.9 3.8 0.05

A23 0.5 2.5 1.25 0.1

A24 0.5 2.5 1.37 0.1

A25 1 10 3.63 0.2

A26 1.25 70 5.3 1.27

A27 0.75 205 4 2.03

Collected from the Source: (Khouja and Booth 1991), (Karsak et al. 2012), (David et al. 1992) , (Dilip

Kumar et al. 2015), (Parkan and Wu 1999)




case example.


Robot selection normalized matrix is shown in Table 4.34.

TABLE 4.34: Robot Selection Normalized Matrix using VNM

Alternatives

(Sr. No.) C1 (+) C2 (+) C3(-) C4 (-)

A1 0.2516 0.2310 0.7154 0.9686

A2 0.2050 0.0237 0.8103 0.9895

A3 0.2367 0.1781 0.8023 0.7344

A4 0.1230 0.0059 0.7154 0.9948

A5 0.0093 0.1979 0.6205 0.9477

A6 0.0559 0.0040 0.9577 0.9791

A7 0.1864 0.0198 0.9304 0.9791

A8 0.1864 0.0594 0.8735 0.9791

A9 0.2050 0.0396 0.7344 0.9582

A10 0.1864 0.0237 0.9051 0.9895

A11 0.1678 0.1187 0.8862 0.8954

A12 0.0280 0.0538 0.7272 0.7909

A13 0.2237 0.0396 0.8735 0.9895

A14 0.2237 0.1187 0.8419 0.9895

A15 0.2237 0.1860 0.8545 0.7909

A16 0.1864 0.3166 0.7280 0.7909

A17 0.3728 0.0594 0.6838 0.5818

A18 0.1864 0.0396 0.7510 0.9582

A19 0.0559 0.0396 0.9628 0.9895

A20 0.1491 0.0059 0.9937 0.5818

A21 0.3169 0.1069 0.8889 0.5818

A22 0.1864 0.0036 0.8498 0.9895

A23 0.0932 0.0099 0.9506 0.9791

A24 0.0932 0.0099 0.9458 0.9791


123

A25 0.1864 0.0396 0.8565 0.9582

A26 0.2330 0.2770 0.7905 0.7344

A27 0.1398 0.8114 0.8419 0.5755







same calculation is also carried out for attribute C2.



SVNS gives the value⟨ ⟩

⟨ ⟩. The same calculation is also carried out for attribute C4.


solution.



⟩

⟨ ⟩ and ⟨

⟩ ⟨ ⟩.

4.6.1 Proposed Method 1: F-SVNS-N-MADM for Robot Selection




TABLE 4.35: F-SVNS N-MADM Ranking for Robot Selection

Alternatives

(Sr. No.) C1 (+) C2 (+) C3(-) C4 (-) Rank

A1

<0.2516,

0.7484,

0.7484>

<0.2310,

0.7690,

0.7690>

<0.2846,

0.7154,

0.7154>

<0.0314,

0.9686,

0.9686>

3.8507 12

A2

<0.2050,

0.7950,

0.7950>

<0.0231,

0.9759,

0.9759>

<0.1897,

0.8103,

0.8103>

<0.0105,

0.9895,

0.9895>

3.8277 14

A3

<0.2367,

0.7633,

0.7633>

<0.1733,

0.8267,

0.8267>

<0.1977,

0.8023,

0.8023>

<0.2656,

0.7344,

0.7344>

3.4835 22


124

A4

<0.1230,

0.8770,

0.8770>

<0.0058,

0.9942,

0.9942>

<0.2846,

0.7154,

0.7154>

<0.0052,

0.9948,

0.9948>

3.5491 20

A5

<0.0093,

0.9907,

0.9907>

<0.1925,

0.8075,

0.8075>

<0.3795,

0.6205,

0.6205>

<0.0523,

0.9477,

0.9477>

3.3383 24

A6

<0.0559,

0.9441,

0.9441>

<0.0039,

0.9961,

0.9961>

<0.0423,

0.9577,

0.9577>

<0.0209,

0.9791,

0.9791>

3.9334 9

A7

<0.1864,

0.8136,

0.8136>

<0.0193,

0.9807,

0.9807>

<0.0696,

0.9304,

0.9304>

<0.0209,

0.9791,

0.9791>

4.0247 1

A8

<0.1864,

0.8136,

0.8136>

<0.0578,

0.9422,

0.9422>

<0.1265,

0.8735,

0.8735>

<0.0209,

0.9791,

0.9791>

3.9493 8

A9

<0.2050,

0.7950,

0.7950>

<0.0385,

0.9615,

0.9615>

<0.2656,

0.7344,

0.7344>

<0.0418,

0.9582,

0.9582>

3.6286 18

A10

<0.1864,

0.8136,

0.8136>

<0.0231,

0.9769,

0.9769>

<0.0949,

0.9051,

0.9051>

<0.0105,

0.9895,

0.9895>

3.9988 4

A11

<0.1678,

0.8322,

0.8322>

<0.1155,

0.8845,

0.8845>

<0.1138,

0.8862,

0.8862>

<0.1046,

0.8954,

0.8954>

3.8465 13

A12

<0.0280,

0.9720,

0.9720>

<0.0524,

0.9476,

0.9476>

<0.2728,

0.7272,

0.7272>

<0.2091,

0.7909,

0.7909>

3.1166 26

A13

<0.2237,

0.7763,

0.7763>

<0.0385,

0.9615,

0.9615>

<0.1265,

0.8735,

0.8735>

<0.0105,

0.9895,

0.9895>

3.9883 5

A14

<0.2237,

0.7763,

0.7763>

<0.1155,

0.8845,

0.8845>

<0.1581,

0.8419,

0.8419>

<0.0105,

0.9895,

0.9895>

4.0020 2

A15

<0.2237,

0.7763,

0.7763>

<0.1810,

0.8190,

0.8190>

<0.1455,

0.8545,

0.8545>

<0.2091,

0.7909,

0.7909>

3.6955 16

A16

<0.1864,

0.8136,

0.8136>

<0.3081,

0.6919,

0.6919

<0.2720,

0.7280,

0.7280>

<0.2091,

0.7909,

0.7909>

3.5323 21

A17

<0.3728,

0.6272,

0.6272>

<0.0578,

0.9422,

0.9422>

<0.3162,

0.6838,

0.6838>

<0.4182,

0.5818,

0.5818>

2.9616 27

A18

<0.1864,

0.8136,

0.8136>

<0.0385,

0.9615,

0.9615>

<0.2490,

0.7510,

0.7510>

<0.0418,

0.9582,

0.9582>

3.6432 17

A19

<0.0559,

0.9441,

0.9441>

<0.0385,

0.9615,

0.9615>

<0.0372,

0.9628,

0.9628>

<0.0105,

0.9895,

0.9895>

3.9992 3

A20

<0.1491,

0.8509,

0.8509>

<0.0058,

0.9942,

0.9942>

<0.0063,

0.9937,

0.9937>

<0.4182,

0.5818,

0.5818>

3.3058 25

A21

<0.3169,

0.6831,

0.6831>

<0.1040,

0.8960,

0.8960>

<0.1111,

0.8889,

0.8889>

<0.4182,

0.5818,

0.5818>

3.3622 23

A22

<0.1864,

0.8136,

0.8136>

<0.0035,

0.9965,

0.9965>

<0.1502,

0.8498,

.8498>

<0.0105,

0.9895,

0.9895>

3.8685 10

A23

<0.0932,

0.9068,

0.9068>

<0.0096,

0.9904,

0.9904>

<0.0494,

0.9506,

0.9506>

<0.0209,

0.9791,

0.9791>

3.9622 6


125

A24

<0.0932,

0.9068,

0.9068>

<0.0096,

0.9904,

0.9904>

<0.0542,

0.9458,

0.9458>

<0.0209,

0.9791,

0.9791>

3.9527 7

A25

<0.1864,

0.8136,

0.8136>

<0.0385,

0.9615,

0.9615>

<0.1435,

0.8565,

0.8565>

<0.0418,

0.9582,

0.9582>

3.8543 11

A26

<0.2330,

0.7670,

0.7670>

<0.2696,

0.7304,

0.7304>

<0.2095,

0.7905,

0.7905>

<0.2656,

0.7344,

0.7344>

3.5524 19

A27

<0.1398,

0.8602,

0.8602>

<0.7894,

0.2106,

0.2106>

<0.1581,

0.8419,

0.8419>

<0.4245,

0.5755,

0.5755>

3.7639 15

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>

<0.0000,

1.0000,

1.0000>

<0.0000,

1.0000,

1.0000>

4.6.2 Proposed Method 2: F-SVNS EW-MADM for Robot Selection


The calculations of step 8 to step 11 are shown briefly in the Annexure – B[6]. The rank is


TABLE 4.36: F-SVNS EW-MADM Ranking for Robot Selection

Alternatives

(Sr. No.) C1 (+) C2 (+) C3(-) C4 (-) Rank

A1

<0.2516,

0.7484,

0.7484>

<0.2310,

0.7690,

0.7690>

<0.2846,

0.7154,

0.7154>

<0.0314,

0.9686,

0.9686>

0.9558 10

A2

<0.2050,

0.7950,

0.7950>

<0.0231,

0.9759,

0.9759>

<0.1897,

0.8103,

0.8103>

<0.0105,

0.9895,

0.9895>

0.9406 15

A3

<0.2367,

0.7633,

0.7633>

<0.1733,

0.8267,

0.8267>

<0.1977,

0.8023,

0.8023>

<0.2656,

0.7344,

0.7344>

0.8541 22

A4

<0.1230,

0.8770,

0.8770>

<0.0058,

0.9942,

0.9942>

<0.2846,

0.7154,

0.7154>

<0.0052,

0.9948,

0.9948>

0.8763 20

A5

<0.0093,

0.9907,

0.9907>

<0.1925,

0.8075,

0.8075>

<0.3795,

0.6205,

0.6205>

<0.0523,

0.9477,

0.9477>

0.8358 23

A6

<0.0559,

0.9441,

0.9441>

<0.0039,

0.9961,

0.9961>

<0.0423,

0.9577,

0.9577>

<0.0209,

0.9791,

0.9791>

0.9640 9

A7

<0.1864,

0.8136,

0.8136>

<0.0193,

0.9807,

0.9807>

<0.0696,

0.9304,

0.9304>

<0.0209,

0.9791,

0.9791>

0.9852 2

A8

<0.1864,

0.8136,

0.8136>

<0.0578,

0.9422,

0.9422>

<0.1265,

0.8735,

0.8735>

<0.0209,

0.9791,

0.9791>

0.9700 7

A9

<0.2050,

0.7950,

0.7950>

<0.0385,

0.9615,

0.9615>

<0.2656,

0.7344,

0.7344>

<0.0418,

0.9582,

0.9582>

0.8938 18


126

A10

<0.1864,

0.8136,

0.8136>

<0.0231,

0.9769,

0.9769>

<0.0949,

0.9051,

0.9051>

<0.0105,

0.9895,

0.9895>

0.9801 4

A11

<0.1678,

0.8322,

0.8322>

<0.1155,

0.8845,

0.8845>

<0.1138,

0.8862,

0.8862>

<0.1046,

0.8954,

0.8954>

0.9445 13

A12

<0.0280,

0.9720,

0.9720>

<0.0524,

0.9476,

0.9476>

<0.2728,

0.7272,

0.7272>

<0.2091,

0.7909,

0.7909>

0.7675 26

A13

<0.2237,

0.7763,

0.7763>

<0.0385,

0.9615,

0.9615>

<0.1265,

0.8735,

0.8735>

<0.0105,

0.9895,

0.9895>

0.9783 5

A14

<0.2237,

0.7763,

0.7763>

<0.1155,

0.8845,

0.8845>

<0.1581,

0.8419,

0.8419>

<0.0105,

0.9895,

0.9895>

0.9857 1

A15

<0.2237,

0.7763,

0.7763>

<0.1810,

0.8190,

0.8190>

<0.1455,

0.8545,

0.8545>

<0.2091,

0.7909,

0.7909>

0.9067 16

A16

<0.1864,

0.8136,

0.8136>

<0.3081,

0.6919,

0.6919

<0.2720,

0.7280,

0.7280>

<0.2091,

0.7909,

0.7909>

0.8763 19

A17

<0.3728,

0.6272,

0.6272>

<0.0578,

0.9422,

0.9422>

<0.3162,

0.6838,

0.6838>

<0.4182,

0.5818,

0.5818>

0.7177 27

A18

<0.1864,

0.8136,

0.8136>

<0.0385,

0.9615,

0.9615>

<0.2490,

0.7510,

0.7510>

<0.0418,

0.9582,

0.9582>

0.8972 17

A19

<0.0559,

0.9441,

0.9441>

<0.0385,

0.9615,

0.9615>

<0.0372,

0.9628,

0.9628>

<0.0105,

0.9895,

0.9895>

0.9817 3

A20

<0.1491,

0.8509,

0.8509>

<0.0058,

0.9942,

0.9942>

<0.0063,

0.9937,

0.9937>

<0.4182,

0.5818,

0.5818>

0.7952 25

A21

<0.3169,

0.6831,

0.6831>

<0.1040,

0.8960,

0.8960>

<0.1111,

0.8889,

0.8889>

<0.4182,

0.5818,

0.5818>

0.8127 24

A22

<0.1864,

0.8136,

0.8136>

<0.0035,

0.9965,

0.9965>

<0.1502,

0.8498,

.8498>

<0.0105,

0.9895,

0.9895>

0.9490 11

A23

<0.0932,

0.9068,

0.9068>

<0.0096,

0.9904,

0.9904>

<0.0494,

0.9506,

0.9506>

<0.0209,

0.9791,

0.9791>

0.9708 6

A24

<0.0932,

0.9068,

0.9068>

<0.0096,

0.9904,

0.9904>

<0.0542,

0.9458,

0.9458>

<0.0209,

0.9791,

0.9791>

0.9686 8

A25

<0.1864,

0.8136,

0.8136>

<0.0385,

0.9615,

0.9615>

<0.1435,

0.8565,

0.8565>

<0.0418,

0.9582,

0.9582>

0.9458 12

A26

<0.2330,

0.7670,

0.7670>

<0.2696,

0.7304,

0.7304>

<0.2095,

0.7905,

0.7905>

<0.2656,

0.7344,

0.7344>

0.8752 21

A27

<0.1398,

0.8602,

0.8602>

<0.7894,

0.2106,

0.2106>

<0.1581,

0.8419,

0.8419>

<0.4245,

0.5755,

0.5755>

0.9432 14

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>

<0.0000,

1.0000,

1.0000>

<0.0000,

1.0000,

1.0000>

0.3491 0.1752 0.3340 0.2462


127

0.2248 0.2849 0.2300 0.2603

1

4.6.3 Proposed Method: 3 F-SVNS-ACC-MADM for Robot selection




TABLE 4.37: F-SVNS ACC-MADM Ranking of Robot Selection

Alternatives

(Sr. No.) C1 (+) C2 (+) C3(-) C4 (-) Rank

A1

<0.2516,

0.7484,

0.7484>

<0.2310,

0.7690,

0.7690>

<0.2846,

0.7154,

0.7154>

<0.0314,

0.9686,

0.9686>

0.6418 12

A2

<0.2050,

0.7950,

0.7950>

<0.0231,

0.9759,

0.9759>

<0.1897,

0.8103,

0.8103>

<0.0105,

0.9895,

0.9895>

0.6380 14

A3

<0.2367,

0.7633,

0.7633>

<0.1733,

0.8267,

0.8267>

<0.1977,

0.8023,

0.8023>

<0.2656,

0.7344,

0.7344>

0.5806 22

A4

<0.1230,

0.8770,

0.8770>

<0.0058,

0.9942,

0.9942>

<0.2846,

0.7154,

0.7154>

<0.0052,

0.9948,

0.9948>

0.5915 20

A5

<0.0093,

0.9907,

0.9907>

<0.1925,

0.8075,

0.8075>

<0.3795,

0.6205,

0.6205>

<0.0523,

0.9477,

0.9477>

0.5564 24

A6

<0.0559,

0.9441,

0.9441>

<0.0039,

0.9961,

0.9961>

<0.0423,

0.9577,

0.9577>

<0.0209,

0.9791,

0.9791>

0.6556 9

A7

<0.1864,

0.8136,

0.8136>

<0.0193,

0.9807,

0.9807>

<0.0696,

0.9304,

0.9304>

<0.0209,

0.9791,

0.9791>

0.6708 1

A8

<0.1864,

0.8136,

0.8136>

<0.0578,

0.9422,

0.9422>

<0.1265,

0.8735,

0.8735>

<0.0209,

0.9791,

0.9791>

0.6582 8

A9

<0.2050,

0.7950,

0.7950>

<0.0385,

0.9615,

0.9615>

<0.2656,

0.7344,

0.7344>

<0.0418,

0.9582,

0.9582>

0.6048 18

A10

<0.1864,

0.8136,

0.8136>

<0.0231,

0.9769,

0.9769>

<0.0949,

0.9051,

0.9051>

<0.0105,

0.9895,

0.9895>

0.6665 4

A11

<0.1678,

0.8322,

0.8322>

<0.1155,

0.8845,

0.8845>

<0.1138,

0.8862,

0.8862>

<0.1046,

0.8954,

0.8954>

0.6411 13

A12

<0.0280,

0.9720,

0.9720>

<0.0524,

0.9476,

0.9476>

<0.2728,

0.7272,

0.7272>

<0.2091,

0.7909,

0.7909>

0.5194 26

A13

<0.2237,

0.7763,

0.7763>

<0.0385,

0.9615,

0.9615>

<0.1265,

0.8735,

0.8735>

<0.0105,

0.9895,

0.9895>

0.6647 5

A14 <0.2237,

0.7763,

<0.1155,

0.8845,

<0.1581,

0.8419,

<0.0105,

0.9895,

0.6670 2


128

0.7763> 0.8845> 0.8419> 0.9895>

A15

<0.2237,

0.7763,

0.7763>

<0.1810,

0.8190,

0.8190>

<0.1455,

0.8545,

0.8545>

<0.2091,

0.7909,

0.7909>

0.6159 16

A16

<0.1864,

0.8136,

0.8136>

<0.3081,

0.6919,

0.6919

<0.2720,

0.7280,

0.7280>

<0.2091,

0.7909,

0.7909>

0.5887 21

A17

<0.3728,

0.6272,

0.6272>

<0.0578,

0.9422,

0.9422>

<0.3162,

0.6838,

0.6838>

<0.4182,

0.5818,

0.5818>

0.4936 27

A18

<0.1864,

0.8136,

0.8136>

<0.0385,

0.9615,

0.9615>

<0.2490,

0.7510,

0.7510>

<0.0418,

0.9582,

0.9582>

0.6072 17

A19

<0.0559,

0.9441,

0.9441>

<0.0385,

0.9615,

0.9615>

<0.0372,

0.9628,

0.9628>

<0.0105,

0.9895,

0.9895>

0.6665 3

A20

<0.1491,

0.8509,

0.8509>

<0.0058,

0.9942,

0.9942>

<0.0063,

0.9937,

0.9937>

<0.4182,

0.5818,

0.5818>

0.5510 25

A21

<0.3169,

0.6831,

0.6831>

<0.1040,

0.8960,

0.8960>

<0.1111,

0.8889,

0.8889>

<0.4182,

0.5818,

0.5818>

0.5604 23

A22

<0.1864,

0.8136,

0.8136>

<0.0035,

0.9965,

0.9965>

<0.1502,

0.8498,

.8498>

<0.0105,

0.9895,

0.9895>

0.6448 10

A23

<0.0932,

0.9068,

0.9068>

<0.0096,

0.9904,

0.9904>

<0.0494,

0.9506,

0.9506>

<0.0209,

0.9791,

0.9791>

0.6604 6

A24

<0.0932,

0.9068,

0.9068>

<0.0096,

0.9904,

0.9904>

<0.0542,

0.9458,

0.9458>

<0.0209,

0.9791,

0.9791>

0.6588 7

A25

<0.1864,

0.8136,

0.8136>

<0.0385,

0.9615,

0.9615>

<0.1435,

0.8565,

0.8565>

<0.0418,

0.9582,

0.9582>

0.6424 11

A26

<0.2330,

0.7670,

0.7670>

<0.2696,

0.7304,

0.7304>

<0.2095,

0.7905,

0.7905>

<0.2656,

0.7344,

0.7344>

0.5921 19

A27

<0.1398,

0.8602,

0.8602>

<0.7894,

0.2106,

0.2106>

<0.1581,

0.8419,

0.8419>

<0.4245,

0.5755,

0.5755>

0.6273 15

<1.000, 0.0000,

0.0000>

<1.0000,

0.0000,

0.0000>

<0.0000,

1.0000,

1.0000>

<0.0000,

1.0000,

1.0000>

4.6.4 Performance Measures Comparison: Robots Ranking


validate them for robot selection. To compare the result, all Robot alternatives are ranked

according to alternatives weight values is as shown in Table 4.37.

The Robot alternatives are ranked first whose alternative weight value is highest;

Robot alternative is ranked second whose alternatives weight values is second highest.


129

Finally the ranking order obtained by the proposed three different methodologies is

compared with the ranking order published in the literature and result comparisons are

shown in Table 4.38

TABLE 4.38: Robot Selection Performance Measures Comparison

Alternatives

(Sr. No.)

F-SVNS MADMs Collected ranking from

(Khouja and Booth 1991)

Collected ranking from (Karsak et

al. 2012)

Novel Entropy

Weight ACC

Regression

method

Fuzzy

Regression

method

PROMETHEE-

II (Equal

criteria weight)

PROMETHEE-II

(Unequal criteria

weight)

A1 12 10 12 2 3 6 4

A2 14 15 14 4 6 13 7

A3 22 22 22 22 22 21 19

A4 20 20 20 8 14 23 21

A5 24 23 24 10 18 26 25

A6 9 9 9 24 15 15 17

A7 1 2 1 9 5 1 1

A8 8 7 8 6 7 5 6

A9 18 18 18 11 13 17 11

A10 4 4 4 5 4 4 5

A11 13 13 13 16 17 12 10

A12 26 26 26 26 23 27 27

A13 5 5 5 3 2 3 3

A14 2 1 2 1 1 2 2

A15 16 16 16 21 20 16 18

A16 21 19 21 15 19 22 20

A17 27 27 27 25 26 25 24

A18 17 17 17 13 16 19 12

A19 3 3 3 7 9 10 15

A20 25 25 25 27 27 24 26

A21 23 24 23 23 25 20 22

A22 10 11 10 14 8 9 8

A23 6 6 6 19 11 7 13

A24 7 8 7 20 12 11 14

A25 11 12 11 12 10 8 9

A26 19 21 19 17 21 18 16

A27 15 14 15 18 24 14 23


proposed methodologies are roughly similar to the result reported in the literature. Initially

robot selection problem was solved by (Khouja and Booth 1991)using regression and

fuzzy regression method which showed that robot with alternative A14 is the first choice,

which is based on mathematical modeling, The same robot selection problem was solved

by (Karsak et al. 2012) using PROMETHEE-II considering equal weight criteria and

unequal weight criteria and it is showed that robot with alternative A7 is the first choice.

Both methodologies differ from the proposed methodology and it has been found that the

first robot ranking solution given by the two methodologies is nearer to each other. Hence,

ranking solution using the proposed method is obviously more genuine.

4.7 Collected Case Example 7: Metal Stamping Layout Selection

130

Further, 2nd

rank is calculated by F-SVNS N-MADM and F-SVNS ACC-MADM matched

with published results of PROMETHEE-II with equal and unequal criteria weight

consideration. While F- SVNS EW-MADM 2nd

Rank shows for alternative A7 which is

nearer to similar ranking with PROMETHEE-II published result.

While for 4th

rank is calculated by proposed methods matched with published results of

fuzzy regression and PROMETHEE-II equal criteria weight method. Where, actually

regression method is not a part of MADM method though it shows similarity in ranking.

While, regression method and PROMETHEE-II with unequal weight method published

results their selves not match among each other, due to different weight criteria

calculation/ assumption/ expert opinion. It also shows that if there are more numbers of

alternatives its gives comparative good ranking solutions. Further, First ranking similarity

of proposed MADMs is briefly discussed in point 4.12.

Proposed methodologies work with minimum calculations, without calculating any kind of

relative importance of attributes, without need to resize the assignment matrix and it is

gifted to convert simple set or lingustic set to F-SVNS.





robots selection for manufacturing environment which leads to improve manufacturing

function.


Step 1. One case example of metal stamping layout selection was adopted demonstrate

(Singh and Sekhon 1996) with diagraph and matrix approach. The same case example was

further calculated by (Rao 2007) with GTMA, SAW, WPM, AHP, TOPSIS and modified

TOPSIS, (Das and Srinivas 2013) was demonstrated in the same problem with TOPSIS

and AHP methodologies.

Step 2. Here, six different alternatives with five attributes and their attributes measures

are economical C1: material utilization in Percentage, C2: die cost in Rupees, C3:

stamping operational cost in Rupees/1000 pieces, C4: required production rate


131

pieces/minute and C5: job accuracy relevant to the given case. Here, beneficial attributes

are C1, C4 and C5; whereas Non-beneficial attributes are C2 and C3.

Step 3. Decision matrix was collected from from(Singh and Sekhon 1996), (Das and

Srinivas 2013) is as shown in Table 4.39

TABLE 4.39: Metal Stamping Layout Selection Input Matrix (Collected Case Example)

Sr. No. Alternative C1 (+) C2 (-) C3 (-) C4 (+) C5 (+)

A1 0.26 25000 130 80 4

A2 0.4 28560 138 120 3

A3 0.33 31109 90 150 3

A4 0.32 31702 150 125 2

A5 0.31 32390 160 110 2

A6 0.31 32663 116 108 2

Collected from the Source (Singh and Sekhon 1996), (Rao 2007) , (Das and Srinivas 2013)




case example.

Step 5: Normalization of Table 4.39 is carried out with the Equation 3.1/ Equation 3.2.

Metal stamping layout selection normalized matrix is shown in Table 4.40.

TABLE 4.40: Metal Stamping Layout Selection Normalized Matrix using VNM

Layout

Alternatives

(Sr. No.)

C1 (+) C2 (-) C3 (-) C4 (+) C5 (+)

1 0.3273 0.6638 0.6000 0.2782 0.5898

2 0.5035 0.6159 0.5753 0.4173 0.4423

3 0.4154 0.5816 0.7230 0.5216 0.4423

4 0.4028 0.5737 0.5384 0.4347 0.2949

5 0.3902 0.5644 0.5076 0.3825 0.2949

6 0.3902 0.5607 0.6430 0.3756 0.2949



falsehood form.

Beneficial attributes i.e. Alternative A1 and attribute C1 having value 0.3273


⟨ ⟩. The same calculation is also carried out for attribute

C4, C5.


132



⟨ ⟩. The same calculation is also carried out for attribute C3.


solution.



⟩

⟨ ⟩ and ⟨

⟩ ⟨ ⟩.

4.7.1 Proposed Method 1: F-SVNS-N-MADM for Metal Stamping Layout Selection




TABLE 4.41: F-SVNS N-MADM Ranking for Metal Stamping Layout Selection

(Sr. No.) C1 (+) C2 (-) C3 (-) C4 (+) C5 (+) Rank

A1

<0.3273,

0.6727,

0.6727>

<0.3362,

0.6638,

0. 6638>

<0.4000,

0.6000,

0.6000>

<0.2782,

0.7218,

0.7218>

<0.5898,

0.4102,

0.4102>

3.7228 3

A2

<0.5035,

0.4965,

0.4965>

<0.3841,

0.6159,

0.6159>

<0.4247,

0.5753,

0. 5753>

<0.4173,

0.5827,

0.5827>

<0.4423,

0.5577,

0.5577>

3.7457 2

A3

<0.4154,

0.5846,

0.5846>

<0.4184,

0.5816,

0.5816>

<0.2770,

0.7230,

0.7230>

<0.5216,

0.4784,

0.4784>

<0.4423,

0.5577,

0.5577>

3.9887 1

A4

<0.4028,

0.5972,

0.5972>

<0.4263,

0.5737,

0.5737>

<0.4616,

0.5384,

0.5384>

<0.4347,

0.5653,

0.5653>

<0.2949,

0.7051,

0.7051>

3.3565 5

A5

<0.3902,

0.6098,

0.6098>

<0.4356,

0.5644,

0.5644>

<0.4924,

0.5076,

0.5076>

<0.3825,

0.6175,

0.6175>

<0.2949,

0.7051,

0.7051>

3.2117 6

A6

<0.3902,

0.6098,

0.6098>

<0.4393,

0.5607,

0.5607>

<0.3570,

0.6430,

0.6430>

<0.3756,

0.6244,

0.6244>

<0.2949,

0.7051,

0.7051>

3.4682 4

<1.000,

0.0000,

0.0000>

<0.0000,

1.0000,

1.0000>

<0.0000,

1.0000,

1.0000>

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>


133

4.7.2 Proposed Method 2: F-SVNS-EW-MADM for Metal Stamping Layout

Selection




TABLE 4.42: F-SVNS EW-MADM Ranking for Metal Stamping Layout Selection

(Sr. No.) C1 (+) C2 (-) C3 (-) C4 (+) C5 (+) Rank

A1

<0.3273,

0.6727,

0.6727>

<0.3362,

0.6638,

0. 6638>

<0.4000,

0.6000,

0.6000>

<0.2782,

0.7218,

0.7218>

<0.5898,

0.4102,

0.4102>

0.7228 2

A2

<0.5035,

0.4965,

0.4965>

<0.3841,

0.6159,

0.6159>

<0.4247,

0.5753,

0. 5753>

<0.4173,

0.5827,

0.5827>

<0.4423,

0.5577,

0.5577>

0.7185 3

A3

<0.4154,

0.5846,

0.5846>

<0.4184,

0.5816,

0.5816>

<0.2770,

0.7230,

0.7230>

<0.5216,

0.4784,

0.4784>

<0.4423,

0.5577,

0.5577>

0.7658 1

A4

<0.4028,

0.5972,

0.5972>

<0.4263,

0.5737,

0.5737>

<0.4616,

0.5384,

0.5384>

<0.4347,

0.5653,

0.5653>

<0.2949,

0.7051,

0.7051>

0.6371 5

A5

<0.3902,

0.6098,

0.6098>

<0.4356,

0.5644,

0.5644>

<0.4924,

0.5076,

0.5076>

<0.3825,

0.6175,

0.6175>

<0.2949,

0.7051,

0.7051>

0.6097 6

A6

<0.3902,

0.6098,

0.6098>

<0.4393,

0.5607,

0.5607>

<0.3570,

0.6430,

0.6430>

<0.3756,

0.6244,

0.6244>

<0.2949,

0.7051,

0.7051>

0.6571 4

<1.000,

0.0000,

0.0000>

<0.0000,

1.0000,

1.0000>

<0.0000,

1.0000,

1.0000>

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>

0.8075 0.8133 0.8042 0.7889 0.7265

0.1817 0.1762 0.1848 0.1992 0.2581 1

4.7.3 Proposed Method 3: F-SVNS-ACC-MADM for Metal Stamping Layout

Selection




TABLE 4.43: F-SVNS ACC-MADM Ranking for Metal Stamping Layout Selection

(Sr. No.) C1 (+) C2 (-) C3 (-) C4 (+) C5 (+) Rank

A1 <0.3273,

0.6727,

<0.3362,

0.6638,

<0.4000,

0.6000,

<0.2782,

0.7218,

<0.5898,

0.4102, 0.5318 3


134

0.6727> 0. 6638> 0.6000> 0.7218> 0.4102>

A2

<0.5035,

0.4965,

0.4965>

<0.3841,

0.6159,

0.6159>

<0.4247,

0.5753,

0. 5753>

<0.4173,

0.5827,

0.5827>

<0.4423,

0.5577,

0.5577>

0.5351 2

A3

<0.4154,

0.5846,

0.5846>

<0.4184,

0.5816,

0.5816>

<0.2770,

0.7230,

0.7230>

<0.5216,

0.4784,

0.4784>

<0.4423,

0.5577,

0.5577>

0.5698 1

A4

<0.4028,

0.5972,

0.5972>

<0.4263,

0.5737,

0.5737>

<0.4616,

0.5384,

0.5384>

<0.4347,

0.5653,

0.5653>

<0.2949,

0.7051,

0.7051>

0.4795 5

A5

<0.3902,

0.6098,

0.6098>

<0.4356,

0.5644,

0.5644>

<0.4924,

0.5076,

0.5076>

<0.3825,

0.6175,

0.6175>

<0.2949,

0.7051,

0.7051>

0.4588 6

A6

<0.3902,

0.6098,

0.6098>

<0.4393,

0.5607,

0.5607>

<0.3570,

0.6430,

0.6430>

<0.3756,

0.6244,

0.6244>

<0.2949,

0.7051,

0.7051>

0.4955 4

<1.000,

0.0000,

0.0000>

<0.0000,

1.0000,

1.0000>

<0.0000,

1.0000,

1.0000>

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>

4.7.4 Performance Measures Comparison: Metal Stamping Layout Ranking


validate them for metal stamping layout selection. To compare the result, all metal

stamping layout alternatives are ranked according to alternatives weight values is as shown

in Table 4.44. The metal stamping layout alternative is ranked first whose alternative

weight value is highest; metal stamping layout alternative is ranked second whose

alternatives weight values is second highest. Finally the ranking order obtained by the

proposed three different methodologies are compared with the ranking order published in

the literature and result comparisons are shown in Table 4.44

TABLE 4.44: Metal Stamping Layout Selection Performance Measures Comparison

Alternatives

Layout

(Sr. No.)

F-SVNS MADMs Source of ranking collected from (Rao 2007)

GTMA SAW WPM AHP TOPSIS MODIFIED

TOPSIS Novel

Entropy

Weight ACC

A1 3 2 3 3 3 3 3 3 3

A2 2 3 2 2 2 2 2 2 2

A3 1 1 1 1 1 1 1 1 1

A4 5 5 5 5 4 4 4 4 4

A5 6 6 6 6 6 6 6 5 6

A6 4 4 4 4 5 5 5 6 5

The result comparisons presented in Table 4.44 shows that the results obtained by the

proposed methodologies are relatively similar to the results reported in the literature. All


135

methods suggested alternative A3 is the first choice of metal stamping layout selection and

alternative A5 is poorest choice. (Rao 2007) used GTMA, SAW, WPM, AHP, TOPSIS

and Modified TOPSIS for solving metal stamping layout selection problem.

Further, 2nd

rank is calculated by F-SVNS N-MADM and F-SVNS ACC-MADM methods

matched with all published results except F-SVNS EW-MADM here minor change occurs

due to entropy weight criteria. Here, 4th

rank calculated by proposed methods are same

which are match with published result of GTMA, while other MADM like SAW, WPM,

AHP, TOPSIS and modified TOPSIS methodologies again shows different ranking with

minor ranking change 5th

rank due to different weight criteria calculation/ assumption/

expert opinion. The lowest 6th

ranking is calculated by the proposed methods shows that

alternative A6 match with published results except TOPSIS method. It shows that the

weight criteria make change in rank position in further ranking result, but it hold well for

the first ranking purpose.


Proposed methodologies work with minimum calculations, without calculating any kind of

relative importance of attributes, without need to resize the assignment matrix and it is

gifted to convert simple set or lingustic set to F-SVNS. This methods show also gives

better result for the last ranking solution. Drawbacks of these methodologies are also

described in chapter 3.





metal stamping layout selection for manufacturing environment which leads to improve


4.8 Collected Case Example 8: Electro Chemical Machining


Step 1. One case example of ECM programming selection for industrial application

was demonstrated by (Sarkis 1999) with data envelopment analysis. Input matrix is having

the quantitative information on how each program (alternatives) is expected to perform

4.8 Collected Case Example 8: Electro Chemical Machining Programming Selection

136

with respective process parameters (attributes). The same case example was further

calculated by (Rao 2007) with GTMA, SAW, WPM, AHP, TOPSIS and modified TOPSIS

also was carried out by (Rao 2008a). The same case example was also solved by (Maniya

2012) with the help of PSI methodology.

Step 2. The given matrix considering fifteen ECM programs as alternatives and six

attributes measures are C1: cost in dollar, C2: quality in percentage of defects, C3:

recyclability in recyclable material in percentage, C4: Process waste reduction in

percentage, C5: packaging waste reduction in percentage and C6: regulatory compliance in

percentage in Here, beneficial attributes are C3, C4, C5 and C6; whereas Non-beneficial

attributes are C1 and C2.

Step 3. Decision matrix was collected from (Sarkis 1999), (Rao 2007) is as shown in

Table 4.45.

TABLE 4.45: ECM programming Selection Input Matrix (Collected Case Example)

Alternatives Sr. No. C1 (-) C2 (-) C3 (+) C4 (+) C5 (+) C6 (+)

A1 706967 2 29 17 0 51

A2 181278 3 5 14 7 45

A3 543399 4 5 3 7 71

A4 932027 7 15 10 17 57

A5 651411 4 19 7 0 21

A6 714917 5 15 6 19 5

A7 409744 1 8 17 1 35

A8 310013 6 23 15 18 32

A9 846595 2 28 16 19 24

A10 625402 3 21 16 7 34

A11 285869 2 1 13 12 54

A12 730637 3 3 4 1 12

A13 794656 5 27 14 14 65

A14 528001 1 6 5 9 41

A15 804090 2 26 6 5 70

Collected from the sources (Sarkis 1999), (Rao 2007), (Rao 2008a), (Maniya 2012)


Here, the input information contains quantitative information only, So there is no need to


case example.


ECM programming selection normalized matrix is shown in Table 4.46.

TABLE 4.46: ECM programming Selection Normalized Matrix using VNM

ECM Prog. Sr. No. C1 (-) C2 (-) C3 (+) C4 (+) C5 (+) C6 (+)

A1 0.7155 0.8626 0.4113 0.3669 0.0000 0.2886

A2 0.9271 0.7940 0.0709 0.3021 0.1593 0.2546

A3 0.7813 0.7253 0.0709 0.0647 0.1593 0.4018


137

A4 0.6250 0.5192 0.2127 0.2158 0.3870 0.3225

A5 0.7379 0.7253 0.2695 0.1511 0.0000 0.1188

A6 0.7123 0.6566 0.2127 0.1295 0.4325 0.0283

A7 0.8351 0.9313 0.1135 0.3669 0.0228 0.1981

A8 0.8753 0.5879 0.3262 0.3237 0.4097 0.1811

A9 0.6593 0.8626 0.3971 0.3453 0.4325 0.1358

A10 0.7484 0.7940 0.2978 0.3453 0.1593 0.1924

A11 0.8850 0.8626 0.0142 0.2806 0.2732 0.3056

A12 0.7060 0.7940 0.0425 0.0863 0.0228 0.0679

A13 0.6802 0.6566 0.3829 0.3021 0.3187 0.3678

A14 0.7875 0.9313 0.0851 0.1079 0.2049 0.2320

A15 0.6765 0.8626 0.3688 0.1295 0.1138 0.3961








calculation is also carried out for attribute C2.




same calculation is also carried out for attribute C4, C5, C6.


solution.



⟩

⟨ ⟩ and ⟨

⟩ ⟨ ⟩.

4.8.1 Proposed Method 1: F-SVNS-N-MADM for ECM Programming Selection





138

Table 4.47: F-SVNS N-MADM Ranking for ECM Programming Selection

Sr. No. C1 (-) C2 (-) C3 (+) C4 (+) C5 (+) C6 (+) Rank

A1

<0.2845,

0.7155,

0.7155>

<0.1374,

0.8626,

0.8626>

<0.4113,

0.5887,

0.5887>

<0.3669,

0.6331,

0.6331>

<0.0000,

1.0000,

1.0000>

<0.2886,

0.7114,

0. 7114>

4.2231 5

A2

<0.0729,

0.9271,

0.9271>

<0.2060,

0.7940,

0.7940>

<0.0709,

0.9291,

0. 9291>

<0.3021,

0.6979,

0.6979>

<0.1593,

0.8407,

0.8407>

<0.2546,

0.7454,

0.7454>

4.2291 4

A3

<0.2187,

0.7813,

0.7813>

<0.2747,

0.7253,

0.7253>

<0.0709,

0.9291,

0. 9291>

<0.0647,

0.9353,

0.9353>

<0.1593,

0.8407,

0.8407>

<0.4018,

0.5982,

0.5982>

3.7100 11

A4

<0.3750,

0.6250,

0.6250>

<0.4808,

0.5192,

0.5192>

<0.2127,

0.7873,

0.7873>

<0.2158,

0.7842,

0.7842>

<0.3870,

0.6130,

0.6130>

<0.3225,

0.6775,

0.6775>

3.4265 14

A5

<0.2621,

0.7379,

0.7379>

<0.2747,

0.7253,

0.7253>

<0.2695,

0.7305,

0.7305>

<0.1511,

0.8489,

0.8489>

<0.0000,

1.0000,

1.0000>

<0.1188,

0.8812,

0.8812>

3.4657 13

A6

<0.2877,

0.7123,

0.7123>

<0.3434,

0.6566,

0.6566>

<0.2127,

0.7873,

0.7873>

<0.1295,

0.8705,

0.8705>

<0.4325,

0.5675,

0.5675>

<0.0283,

0.9717,

0.9717>

3.5409 12

A7

<0.1649,

0.8351,

0.8351>

<0.0687,

0.9313,

0.9313>

<0.1135,

0.8865,

0.8865>

<0.3669,

0.6331,

0.6331>

<0.0228,

0.9772,

0. 9772>

<0.1981,

0.8019,

0.8019>

4.2341 3

A8

<0.1247,

0.8753,

0.8753 >

<0.4121,

0.5879,

0.5879>

<0.3262,

0.6738,

0.6738>

<0.3237,

0.6763,

0.6763>

<0.4097,

0.5903,

0. 5903>

<0.1811,

0.8189,

0.8189>

4.1671 6

A9

<0.3407,

0.6593,

0.6593 >

<0.1374,

0.8626,

0.8626>

<0.3971,

0.6029,

0.6029>

<0.3453,

0.6547,

0.6547>

<0.4325,

0.5675,

0.5675>

<0.1358,

0.8642,

0.8642>

4.3547 2

A10

<0.2516,

0.7484,

0.7484 >

<0.2060,

0.7940,

0.7940>

<0.2978,

0.7022,

0.7022>

<0.3453,

0.6547,

0.6547>

<0.1593,

0.8407,

0.8407>

<0.1924,

0.8076,

0.8076>

4.0795 8

A11

<0.1150,

0.8850,

0.8850 >

<0.1374,

0.8626,

0.8626>

<0.0142,

0.9858,

0.9858>

<0.2806,

0.7194,

0.7194>

<0.2732,

0.7268,

0.7268>

<0.3056,

0.6944,

0.6944>

4.3687 1

A12

<0.2940,

0.7060,

0.7060 >

<0.2060,

0.7940,

0.7940>

<0.0425,

0.9575,

0.9575>

<0.0863,

0.9137,

0.9137>

<0.0228,

0.9772,

0.9772>

<0.0679,

0.9321,

0.9321>

3.2195 15

A13

<0.3198,

0.6802,

0.6802 >

<0.3434,

0.6566,

0.6566>

<0.3829,

0.6171,

0.6171>

<0.3021,

0.6979,

0.6979>

<0.3187,

0.6813,

0.6813>

<0.3678,

0.6322,

0.6322>

4.0453 10

A14

<0.2125,

0.7875,

0.7875 >

<0.0687,

0.9313,

0.9313>

<0.0851,

0.9149,

0.9149>

<0.1079,

0.8921,

0.8921>

<0.2049,

0.7951,

0.7951>

<0.2320,

0.7680,

0.7680>

4.0676 9

A15

<0.3235,

0.6765,

0.6765 >

<0.1374,

0.8626,

0.8626>

<0.3688,

0.6312,

0.6312>

<0.1295,

0.8705,

0.8705>

<0.1138,

0.8862,

0.8862>

<0.3961,

0.6039,

0.6039>

4.0864 7

<0.0000,

1.0000,

1.0000>

<0.0000,

1.0000,

1.0000>

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>

4.8.2 Proposed Method 2: F-SVNS-EW-MADM for ECM Programming Selection



139

The calculations of step 8 to step 11 are shown briefly in the Annexure - B [8]. The rank is


TABLE 4.48: F-SVNS EW-MADM Ranking for ECM Programming Selection

Sr. No. C1 (-) C2 (-) C3 (+) C4 (+) C5 (+) C6 (+) Rank

A1

<0.2845,

0.7155,

0.7155>

<0.1374,

0.8626,

0.8626>

<0.4113,

0.5887,

0.5887>

<0.3669,

0.6331,

0.6331>

<0.0000,

1.0000,

1.0000>

<0.2886,

0.7114,

0. 7114>

0.6881 3

A2

<0.0729,

0.9271,

0.9271>

<0.2060,

0.7940,

0.7940>

<0.0709,

0.9291,

0. 9291>

<0.3021,

0.6979,

0.6979>

<0.1593,

0.8407,

0.8407>

<0.2546,

0.7454,

0.7454>

0.6857 5

A3

<0.2187,

0.7813,

0.7813>

<0.2747,

0.7253,

0.7253>

<0.0709,

0.9291,

0. 9291>

<0.0647,

0.9353,

0.9353>

<0.1593,

0.8407,

0.8407>

<0.4018,

0.5982,

0.5982>

0.6027 11

A4

<0.3750,

0.6250,

0.6250>

<0.4808,

0.5192,

0.5192>

<0.2127,

0.7873,

0.7873>

<0.2158,

0.7842,

0.7842>

<0.3870,

0.6130,

0.6130>

<0.3225,

0.6775,

0.6775>

0.5621 14

A5

<0.2621,

0.7379,

0.7379>

<0.2747,

0.7253,

0.7253>

<0.2695,

0.7305,

0.7305>

<0.1511,

0.8489,

0.8489>

<0.0000,

1.0000,

1.0000>

<0.1188,

0.8812,

0.8812>

0.5624 13

A6

<0.2877,

0.7123,

0.7123>

<0.3434,

0.6566,

0.6566>

<0.2127,

0.7873,

0.7873>

<0.1295,

0.8705,

0.8705>

<0.4325,

0.5675,

0.5675>

<0.0283,

0.9717,

0.9717>

0.5812 12

A7

<0.1649,

0.8351,

0.8351>

<0.0687,

0.9313,

0.9313>

<0.1135,

0.8865,

0.8865>

<0.3669,

0.6331,

0.6331>

<0.0228,

0.9772,

0. 9772>

<0.1981,

0.8019,

0.8019>

0.6864 4

A8

<0.1247,

0.8753,

0.8753 >

<0.4121,

0.5879,

0.5879>

<0.3262,

0.6738,

0.6738>

<0.3237,

0.6763,

0.6763>

<0.4097,

0.5903,

0. 5903>

<0.1811,

0.8189,

0.8189>

0.6815 6

A9

<0.3407,

0.6593,

0.6593 >

<0.1374,

0.8626,

0.8626>

<0.3971,

0.6029,

0.6029>

<0.3453,

0.6547,

0.6547>

<0.4325,

0.5675,

0.5675>

<0.1358,

0.8642,

0.8642>

0.7171 1

A10

<0.2516,

0.7484,

0.7484 >

<0.2060,

0.7940,

0.7940>

<0.2978,

0.7022,

0.7022>

<0.3453,

0.6547,

0.6547>

<0.1593,

0.8407,

0.8407>

<0.1924,

0.8076,

0.8076>

0.6655 8

A11

<0.1150,

0.8850,

0.8850 >

<0.1374,

0.8626,

0.8626>

<0.0142,

0.9858,

0.9858>

<0.2806,

0.7194,

0.7194>

<0.2732,

0.7268,

0.7268>

<0.3056,

0.6944,

0.6944>

0.7107 2

A12

<0.2940,

0.7060,

0.7060 >

<0.2060,

0.7940,

0.7940>

<0.0425,

0.9575,

0.9575>

<0.0863,

0.9137,

0.9137>

<0.0228,

0.9772,

0.9772>

<0.0679,

0.9321,

0.9321>

0.5213 15

A13

<0.3198,

0.6802,

0.6802 >

<0.3434,

0.6566,

0.6566>

<0.3829,

0.6171,

0.6171>

<0.3021,

0.6979,

0.6979>

<0.3187,

0.6813,

0.6813>

<0.3678,

0.6322,

0.6322>

0.6635 9

A14

<0.2125,

0.7875,

0.7875 >

<0.0687,

0.9313,

0.9313>

<0.0851,

0.9149,

0.9149>

<0.1079,

0.8921,

0.8921>

<0.2049,

0.7951,

0.7951>

<0.2320,

0.7680,

0.7680>

0.6628 10

A15

<0.3235,

0.6765,

0.6765 >

<0.1374,

0.8626,

0.8626>

<0.3688,

0.6312,

0.6312>

<0.1295,

0.8705,

0.8705>

<0.1138,

0.8862,

0.8862>

<0.3961,

0.6039,

0.6039>

0.6679 7

<0.0000,1.00

00, 1.0000>

<0.0000,1.0

000,

1.0000>

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>

0.4863 0.4579 0.4368 0.4690 0.4128 0.4655

0.1570 0.1657 0.1721 0.1623 0.1795 0.1634 1


140

4.8.3 Proposed Method 3: F-SVNS-ACC-MADM for ECM Programming Selection




TABLE 4.49: F-SVNS ACC-MADM Ranking for ECM Programming Selection

Sr. No. C1 (-) C2 (-) C3 (+) C4 (+) C5 (+) C6 (+) Rank

A1

<0.2845,

0.7155,

0.7155>

<0.1374,

0.8626,

0.8626>

<0.4113,

0.5887,

0.5887>

<0.3669,

0.6331,

0.6331>

<0.0000,

1.0000,

1.0000>

<0.2886,

0.7114,

0. 7114>

0.5279 5

A2

<0.0729,

0.9271,

0.9271>

<0.2060,

0.7940,

0.7940>

<0.0709,

0.9291,

0. 9291>

<0.3021,

0.6979,

0.6979>

<0.1593,

0.8407,

0.8407>

<0.2546,

0.7454,

0.7454>

0.5286 4

A3

<0.2187,

0.7813,

0.7813>

<0.2747,

0.7253,

0.7253>

<0.0709,

0.9291,

0. 9291>

<0.0647,

0.9353,

0.9353>

<0.1593,

0.8407,

0.8407>

<0.4018,

0.5982,

0.5982>

0.4638 11

A4

<0.3750,

0.6250,

0.6250>

<0.4808,

0.5192,

0.5192>

<0.2127,

0.7873,

0.7873>

<0.2158,

0.7842,

0.7842>

<0.3870,

0.6130,

0.6130>

<0.3225,

0.6775,

0.6775>

0.4283 14

A5

<0.2621,

0.7379,

0.7379>

<0.2747,

0.7253,

0.7253>

<0.2695,

0.7305,

0.7305>

<0.1511,

0.8489,

0.8489>

<0.0000,

1.0000,

1.0000>

<0.1188,

0.8812,

0.8812>

0.4332 13

A6

<0.2877,

0.7123,

0.7123>

<0.3434,

0.6566,

0.6566>

<0.2127,

0.7873,

0.7873>

<0.1295,

0.8705,

0.8705>

<0.4325,

0.5675,

0.5675>

<0.0283,

0.9717,

0.9717>

0.4426 12

A7

<0.1649,

0.8351,

0.8351>

<0.0687,

0.9313,

0.9313>

<0.1135,

0.8865,

0.8865>

<0.3669,

0.6331,

0.6331>

<0.0228,

0.9772,

0. 9772>

<0.1981,

0.8019,

0.8019>

0.5293 3

A8

<0.1247,

0.8753,

0.8753 >

<0.4121,

0.5879,

0.5879>

<0.3262,

0.6738,

0.6738>

<0.3237,

0.6763,

0.6763>

<0.4097,

0.5903,

0. 5903>

<0.1811,

0.8189,

0.8189>

0.5209 6

A9

<0.3407,

0.6593,

0.6593 >

<0.1374,

0.8626,

0.8626>

<0.3971,

0.6029,

0.6029>

<0.3453,

0.6547,

0.6547>

<0.4325,

0.5675,

0.5675>

<0.1358,

0.8642,

0.8642>

0.5443 2

A10

<0.2516,

0.7484,

0.7484 >

<0.2060,

0.7940,

0.7940>

<0.2978,

0.7022,

0.7022>

<0.3453,

0.6547,

0.6547>

<0.1593,

0.8407,

0.8407>

<0.1924,

0.8076,

0.8076>

0.5099 8

A11

<0.1150,

0.8850,

0.8850 >

<0.1374,

0.8626,

0.8626>

<0.0142,

0.9858,

0.9858>

<0.2806,

0.7194,

0.7194>

<0.2732,

0.7268,

0.7268>

<0.3056,

0.6944,

0.6944>

0.5461 1

A12

<0.2940,

0.7060,

0.7060 >

<0.2060,

0.7940,

0.7940>

<0.0425,

0.9575,

0.9575>

<0.0863,

0.9137,

0.9137>

<0.0228,

0.9772,

0.9772>

<0.0679,

0.9321,

0.9321>

0.4024 15

A13

<0.3198,

0.6802,

0.6802 >

<0.3434,

0.6566,

0.6566>

<0.3829,

0.6171,

0.6171>

<0.3021,

0.6979,

0.6979>

<0.3187,

0.6813,

0.6813>

<0.3678,

0.6322,

0.6322>

0.5057 10

A14

<0.2125,

0.7875,

0.7875 >

<0.0687,

0.9313,

0.9313>

<0.0851,

0.9149,

0.9149>

<0.1079,

0.8921,

0.8921>

<0.2049,

0.7951,

0.7951>

<0.2320,

0.7680,

0.7680>

0.5085 9

A15

<0.3235,

0.6765,

0.6765 >

<0.1374,

0.8626,

0.8626>

<0.3688,

0.6312,

0.6312>

<0.1295,

0.8705,

0.8705>

<0.1138,

0.8862,

0.8862>

<0.3961,

0.6039,

0.6039>

0.5108 7


141

<0.0000,

1.0000,

1.0000>

<0.0000,1

.0000,

1.0000>

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>

4.8.4 Performance Measures Comparison: ECM Programming Ranking


validate them for ECM programming selection. To compare the result, all ECM

programming alternatives are ranked according to alternatives weight values is as shown in

Table 4.50.

The ECM programming alternatives are ranked first whose alternative weight value is

highest; ECM programming alternative is ranked second whose alternatives weight values

is second highest. As per (Nirmal and Bhatt 2019),(Kahraman and Otay 2019), the ranking

order calculated by the proposed three different methods is compared with the ranking

order published in the literature and result comparisons are shown in Table 4.50.

TABLE 4.50: ECM Programming Selection Performance Measures Comparison

ECM

Alternatives

(Sr. No.)

F-SVNS MADMs

PSI* DEA

* GTMA

# PROMETHEE

$ SAW

#

AHP

and its

version#

TOPSIS#

Novel Entropy

Weight ACC

A1 5 3 5 8 6 4 3 3 3 8

A2 4 5 4 10 5 6 5 8 8 4

A3 11 11 11 12 12 12 13 14 14 13

A4 14 14 14 4 13 10 12 10 10 9

A5 13 13 13 14 14 14 14 13 13 14

A6 12 12 12 5 11 13 10 12 12 10

A7 3 4 3 13 4 7 2 5 5 7

A8 6 6 6 2 2 3 1 2 2 1

A9 2 1 2 1 3 1 4 1 1 2

A10 8 8 8 6 8 9 6 6 6 6

A11 1 2 1 9 1 5 7 7 7 3

A12 15 15 15 15 15 14 15 15 15 15

A13 10 9 10 3 10 2 8 4 4 5

A14 9 10 9 11 9 11 9 11 11 11

A15 7 7 7 7 7 8 11 9 9 12

[*Collected ranking solution from (Maniya 2012), #

Collected ranking solution from (Rao 2007),$

Collected

ranking solution from (Venkata Rao and Patel 2010)]

The result comparisons presented in Table 4.50 shows that the results obtained

from the proposed methodologies are quite similar to the result of PSI, DEA, GTMA,

SAW and AHP and its versions. The proposed method F-SVNS N-MADM and F-SVNS

CC- MADM which work without calculation of attribute weight recommends the ECM

alternative A11 as first choice. While F-SVNS EW- MADM works with attribute weight is


142

recommends alternative A9 is first choice. Now which methods gives better solution from

proposed methodologies will be briefly validated in chapter 5. The comparisons of results

show that the major or minor ranking difference is available in MADM for generous

selection process.

Further, 2nd

rank and 4th

rank is calculated by F-SVNS N-MADM and F-SVNS ACC-

MADM methods matched with only one TOPSIS method (which is also work with weight

criteria) while other published ranking shows results their selves not match among each

other, due to different weight criteria calculation/ assumption/ expert opinion. F-SVNS

EW- MADM 2nd

rank shows alternative A11, which is not match with published result. In

this case example, one another reason behind mismatch with published result is that, some

methods work with considering same equation for the normalization for beneficial and

non-beneficial criteria. Here, 2 non beneficial criteria and 4 beneficial criteria are present,

which may leads to change ranking order. Here, it is also very default to predict which

method works well for all ranking solution. Again, lowest 15th

Rank is matched with the

published result except GTMA. It shows that the weight criteria and normalization

equation/ method make change in rank position in further ranking result, but it hold well

for the first ranking purpose.

Further, First ranking similarity of proposed MADMs is briefly discussed in point

4.12. Relative comparison shows that the ranking (Rao 2007) with little difference in

calculation method, i.e. some methods work with calculating attribute weight while other

methods works without calculating attribute weight. Proposed methodologies works with

minimum calculations, without calculating any kind of relative importance of attributes,

without the need to resize the assignment matrix and it is gifted to convert simple set or

lingustic set to F-SVNS. Furthermore, the various drawbacks of the PROMETHEE,

GTMA, DEA, TOPSIS and AHP are also mentioned in chapter 2.





ECM programming selection for manufacturing environment which leads to improve



143

4.9 Case Example 9: Cutting Fluid (Coolant) Selection

Step 1. One case example of cutting fluid selection for cylindrical turning test operation

was carried out by (Rao 2007) with GTMA, SAW, WPM, AHP, TOPSIS and modified

TOPSIS.

Step 2. The given matrix considering five different cutting fluids for cylindrical turning

test operation as alternatives and four attributes measures are C1: cutting force in Newton,

C2: thrust force in Newton, C3: wear land in cm 10, C4: processes surface roughness

expressed in rms value (Rrms). Here all attributes are non-beneficial.

Step 3. Decision matrix was collected from (Rao 2007) is as shown in Table 4.51

TABLE 4.51: Cutting Fluid Selection Input Matrix (Collected Case Study)

Alternatives C1 (-) C2 (-) C3 (-) C4 (-)

A1 1324 725 7 9

A2 1082 485 16 7

A3 1098 516 8 4.7

A4 1158 494 15 4.9

A5 962 393 6 8

Collected from the source (Rao 2007)




case example.


Cutting fluid selection normalized matrix is shown in Table 4.52.

TABLE 4.52: Cutting Fluid Selection Normalized Matrix using VNM

Alternatives C1 (-) C2 (-) C3 (-) C4 (-)

A1 0.4765 0.3928 0.7211 0.4192

A2 0.5722 0.5938 0.36254 0.54825

A3 0.5658 0.5678 0.6813 0.6967

A4 0.5421 0.5863 0.4024 0.6838

A5 0.6196 0.6709 0.7610 0.4837





attributes i.e. Alternative A1 and attribute c1 having value converted in


144



calculation is also is carried out for attributes C2, C3, C4.


solution.



⟩

⟨ ⟩ and ⟨

⟩ ⟨ ⟩.

4.9.1 Proposed Method 1: F-SVNS-N-MADM for Cutting Fluid (Coolant) Selection


The calculations of step 8 and step 9 are shown briefly in the Annexure A[9] . The rank is


TABLE 4.53: F-SVNS N-MADM Ranking for Cutting Fluid Selection

Sr.

No. C1 (-) C2 (-) C3 (-) C4 (-) Rank

A1

<0.5235,

0.4765,

0.4765>

<0.6072,

0.3928,

0.3928>

<0.2789,

0.7211,

0.7211>

<0.5808,

0.4192,

0.4192>

4.0191 5

A2

<0.4278,

0.5722,

0.5722>

<0.4062,

0.5938,

0.5938>

<0.6375,

0.3625,

0.3625>

<0.4518,

0.5482,

0. 5482>

4.1535 4

A3

<0.4342,

0.5658,

0.5658>

<0.4322,

0.5678,

0.5678>

<0.3187,

0.6813,

0.6813>

<0.3033,

0.6967,

0. 6967>

5.0232 2

A4

<0.4579,

0.5421,

0.5421>

<0.4137,

0.5863,

0.5863>

<0.5976,

0.4024,

0.4024>

<0.3162,

0.6838,

0.6838>

4.4290 3

A5

<0.3804,

0.6196,

0.6196>

<0.3292,

0.6708,

0.6708>

<0.2390,

0.7610,

0.7610>

<0.5163,

0.4837,

0.4837>

5.0702 1

<0.0000,

1.0000,

1.0000>

<0.0000,

1.0000,

1.0000>

<0.0000,

1.0000,

1.0000>

<0.0000,

1.0000,

1.0000>


145

4.9.2 Proposed Method 2: F-SVNS-EW-MADM for Cutting Fluid (Coolant)

Selection

Step 1 to step 7 are described earlier in point 4.9. The calculations of step 8 to step 11 are

shown briefly in the Annexure –B[9]. The rank is calculated with F-SVNS-EW-MADM is

as shown in Table 4.54

TABLE 4.54: F-SVNS EW-MADM Ranking for Cutting Fluid Selection

Sr. No. A1 (-) A2 (-) A3 (-) A4 (-) Rank

A1

<0.5235,

0.4765,

0.4765>

<0.6072,

0.3928,

0.3928>

<0.2789,

0.7211,

0.7211>

<0.5808,

0.4192,

0.4192>

1.0811 3

A2

<0.4278,

0.5722,

0.5722>

<0.4062,

0.5938,

0.5938>

<0.6375,

0.3625,

0.3625>

<0.4518,

0.5482,

0. 5482>

0.9776 5

A3

<0.4342,

0.5658,

0.5658>

<0.4322,

0.5678,

0.5678>

<0.3187,

0.6813,

0.6813>

<0.3033,

0.6967,

0. 6967>

1.2844 2

A4

<0.4579,

0.5421,

0.5421>

<0.4137,

0.5863,

0.5863>

<0.5976,

0.4024,

0.4024>

<0.3162,

0.6838,

0.6838>

1.0597 4

A5

<0.3804,

0.6196,

0.6196>

<0.3292,

0.6708,

0.6708>

<0.2390,

0.7610,

0.7610>

<0.5163,

0.4837,

0.4837>

1.3118 1

<0.0000,

1.0000,

1.0000>

<0.0000,

1.0000,

1.0000>

<0.0000,

1.0000,

1.0000>

<0.0000,

1.0000,

1.0000>

0.8707 0.7896 0.6406 0.7897

0.1422 0.2313 0.3952 0.2313 1.0000

4.9.3 Proposed Method 3: F-SVNS-ACC-MADM for Cutting Fluid (Coolant)

Selection




TABLE 4.55: F-SVNS ACC-MADM Ranking for Cutting Fluid Selection

Sr.

No. A1 (-) A2 (-) A3 (-) A4 (-) Rank

A1

<0.5235,

0.4765,

0.4765>

<0.6072,

0.3928,

0.3928>

<0.2789,

0.7211,

0.7211>

<0.5808,

0.4192,

0.4192>

0.5024 5

A2 <0.4278,

0.5722,

<0.4062,

0.5938,

<0.6375,

0.3625,

<0.4518,

0.5482, 0.5192 4


146

0.5722> 0.5938> 0.3625> 0. 5482>

A3

<0.4342,

0.5658,

0.5658>

<0.4322,

0.5678,

0.5678>

<0.3187,

0.6813,

0.6813>

<0.3033,

0.6967,

0. 6967>

0.6279 2

A4

<0.4579,

0.5421,

0.5421>

<0.4137,

0.5863,

0.5863>

<0.5976,

0.4024,

0.4024>

<0.3162,

0.6838,

0.6838>

0.5536 3

A5

<0.3804,

0.6196,

0.6196>

<0.3292,

0.6708,

0.6708>

<0.2390,

0.7610,

0.7610>

<0.5163,

0.4837,

0.4837>

0.6338 1

<0.0000,

1.0000,

1.0000>

<0.0000,

1.0000,

1.0000>

<0.0000,

1.0000, 1.0000>

<0.0000,

1.0000,

1.0000>

4.9.4 Performance Measures Comparison: Cutting Fluids Ranking


validate them for cutting fluid selection. To compare the result, all cutting fluid alternatives

are ranked according to alternatives weight values is as shown in Table 4.56. The cutting

fluid alternative is ranked first whose alternative weight value is highest; cutting fluid

alternative is ranked second whose alternatives weight values is second highest. Finally the

ranking orders obtained by the proposed three different methodologies are compared with

the ranking order published in the literature and result comparisons are shown in Table

4.56.

TABLE 4.56: Cutting Fluid Selection Performance Measures Comparison

Alternatives

(Sr. No.)

F-SVNS MADMs Collected ranking solution from (Rao 2007)

Novel Entropy

Weight ACC GTMA SAW WPM AHP TOPSIS

Modified

TOPSIS

A1 5 3 5 5 5 5 5 3 4

A2 4 5 4 4 3 4 4 5 5

A3 2 2 2 2 2 2 2 2 2

A4 3 4 3 3 4 3 3 4 3

A5 1 1 1 1 1 1 1 1 1


proposed methodologies are quite similar to the result of reported in the literature.

The proposed method suggests the cutting fluid alternative A5 as the best cutting fluid,

which is same as suggested by (Rao 2007). (Rao 2007) solved same cutting fluid selection

problem by using GTMA, SAW, WPM, AHP, TOPSIS and modified TOPSIS.

Further, 2nd

rank is calculated by all proposed methods matched with all published results.

While 4th

rank is calculated by F-SVVNS N-MADM, F-SVNS ACC-MADM methods

matched with GTMA, WPM, and AHP, while other MADM like SAW, TOPSIS and


147

modified TOPSIS methodologies published results their selves not match among each

other, due to different weight criteria calculation/ assumption/ expert opinion or same

equation of normalization/ without normalization. 4th

rank of proposed F-SVNS EW-

MADM shows A4 which is matched with AHP, TOPSIS. It shows that the weight criteria

and normalization equation/ method make change in rank position in further ranking result,

but it hold well for the first ranking purpose.


4.12. GTMA and TOPSIS method are lengthy and requires more complex calculations.

The ranking order and selection indicates that results obtained using proposed method

matches with published results without solving size of matrix using computer

programming. Proposed methodologies work with minimum calculations, without

calculating any kind of relative importance of attributes, without the need to resize the

assignment matrix and it is gifted to convert simple set or lingustic set to F-SVNS. The

weaknesses of GTMA, TOPSIS, modified TOPSIS and AHP are already discussed in

chapter 2.





cutting fluid (coolant) selection for manufacturing environment which leads to improve


4.10 Collected Case Example 10: Supplier Selection

Step 1. One case example of supplier selection was adopted and demonstrate by (Liu et

al. 2000) with DEA. The same case example was further calculated by (Kuo et al. 2008)

with DEA non-parametric approach. (Rao 2007) was calculated the same matrix with

GTMA, SAW, WPM, AHP, TOPSIS and modified TOPSIS methodology.

Step 2. Here, (Rao 2007) explained that in input matrix contains eighteen different

alternatives with five attributes. As per (Rao 2007) attributes measures are C1: supply

variety, means the company first listed all parts supplied by each vendor to obtained the

supply variety. (Rao 2007) explained that, if a vendor supplies more than one commodity

group, then the supply variety of this vendor in each group is the sum of the number of part


148

in the entire group. C2: aggregate quality with their weighted percentage of non-defective

parts supplied by the supplier with regard to alternatives, C3: Distance (in Mile), C4:

delivery is represented by percentage of purchase order within the delivery window

according to purchase order, C5: price index, average prices were assigned to each part by

the material department of the company. Where, (Rao 2007) considered that beneficial

attributes are C1 (Supply variety), C2 (aggregate quality), C4 (delivery) and C5 (price

index) are the desirable criteria; whereas Non-beneficial attribute is C3 (distance) is non-

desirable/ non beneficial criteria.

Step 3. Decision matrix is collected (Liu et al. 2000), (Kuo et al. 2008), (Rao 2007) and

(Das and Srinivas 2013) shown in Table 4.57

TABLE 4.57: Supplier Selection Input Matrix (Collected Case Example)

Alternatives (Sr. No.) C1 (+) C2 (+) C3 (-) C4 (+) C5 (+)

A1 2 100 249 90 100

A2 13 99.79 643 80 100

A3 3 100 714 90 100

A4 3 100 1809 90 100

A5 24 99.83 238 90 100

A6 28 96.59 241 90 100

A7 1 100 1404 85 100

A8 24 100 984 97 100

A9 11 99.91 641 90 100

A10 53 97.54 588 100 100

A11 10 99.95 241 95 100

A12 7 99.85 567 98 100

A13 19 99.97 567 90 100

A14 12 91.89 967 90 100

A15 33 99.99 635 95 80

A16 2 100 795 95 100

A17 34 99.99 689 95 80

A18 9 99.36 913 85 100

Collected from the Source: (Liu et al. 2000), (Kuo et al. 2008), (Rao 2007), (Das and Srinivas 2013)


As per (Nirmal and Bhatt 2019),(Kahraman and Otay 2019), Here, the input information

contains quantitative information only, so there is no need to convert qualitative value in to

quantitative value. So, this step is eliminated in the current case example.


Supplier selection normalized matrix is shown in Table 4.58.


149

TABLE 4.58: Supplier Selection Normalized Matrix using VNM

Alternatives (Sr. No.) C1 (+) C2 (+) C3 (-) C4 (+) C5 (+)

A1 0.0223 0.2377 0.9283 0.2318 0.2406

A2 0.1450 0.2372 0.8148 0.2060 0.2406

A3 0.0335 0.2377 0.7943 0.2318 0.2406

A4 0.0335 0.2377 0.4788 0.2318 0.2406

A5 0.2676 0.2373 0.9314 0.2318 0.2406

A6 0.3122 0.2296 0.9306 0.2318 0.2406

A7 0.0112 0.2377 0.5955 0.2189 0.2406

A8 0.2676 0.2377 0.7165 0.2498 0.2406

A9 0.1227 0.2375 0.8153 0.2318 0.2406

A10 0.5910 0.2318 0.8306 0.2575 0.2406

A11 0.1115 0.2376 0.9306 0.2447 0.2406

A12 0.0781 0.2373 0.8366 0.2524 0.2406

A13 0.2119 0.2376 0.8366 0.2318 0.2406

A14 0.1338 0.2184 0.7214 0.2318 0.2406

A15 0.3680 0.2377 0.8171 0.2447 0.1925

A16 0.0223 0.2377 0.7710 0.2447 0.2406

A17 0.3791 0.2377 0.8015 0.2447 0.1925

A18 0.1004 0.2362 0.7370 0.2189 0.2406







same calculation is also carried out for attribute C2, C4 and C5.




⟨ ⟩ ⟨ ⟩.


solution.



⟩

⟨ ⟩ and ⟨

⟩ ⟨ ⟩.

4.10.1 Proposed Method 1: 1 F-SVNS-N-MADM for Supplier Selection



150



TABLE 4.59: F-SVNS N-MADM Ranking for Supplier Selection

Sr. No. C1 (+) C2 (+) C3 (-) C4 (+) C5 (+) Rank

A1

<0.0223,

0.9777,

0.9777>

<0.2377,

0.7623,

0.7623>

<0.0717,

0.9283,

0.9283>

<0.2318,

0.7682,

0.7682>

<0.2406,

0.7594,

0.7594>

2.5889 8

A2

<0.1450,

0.8550,

0.8550>

<0.2372,

0.7628,

0.7628>

<0.1852,

0.8148,

0.8148>

<0.2060,

0.7940,

0.7940>

<0.2406,

0.7594,

0.7594>

2.4583 11

A3

<0.0335,

0.9665,

0.9665>

<0.2377,

0.7623,

0.7623>

<0.2057,

0.7943,

0.7943>

<0.2318,

0.7682,

0.7682>

<0.2406,

0.7594,

0.7594>

2.3321 13

A4

<0.0335,

0.9665,

0.9665>

<0.2377,

0.7623,

0.7623>

<0.5212,

0.4788,

0.4788>

<0.2318,

0.7682,

0.7682>

<0.2406,

0.7594,

0.7594>

1.7012 18

A5

<0.2676,

0.7324,

0.7324>

<0.2373,

0.7627,

0.7627>

<0.0686,

0.9314,

0.9314>

<0.2318,

0.7682,

0.7682>

<0.2406,

0.7594,

0.7594>

2.8401 3

A6

<0.3122,

0.6878,

0.6878>

<0.2296,

0.7704,

0.7704>

<0.0694,

0.9306,

0.9306>

<0.2318,

0.7682,

0.7682>

<0.2406,

0.7594,

0.7594>

2.8753 2

A7

<0.0112,

0.9888,

0.9888>

<0.2377,

0.7623,

0.7623>

<0.4045,

0.5955,

0.5955>

<0.2189,

0.7811,

0.7811>

<0.2406,

0.7594,

0.7594>

1.8993 17

A8

<0.2676,

0.7324,

0.7324>

<0.2377,

0.7623,

0.7623>

<0.2835,

0.7165,

0.7165>

<0.2498,

0.7502,

0.7502>

<0.2406,

0.7594,

0.7594>

2.4287 12

A9

<0.1227,

0.8773,

0.8773>

<0.2375,

0.7625,

0.7625>

<0.1847,

0.8153,

0.8153>

<0.2318,

0.7682,

0.7682>

<0.2406,

0.7594,

0.7594>

2.4631 10

A10

<0.5910,

0.4090,

0.4090>

<0.2318,

0.7682,

0.7682>

<0.1694,

0.8306,

0.8306>

<0.2575,

0.7425,

0.7425>

<0.2406,

0.7594,

0.7594>

2.9821 1

A11

<0.1115,

0.8885,

0.8885>

<0.2376,

0.7624,

0.7624>

<0.0694,

0.9306,

0.9306>

<0.2447,

0.7553,

0.7553>

<0.2406,

0.7594,

0.7594>

2.6954 4

A12

<0.0781,

0.9219,

0.9219>

<0.2373,

0.7627,

0.7627>

<0.1634,

0.8366,

0.8366>

<0.2524,

0.7476,

0.7476>

<0.2406,

0.7594,

0.7594>

2.4816 9

A13

<0.2119,

0.7881,

0.7881>

<0.2376,

0.7624,

0.7624>

<0.1634,

0.8366,

0.8366>

<0.2318,

0.7682,

0.7682>

<0.2406,

0.7594,

0.7594>

2.5951 7

A14

<0.1338,

0.8662,

0.8662>

<0.2184,

0.7816,

0.7816>

<0.2786,

0.7214,

0.7214>

<0.2318,

0.7682,

0.7682>

<0.2406,

0.7594,

0.7594>

2.2674 16

A15

<0.3680,

0.6320,

0.6320>

<0.2377,

0.7623,

0.7623>

<0.1829,

0.8171,

0.8171>

<0.2447,

0.7553,

0.7553>

<0.1925,

0.8075,

0.8075>

2.6769 5

A16

<0.0223,

0.9777,

0.9777>

<0.2377,

0.7623,

0.7623>

<0.2290,

0.7710,

0.7710>

<0.2447,

0.7553,

0.7553>

<0.2406,

0.7594,

0.7594>

2.2871 14

A17

<0.3791,

0.6209,

0.6209>

<0.2377,

0.7623,

0.7623>

<0.1985,

0.8015,

0.8015>

<0.2447,

0.7553,

0.7553>

<0.1925,

0.8075,

0.8075>

2.6569 6


151

A18

<0.1004,

0.8996,

0.8996>

<0.2362,

0.7638,

0.7638>

<0.2630,

0.7370,

0.7370>

<0.2189,

0.7811,

0.7811>

<0.2406,

0.7594,

0.7594>

2.2699 15

<1.0000,

0.0000,

0.0000>

<0.0000,

1.0000,

1.0000>

<0.0000,

1.0000,

1.0000>

<1.0000,

0.0000,

0.0000>

<1.0000,

0.0000,

0.0000>

4.10.2 Proposed Method 2: F-SVNS-EW-MADM for Supplier Selection




TABLE 4.60: F-SVNS EW-MADM Ranking for Supplier Selection

Sr. No. C1 (+) C2 (+) C3 (-) C4 (+) C5 (+) Ran

k

A1

<0.0223,

0.9777,

0.9777>

<0.2377,

0.7623,

0.7623>

<0.0717,

0.9283,

0.9283>

<0.2318,

0.7682,

0.7682>

<0.2406,

0.7594,

0.7594>

0.5241 8

A2

<0.1450,

0.8550,

0.8550>

<0.2372,

0.7628,

0.7628>

<0.1852,

0.8148,

0.8148>

<0.2060,

0.7940,

0.7940>

<0.2406,

0.7594,

0.7594>

0.5005 10

A3

<0.0335,

0.9665,

0.9665>

<0.2377,

0.7623,

0.7623>

<0.2057,

0.7943,

0.7943>

<0.2318,

0.7682,

0.7682>

<0.2406,

0.7594,

0.7594>

0.4709 13

A4

<0.0335,

0.9665,

0.9665>

<0.2377,

0.7623,

0.7623>

<0.5212,

0.4788,

0.4788>

<0.2318,

0.7682,

0.7682>

<0.2406,

0.7594,

0.7594>

0.3394 18

A5

<0.2676,

0.7324,

0.7324>

<0.2373,

0.7627,

0.7627>

<0.0686,

0.9314,

0.9314>

<0.2318,

0.7682,

0.7682>

<0.2406,

0.7594,

0.7594>

0.5826 3

A6

<0.3122,

0.6878,

0.6878>

<0.2296,

0.7704,

0.7704>

<0.0694,

0.9306,

0.9306>

<0.2318,

0.7682,

0.7682>

<0.2406,

0.7594,

0.7594>

0.5912 2

A7

<0.0112,

0.9888,

0.9888>

<0.2377,

0.7623,

0.7623>

<0.4045,

0.5955,

0.5955>

<0.2189,

0.7811,

0.7811>

<0.2406,

0.7594,

0.7594>

0.3805 17

A8

<0.2676,

0.7324,

0.7324>

<0.2377,

0.7623,

0.7623>

<0.2835,

0.7165,

0.7165>

<0.2498,

0.7502,

0.7502>

<0.2406,

0.7594,

0.7594>

0.4965 12

A9

<0.1227,

0.8773,

0.8773>

<0.2375,

0.7625,

0.7625>

<0.1847,

0.8153,

0.8153>

<0.2318,

0.7682,

0.7682>

<0.2406,

0.7594,

0.7594>

0.5004 11

A10

<0.5910,

0.4090,

0.4090>

<0.2318,

0.7682,

0.7682>

<0.1694,

0.8306,

0.8306>

<0.2575,

0.7425,

0.7425>

<0.2406,

0.7594,

0.7594>

0.6198 1

A11

<0.1115,

0.8885,

0.8885>

<0.2376,

0.7624,

0.7624>

<0.0694,

0.9306,

0.9306>

<0.2447,

0.7553,

0.7553>

<0.2406,

0.7594,

0.7594>

0.5482 5

A12

<0.0781,

0.9219,

0.9219>

<0.2373,

0.7627,

0.7627>

<0.1634,

0.8366,

0.8366>

<0.2524,

0.7476,

0.7476>

<0.2406,

0.7594,

0.7594>

0.5027 9

A13 <0.2119, <0.2376, <0.1634, <0.2318, <0.2406, 0.5301 7


152

0.7881,

0.7881>

0.7624,

0.7624>

0.8366,

0.8366>

0.7682,

0.7682>

0.7594,

0.7594>

A14

<0.1338,

0.8662,

0.8662>

<0.2184,

0.7816,

0.7816>

<0.2786,

0.7214,

0.7214>

<0.2318,

0.7682,

0.7682>

<0.2406,

0.7594,

0.7594>

0.4603 15

A15

<0.3680,

0.6320,

0.6320>

<0.2377,

0.7623,

0.7623>

<0.1829,

0.8171,

0.8171>

<0.2447,

0.7553,

0.7553>

<0.1925,

0.8075,

0.8075>

0.5518 4

A16

<0.0223,

0.9777,

0.9777>

<0.2377,

0.7623,

0.7623>

<0.2290,

0.7710,

0.7710>

<0.2447,

0.7553,

0.7553>

<0.2406,

0.7594,

0.7594>

0.4609 14

A17

<0.3791,

0.6209,

0.6209>

<0.2377,

0.7623,

0.7623>

<0.1985,

0.8015,

0.8015>

<0.2447,

0.7553,

0.7553>

<0.1925,

0.8075,

0.8075>

0.5480 6

A18

<0.1004,

0.8996,

0.8996>

<0.2362,

0.7638,

0.7638>

<0.2630,

0.7370,

0.7370>

<0.2189,

0.7811,

0.7811>

<0.2406,

0.7594,

0.7594>

0.4599 16

<1.0000,0.000

0, 0.0000>

<0.0000,

1.0000,

1.0000>

<0.0000,

1.0000,

1.0000>

<1.0000,

0.0000,

0.0000>

<1.0000,

0.0000,

0.0000>

0.3366 0.4713 0.4078 0.4707 0.4704

0.2333 0.1860 0.2083 0.1862 0.1862 1

4.10.3 Proposed Method 3: F-SVNS ACC MADM for Supplier Selection


The calculations of step 8 and step 9 are shown briefly in the Annexure -C [10]. The rank

is calculated with F-SVNS-EW-MADM is as shown in Table 4.61

TABLE 4.61: F-SVNS ACC-MADM Ranking for Supplier Selection

Sr. No. C1 (+) C2 (+) C3 (-) C4 (+) C5 (+) Rank

A1

<0.0223,

0.9777,

0.9777>

<0.2377,

0.7623,

0.7623>

<0.0717,

0.9283,

0.9283>

<0.2318,

0.7682,

0.7682>

<0.2406,

0.7594,

0.7594>

0.4315 8

A2

<0.1450,

0.8550,

0.8550>

<0.2372,

0.7628,

0.7628>

<0.1852,

0.8148,

0.8148>

<0.2060,

0.7940,

0.7940>

<0.2406,

0.7594,

0.7594>

0.4097 11

A3

<0.0335,

0.9665,

0.9665>

<0.2377,

0.7623,

0.7623>

<0.2057,

0.7943,

0.7943>

<0.2318,

0.7682,

0.7682>

<0.2406,

0.7594,

0.7594>

0.3887 13

A4

<0.0335,

0.9665,

0.9665>

<0.2377,

0.7623,

0.7623>

<0.5212,

0.4788,

0.4788>

<0.2318,

0.7682,

0.7682>

<0.2406,

0.7594,

0.7594>

0.2835 18

A5

<0.2676,

0.7324,

0.7324>

<0.2373,

0.7627,

0.7627>

<0.0686,

0.9314,

0.9314>

<0.2318,

0.7682,

0.7682>

<0.2406,

0.7594,

0.7594>

0.4734 3

A6

<0.3122,

0.6878,

0.6878>

<0.2296,

0.7704,

0.7704>

<0.0694,

0.9306,

0.9306>

<0.2318,

0.7682,

0.7682>

<0.2406,

0.7594,

0.7594>

0.4792 2

A7

<0.0112,

0.9888,

0.9888>

<0.2377,

0.7623,

0.7623>

<0.4045,

0.5955,

0.5955>

<0.2189,

0.7811,

0.7811>

<0.2406,

0.7594,

0.7594>

0.3166 17


153

A8

<0.2676,

0.7324,

0.7324>

<0.2377,

0.7623,

0.7623>

<0.2835,

0.7165,

0.7165>

<0.2498,

0.7502,

0.7502>

<0.2406,

0.7594,

0.7594>

0.4048 12

A9

<0.1227,

0.8773,

0.8773>

<0.2375,

0.7625,

0.7625>

<0.1847,

0.8153,

0.8153>

<0.2318,

0.7682,

0.7682>

<0.2406,

0.7594,

0.7594>

0.4105 10

A10

<0.5910,

0.4090,

0.4090>

<0.2318,

0.7682,

0.7682>

<0.1694,

0.8306,

0.8306>

<0.2575,

0.7425,

0.7425>

<0.2406,

0.7594,

0.7594>

0.4970 1

A11

<0.1115,

0.8885,

0.8885>

<0.2376,

0.7624,

0.7624>

<0.0694,

0.9306,

0.9306>

<0.2447,

0.7553,

0.7553>

<0.2406,

0.7594,

0.7594>

0.4492 4

A12

<0.0781,

0.9219,

0.9219>

<0.2373,

0.7627,

0.7627>

<0.1634,

0.8366,

0.8366>

<0.2524,

0.7476,

0.7476>

<0.2406,

0.7594,

0.7594>

0.4136 9

A13

<0.2119,

0.7881,

0.7881>

<0.2376,

0.7624,

0.7624>

<0.1634,

0.8366,

0.8366>

<0.2318,

0.7682,

0.7682>

<0.2406,

0.7594,

0.7594>

0.4325 7

A14

<0.1338,

0.8662,

0.8662>

<0.2184,

0.7816,

0.7816>

<0.2786,

0.7214,

0.7214>

<0.2318,

0.7682,

0.7682>

<0.2406,

0.7594,

0.7594>

0.3779 16

A15

<0.3680,

0.6320,

0.6320>

<0.2377,

0.7623,

0.7623>

<0.1829,

0.8171,

0.8171>

<0.2447,

0.7553,

0.7553>

<0.1925,

0.8075,

0.8075>

0.4461 5

A16

<0.0223,

0.9777,

0.9777>

<0.2377,

0.7623,

0.7623>

<0.2290,

0.7710,

0.7710>

<0.2447,

0.7553,

0.7553>

<0.2406,

0.7594,

0.7594>

0.3811 14

A17

<0.3791,

0.6209,

0.6209>

<0.2377,

0.7623,

0.7623>

<0.1985,

0.8015,

0.8015>

<0.2447,

0.7553,

0.7553>

<0.1925,

0.8075,

0.8075>

0.4428 6

A18

<0.1004,

0.8996,

0.8996>

<0.2362,

0.7638,

0.7638>

<0.2630,

0.7370,

0.7370>

<0.2189,

0.7811,

0.7811>

<0.2406,

0.7594,

0.7594>

0.3783 15

<1.0000,

0.0000,

0.0000>

<0.0000,

1.0000,

1.0000>

<0.0000,

1.0000,

1.0000>

<1.0000,

0.0000,

0.0000>

<1.0000,

0.0000,

0.0000>

4.10.4 Performance Measures Comparison: Suppliers Ranking


validate them for supplier selection. To compare the result, all supplier alternatives are

ranked according to alternatives weight values is as shown in Table 4.62. The supplier

alternatives are ranked first whose alternative weight value is highest; supplier alternative

is ranked second whose alternatives weight values is second highest. Finally the ranking

order obtained by the proposed three methodologies is compared with the ranking order

published in the literature and result comparisons are shown in Table 4.62.


154

TABLE 4.62: Supplier Selection Performance Measures Comparison

Alternatives

(Sr. No.)

F-SVNS MADMs

Ranking Solution

Collected from

(Liu et al. 2000)

Ranking Solution

Collected from (Rao 2007)

Novel Entropy

Weight ACC DEA* GTMA TOPSIS

A1 8 8 8 9 7 12

A2 11 10 11 10 12 11

A3 13 13 13 14 15 15

A4 18 18 18 15 17 17

A5 3 3 3 3 2 5

A6 2 2 2 7 1 4

A7 17 17 17 17 18 18

A8 12 12 12 6 9 6

A9 10 11 10 11 11 10

A10 1 1 1 1 3 1

A11 4 5 4 5 6 8

A12 9 9 9 12 10 9

A13 7 7 7 8 8 7

A14 16 15 16 18 13 14

A15 5 4 5 4 4 3

A16 14 14 14 16 16 13

A17 6 6 6 2 5 2

A18 15 16 15 13 14 16


proposed methodologies are quite similar to the result of reported in the literature.

The proposed method suggesting the supplier alternative A10 as the best supplier, which is

same as suggests by (Liu et al. 2000), (Rao 2007) and (Liu et al. 2000) tried to solve same

supplier selection problem by using DEA mathematical technique.

Further, 2nd

rank is calculated by proposed methods doesn‘t match with all published

results. While 4th

rank is calculated by F-SVVNS N-MADM, F-SVNS ACC-MADM

methods doesn‘t match with all published results, F-SVVNS EW-MADM and modified

TOPSIS methodologies published results their selves not match among each other, due to

different weight criteria calculation/ assumption/ expert opinion or same equation of

normalization/ without normalization. 4th

rank of proposed F-SVNS EW-MADM shows

A15 which is matched with DEA, GTMA. It shows that the weight criteria and

normalization equation/ method make change in rank position in further ranking result, but

it hold well for the first ranking purpose.


4.12. The proposed methodologies work with minimum calculations, without calculating

any kind of relative importance of attributes, not need to resize the assignment matrix and


155

it is gifted to convert simple set or lingustic set to F-SVNS technique when compared with

DEA. (Rao 2007) calculated the same problem with the help of GTMA and TOPSIS,

Where TOPSIS suggest supplier alternative 10th

as the best supplier, while through GTMA

methodology alternative 6th

as the best supplier. There is normal change in the rank due to

only one reason which is value of attribute weight. Proposed methodologies work with

minimum calculations, without calculating any kind of relative importance of attributes,

Without the need to resize the assignment matrix and it is gifted to convert simple set or

lingustic set to F-SVNS.





supplier selection for manufacturing environment which leads to improve manufacturing

function.

4.11 Collected Case Example 11: Third Party Reverse Logistic

Provider’s (TPRLP) Selection

Step 1. One case example of third party reverse logistic providers (TPRLP) selection

application in batteries recycling industry in the India was carried out for reducing the total

cost of battery manufacturing the spent or used lead acid batteries are collected by the

TPRLP by (Kannan et al. 2009) was solved using IFS and fuzzy TOPSIS. The (Kannan et

al. 2009) was solved same case example with MAGDM where five different decision

makers give the input value for each alternative and attribute. The normalized decision

matrix not in equal range of [0, 1], here that normalized matrix considered as the input

decision matrix and all other calculation is carried out with proposed methodologies.

Step 2. The given matrix considering seven different attributes C1: Quality C2: Product

delivery, C3: Reverse logistic cost, C4: Rejection rate, C5: Technical/ Engineering

capability, C6: Inability to meet future requirement, C7: willingness and attitude and 15

different third party logistics providers are considered as alternatives. Here, beneficial

attributes are C1, C5, C6 and C7; whereas Non-beneficial attributes are C2, C3 and C4.

Step 3. Decision matrix was collected from (Kannan et al. 2009) is as shown in Table

4.63.

4.11 Collected Case Example 11: Third Party Reverse Logistic Provider‘s (TPRLP) Selection

156

TABLE 4.63: TPRLP Selection Input Matrix (Collected Case Example)

Alternatives

(Sr. No.) C1 (+) C2 (-) C3 (-) C4 (-) C5 (+) C6 (+) C7 (+)

A1 4.2120 6.5052 6.8226 0.8490 4.9471 3.7552 3.8280

A2 0.7281 0.7654 5.4753 5.0511 4.3123 3.5963 2.0020

A3 2.3660 6.5052 7.1378 5.2845 1.1164 1.9932 3.8280

A4 6.4738 3.7720 1.1467 5.4118 5.9539 3.7552 0.9900

A5 7.0457 3.4440 3.9560 5.1571 4.0715 3.6830 0.8800

A6 1.3260 2.5147 4.9880 4.1810 0.5035 0.5778 1.7600

A7 6.6298 6.0132 1.6054 5.4118 0.8756 2.6865 2.0240

A8 4.8099 1.6947 6.4786 5.1571 4.3123 3.6830 5.1039

A9 4.8360 5.5486 7.3098 2.1860 2.5173 2.6865 3.8280

A10 5.8759 6.0132 6.5073 4.1810 5.5818 1.6465 4.5759

A11 5.1219 1.2300 6.9658 4.6690 1.7512 3.8418 4.8620

A12 4.8360 4.4280 7.1378 1.1885 4.3123 3.2641 5.2359

A13 0.8841 1.3940 7.1378 4.4144 0.8756 2.8453 5.2359

A14 6.6298 6.5052 3.6120 5.2845 3.8089 3.0042 5.9838

A15 4.8099 6.0132 3.2680 4.9237 4.3123 0.7366 2.0020

Collected from the source (Kannan et al. 2009)




case example.

Step: 5 Normalization of Table 4.63 is carried out with the Equation 3.1/ Equation 3.2.

TPRLP selection normalized matrix is shown in Table 4.64.

TABLE 4.64: TPRLP Selection Normalized Matrix using VNM

Alternatives

(Sr. No.) C1 (+) C2 (-) C3 (-) C4 (-) C5 (+) C6 (+) C7 (+)

A1 0.2221 0.6392 0.6898 0.9510 0.3422 0.3259 0.2568

A2 0.0384 0.9576 0.7511 0.7086 0.2983 0.3121 0.1343

A3 0.1248 0.6392 0.6755 0.6952 0.0772 0.1730 0.2568

A4 0.3414 0.7908 0.9479 0.6878 0.4119 0.3259 0.0664

A5 0.3715 0.8090 0.8201 0.7025 0.2816 0.3196 0.0590

A6 0.0699 0.8605 0.7732 0.7588 0.0348 0.0501 0.1181

A7 0.3496 0.6665 0.9270 0.6878 0.0606 0.2331 0.1358

A8 0.2536 0.9060 0.7055 0.7025 0.2983 0.3196 0.3424

A9 0.2550 0.6923 0.6677 0.8739 0.1741 0.2331 0.2568

A10 0.3098 0.6665 0.7042 0.7588 0.3861 0.1429 0.3070

A11 0.2701 0.9318 0.6833 0.7307 0.1211 0.3334 0.3262

A12 0.2550 0.7544 0.6755 0.9314 0.2983 0.2833 0.3513

A13 0.0466 0.9227 0.6755 0.7454 0.0606 0.2469 0.3513

A14 0.3496 0.6392 0.8358 0.6952 0.2635 0.2607 0.4014

A15 0.2536 0.6665 0.8514 0.7160 0.2983 0.0639 0.1343





157




same calculation is also carried out for attribute C5, C6 and C7.





calculation is also carried out for attribute C3, C4.


solution.



⟩

⟨ ⟩ and ⟨

⟩ ⟨ ⟩.

4.11.1 Proposed Method 1: F-SVNS-N-MADM for TPRLP Selection




TABLE 4.65: F-SVNS N-MADM Ranking for TPRLP Selection

Sr.

No. C1 (+) C2 (-) C3 (-) C4 (-) C5 (+) C6 (+) C7 (+) Rank

A1

<0.2221,

0.7779,

0.7779>

<0.3608,

0.6392,

0.6392>

<0.3102,

0.6898,

0.6898>

<0.0490,

0.9510,

0.9510>

<0.3422,

0.6578,

0.6578>

<0.3259,

0.6741,

0. 6741>

<0.2568,

0.7432,

0. 7432>

5.7071 5

A2

<0.0384,

0.9616,

0.9616>

<0.0424,

0.9576,

0.9576>

<0.2489,

0.7511,

0. 7511>

<0.2914,

0.7086,

0.7086>

<0.2983,

0.7017,

0.7017>

<0.2546,

0.7454,

0.7454>

<0.1343,

0.8657,

0.8657>

5.6176 7

A3

<0.1248,

0.8752,

0.8752>

<0.3608,

0.6392,

0.6392>

<0.3245,

0.6755,

0. 6755>

<0.3048,

0.6952,

0.6952>

<0.0772,

0.9228,

0.9228>

<0.4018,

0.5982,

0.5982>

<0.2568,

0.7432,

0.7432>

4.6515 15

A4

<0.3414,

0.6586,

0.6586>

<0.2092,

0.7908,

0.7908>

<0.0521,

0.9479,

0.9479>

<0.3122,

0.6878,

0.6878>

<0.4119,

0.5881,

0.5881>

<0.3225,

0.6775,

0.6775>

<0.0664,

0.9336,

0.9336>

5.9985 1

A5

<0.3715,

0.6285,

0.6285>

<0.1910,

0.8090,

0.8090>

<0.1799,

0.8201,

0.8201>

<0.2975,

0.7025,

0.7025>

<0.2816,

0.7184,

0.7184>

<0.1188,

0.8812,

0.8812>

<0.0590,

0.9410,

0.9410>

5.6951 6

A6 <0.0699,

0.9301,

<0.1395,

0.8605,

<0.2268,

0.7732,

<0.2412,

0.7588,

<0.0348,

0.9652,

<0.0283,

0.9717,

<0.1181,

0.8819, 5.0581 14


158

0.9301> 0.8605> 0.7732> 0.7588> 0.9652> 0.9717> 0.8819>

A7

<0.3496,

0.6504,

0.6504>

<0.3335,

0.6665,

0.6665>

<0.0730,

0.9270,

0.9270>

<0.3122,

0.6878,

0.6878>

<0.0606,

0.9394,

0. 9394>

<0.1981,

0.8019,

0.8019>

<0.1358,

0.8642,

0.8642>

5.3418 12

A8

<0.2536,

0.7464,

0.7464 >

<0.0940,

0.9060,

0.9060>

<0.2945,

0.7055,

0.7055>

<0.2975,

0.7025,

0.7025>

<0.2983,

0.7017,

0. 7017>

<0.1811,

0.8189,

0.8189>

<0.3424,

0.6576,

0.6576>

5.8419 3

A9

<0.2550,

0.7450,

0.7450 >

<0.3077,

0.6665,

0.6665>

<0.3323,

0.6677,

0.6677>

<0.1261,

0.8739,

0.8739>

<0.1741,

0.8259,

0.8259>

<0.1358,

0.8642,

0.8642>

<0.2568,

0.7432,

0.7432>

5.3868 11

A10

<0.3098,

0.6902,

0.6902 >

<0.3335,

0.6665,

0.6665>

<0.2958,

0.7042,

0.7042>

<0.2412,

0.7588,

0.7588>

<0.3861,

0.6139,

0.6139>

<0.1924,

0.8076,

0.8076>

<0.3070,

0.6930,

0.6930>

5.4048 9

A11

<0.2701,

0.7299,

0.7299 >

<0.0682,

0.9318,

0.9318>

<0.3167,

0.6833,

0.6833>

<0.2693,

0.7307,

0.7307>

<0.1211,

0.8789,

0.8789>

<0.3056,

0.6944,

0.6944>

<0.3262,

0.6738,

0.6738>

5.7423 4

A12

<0.2550,

0.7450,

0.7450 >

<0.2456,

0.7544,

0.7544>

<0.3245,

0.6755,

0.6755>

<0.0686,

0.9314,

0.9314>

<0.2983,

0.7017,

0.7017>

<0.0679,

0.9321,

0.9321>

<0.3513,

0.6487,

0.6487>

5.9105 2

A13

<0.0466,

0.9534,

0.9534 >

<0.0773,

0.9227,

0.9227>

<0.3245,

0.6755,

0.6755>

<0.2546,

0.7454,

0.7454>

<0.0606,

0.9394,

0.9394>

<0.3678,

0.6322,

0.6322>

<0.3513,

0.6487,

0.6487>

5.3924 10

A14

<0.3496,

0.6504,

0.6504 >

<0.3608,

0.6392,

0.6392>

<0.1642,

0.8358,

0.8358>

<0.3048,

0.6952,

0.6952>

<0.2635,

0.7365,

0.7365>

<0.2320,

0.7680,

0.7680>

<0.4014,

0.5986,

0.5986>

5.6156 8

A15

<0.2536,

0.7464,

0.7464 >

<0.3335,

0.6665,

0.6665>

<0.1486,

0.8514,

0.8514>

<0.2840,

0.7160,

0.7160>

<0.2983,

0.7017,

0.7017>

<0.3961,

0.6039,

0.6039>

<0.1343,

0.8657,

0.8657>

5.2180 13

<1.000,

0.0000,

0.0000>

<0.0000,

1.0000,

1.0000>

<0.0000,

1.0000,

1.0000>

<0.0000,1.

0000,

1.0000>

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>

4.11.2 Proposed Method 2: F-SVNS-EW-MADM for TPRLP Selection




TABLE 4.66: F-SVNS EW-MADM Ranking for TPRLP Selection

Sr. No. A1 (+) A2 (-) A3 (-) A4 (-) A5 (+) A6 (+) A7 (+) Rank

A1

<0.2221,

0.7779,

0.7779>

<0.3608,

0.6392,

0.6392>

<0.3102,

0.6898,

0.6898>

<0.0490,

0.9510,

0.9510>

<0.3422,

0.6578,

0.6578>

<0.3259,

0.6741,

0. 6741>

<0.2568,

0.7432,

0. 7432>

0.8084 6

A2

<0.0384,

0.9616,

0.9616>

<0.0424,

0.9576,

0.9576>

<0.2489,

0.7511,

0. 7511>

<0.2914,

0.7086,

0.7086>

<0.2983,

0.7017,

0.7017>

<0.2546,

0.7454,

0.7454>

<0.1343,

0.8657,

0.8657>

0.7986 7

A3

<0.1248,

0.8752,

0.8752>

<0.3608,

0.6392,

0.6392>

<0.3245,

0.6755,

0. 6755>

<0.3048,

0.6952,

0.6952>

<0.0772,

0.9228,

0.9228>

<0.4018,

0.5982,

0.5982>

<0.2568,

0.7432,

0.7432>

0.6589 15

A4

<0.3414,

0.6586,

0.6586>

<0.2092,

0.7908,

0.7908>

<0.0521,

0.9479,

0.9479>

<0.3122,

0.6878,

0.6878>

<0.4119,

0.5881,

0.5881>

<0.3225,

0.6775,

0.6775>

<0.0664,

0.9336,

0.9336>

0.8518 1


159

A5

<0.3715,

0.6285,

0.6285>

<0.1910,

0.8090,

0.8090>

<0.1799,

0.8201,

0.8201>

<0.2975,

0.7025,

0.7025>

<0.2816,

0.7184,

0.7184>

<0.1188,

0.8812,

0.8812>

<0.0590,

0.9410,

0.9410>

0.8086 5

A6

<0.0699,

0.9301,

0.9301>

<0.1395,

0.8605,

0.8605>

<0.2268,

0.7732,

0.7732>

<0.2412,

0.7588,

0.7588>

<0.0348,

0.9652,

0.9652>

<0.0283,

0.9717,

0.9717>

<0.1181,

0.8819,

0.8819>

0.7171 14

A7

<0.3496,

0.6504,

0.6504>

<0.3335,

0.6665,

0.6665>

<0.0730,

0.9270,

0.9270>

<0.3122,

0.6878,

0.6878>

<0.0606,

0.9394,

0. 9394>

<0.1981,

0.8019,

0.8019>

<0.1358,

0.8642,

0.8642>

0.7561 12

A8

<0.2536,

0.7464,

0.7464 >

<0.0940,

0.9060,

0.9060>

<0.2945,

0.7055,

0.7055>

<0.2975,

0.7025,

0.7025>

<0.2983,

0.7017,

0. 7017>

<0.1811,

0.8189,

0.8189>

<0.3424,

0.6576,

0.6576>

0.8311 3

A9

<0.2550,

0.7450,

0.7450 >

<0.3077,

0.6665,

0.6665>

<0.3323,

0.6677,

0.6677>

<0.1261,

0.8739,

0.8739>

<0.1741,

0.8259,

0.8259>

<0.1358,

0.8642,

0.8642>

<0.2568,

0.7432,

0.7432>

0.7632 11

A10

<0.3098,

0.6902,

0.6902 >

<0.3335,

0.6665,

0.6665>

<0.2958,

0.7042,

0.7042>

<0.2412,

0.7588,

0.7588>

<0.3861,

0.6139,

0.6139>

<0.1924,

0.8076,

0.8076>

<0.3070,

0.6930,

0.6930>

0.7678 9

A11

<0.2701,

0.7299,

0.7299 >

<0.0682,

0.9318,

0.9318>

<0.3167,

0.6833,

0.6833>

<0.2693,

0.7307,

0.7307>

<0.1211,

0.8789,

0.8789>

<0.3056,

0.6944,

0.6944>

<0.3262,

0.6738,

0.6738>

0.8161 4

A12

<0.2550,

0.7450,

0.7450 >

<0.2456,

0.7544,

0.7544>

<0.3245,

0.6755,

0.6755>

<0.0686,

0.9314,

0.9314>

<0.2983,

0.7017,

0.7017>

<0.0679,

0.9321,

0.9321>

<0.3513,

0.6487,

0.6487>

0.8384 2

A13

<0.0466,

0.9534,

0.9534 >

<0.0773,

0.9227,

0.9227>

<0.3245,

0.6755,

0.6755>

<0.2546,

0.7454,

0.7454>

<0.0606,

0.9394,

0.9394>

<0.3678,

0.6322,

0.6322>

<0.3513,

0.6487,

0.6487>

0.7657 10

A14

<0.3496,

0.6504,

0.6504 >

<0.3608,

0.6392,

0.6392>

<0.1642,

0.8358,

0.8358>

<0.3048,

0.6952,

0.6952>

<0.2635,

0.7365,

0.7365>

<0.2320,

0.7680,

0.7680>

<0.4014,

0.5986,

0.5986>

0.7968 8

A15

<0.2536,

0.7464,

0.7464 >

<0.3335,

0.6665,

0.6665>

<0.1486,

0.8514,

0.8514>

<0.2840,

0.7160,

0.7160>

<0.2983,

0.7017,

0.7017>

<0.3961,

0.6039,

0.6039>

<0.1343,

0.8657,

0.8657>

0.7402 13

<1.000,

0.0000,

0.0000>

<0.0000,

1.0000,

1.0000>

<0.0000,

1.0000,

1.0000>

<0.0000,

1.0000,

1.0000>

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>

0.4681 0.4610 0.4822 0.4872 0.4543 0.4831 0.4664

0.1438 0.1458 0.1400 0.1387 0.1476 0.1398 0.1443 1

4.11.3 Proposed Method 3: F-SVNS-ACC-MADM for TPRLP Selection


The calculations of step 8 and step 9 are shown briefly in the Annexure -C [11]. The rank

is calculated with F-SVNS-EW-MADM is as shown in Table 4.67

TABLE 4.67: F-SVNS ACC-MADM Ranking for TPRLP Selection

Sr.

No. A1 (+) A2 (-) A3 (-) A4 (-) A5 (+) A6 (+) A7 (+) Rank

A1

<0.2221,

0.7779,

0.7779>

<0.3608,

0.6392,

0.6392>

<0.3102,

0.6898,

0.6898>

<0.0490,

0.9510,

0.9510>

<0.3422,

0.6578,

0.6578>

<0.3259,

0.6741,

0. 6741>

<0.2568,

0.7432,

0. 7432>

0.5707 5

A2 <0.0384, <0.0424, <0.2489, <0.2914, <0.2983, <0.2546, <0.1343, 0.5618 7


160

0.9616,

0.9616>

0.9576,

0.9576>

0.7511,

0. 7511>

0.7086,

0.7086>

0.7017,

0.7017>

0.7454,

0.7454>

0.8657,

0.8657>

A3

<0.1248,

0.8752,

0.8752>

<0.3608,

0.6392,

0.6392>

<0.3245,

0.6755,

0. 6755>

<0.3048,

0.6952,

0.6952>

<0.0772,

0.9228,

0.9228>

<0.4018,

0.5982,

0.5982>

<0.2568,

0.7432,

0.7432>

0.4652 15

A4

<0.3414,

0.6586,

0.6586>

<0.2092,

0.7908,

0.7908>

<0.0521,

0.9479,

0.9479>

<0.3122,

0.6878,

0.6878>

<0.4119,

0.5881,

0.5881>

<0.3225,

0.6775,

0.6775>

<0.0664,

0.9336,

0.9336>

0.5999 1

A5

<0.3715,

0.6285,

0.6285>

<0.1910,

0.8090,

0.8090>

<0.1799,

0.8201,

0.8201>

<0.2975,

0.7025,

0.7025>

<0.2816,

0.7184,

0.7184>

<0.1188,

0.8812,

0.8812>

<0.0590,

0.9410,

0.9410>

0.5695 6

A6

<0.0699,

0.9301,

0.9301>

<0.1395,

0.8605,

0.8605>

<0.2268,

0.7732,

0.7732>

<0.2412,

0.7588,

0.7588>

<0.0348,

0.9652,

0.9652>

<0.0283,

0.9717,

0.9717>

<0.1181,

0.8819,

0.8819>

0.5058 14

A7

<0.3496,

0.6504,

0.6504>

<0.3335,

0.6665,

0.6665>

<0.0730,

0.9270,

0.9270>

<0.3122,

0.6878,

0.6878>

<0.0606,

0.9394,

0. 9394>

<0.1981,

0.8019,

0.8019>

<0.1358,

0.8642,

0.8642>

0.5342 12

A8

<0.2536,

0.7464,

0.7464 >

<0.0940,

0.9060,

0.9060>

<0.2945,

0.7055,

0.7055>

<0.2975,

0.7025,

0.7025>

<0.2983,

0.7017,

0. 7017>

<0.1811,

0.8189,

0.8189>

<0.3424,

0.6576,

0.6576>

0.5842 3

A9

<0.2550,

0.7450,

0.7450 >

<0.3077,

0.6665,

0.6665>

<0.3323,

0.6677,

0.6677>

<0.1261,

0.8739,

0.8739>

<0.1741,

0.8259,

0.8259>

<0.1358,

0.8642,

0.8642>

<0.2568,

0.7432,

0.7432>

0.5387 11

A10

<0.3098,

0.6902,

0.6902 >

<0.3335,

0.6665,

0.6665>

<0.2958,

0.7042,

0.7042>

<0.2412,

0.7588,

0.7588>

<0.3861,

0.6139,

0.6139>

<0.1924,

0.8076,

0.8076>

<0.3070,

0.6930,

0.6930>

0.5405 9

A11

<0.2701,

0.7299,

0.7299 >

<0.0682,

0.9318,

0.9318>

<0.3167,

0.6833,

0.6833>

<0.2693,

0.7307,

0.7307>

<0.1211,

0.8789,

0.8789>

<0.3056,

0.6944,

0.6944>

<0.3262,

0.6738,

0.6738>

0.5742 4

A12

<0.2550,

0.7450,

0.7450 >

<0.2456,

0.7544,

0.7544>

<0.3245,

0.6755,

0.6755>

<0.0686,

0.9314,

0.9314>

<0.2983,

0.7017,

0.7017>

<0.0679,

0.9321,

0.9321>

<0.3513,

0.6487,

0.6487>

0.5911 2

A13

<0.0466,

0.9534,

0.9534 >

<0.0773,

0.9227,

0.9227>

<0.3245,

0.6755,

0.6755>

<0.2546,

0.7454,

0.7454>

<0.0606,

0.9394,

0.9394>

<0.3678,

0.6322,

0.6322>

<0.3513,

0.6487,

0.6487>

0.5392 10

A14

<0.3496,

0.6504,

0.6504 >

<0.3608,

0.6392,

0.6392>

<0.1642,

0.8358,

0.8358>

<0.3048,

0.6952,

0.6952>

<0.2635,

0.7365,

0.7365>

<0.2320,

0.7680,

0.7680>

<0.4014,

0.5986,

0.5986>

0.5616 8

A15

<0.2536,

0.7464,

0.7464 >

<0.3335,

0.6665,

0.6665>

<0.1486,

0.8514,

0.8514>

<0.2840,

0.7160,

0.7160>

<0.2983,

0.7017,

0.7017>

<0.3961,

0.6039,

0.6039>

<0.1343,

0.8657,

0.8657>

0.5218 13

<1.000,

0.0000,

0.0000>

<0.0000,

1.0000,

1.0000>

<0.0000,

1.0000,

1.0000>

<0.0000,

1.0000,

1.0000>

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>

<1.000,

0.0000,

0.0000>

4.11.4 Performance Measures Comparison: TPRLP Ranking


validate them for third party reverse logistic provider selection. To compare the result, all

reverse logistic provider alternatives are ranked according to alternatives weight values is

as shown in Table 4.68. The reverse logistic provider alternatives are ranked first whose

alternative weight value is highest; reverse logistic provider alternative is ranked second

whose alternatives weight values is second highest. Finally the ranking order obtained by


161

the proposed three different methodologies is compared with the ranking order published

in the literature and result comparisons are shown in Table 4.68

TABLE 4.68: TPRLP Selection Performance Measures Comparison

Alternatives

(Sr. No.)

F-SVNS MADMs ISM& Fuzzy

TOPSIS* Novel Entropy Weight ACC

A1 5 6 5 5

A2 7 7 7 13

A3 15 15 15 10

A4 1 1 1 7

A5 6 5 6 8

A6 14 14 14 15

A7 12 12 12 12

A8 3 3 3 3

A9 11 11 11 6

A10 9 9 9 2

A11 4 4 4 9

A12 2 2 2 4

A13 10 10 10 14

A14 8 8 8 1

A15 13 13 13 11

*Ranking solution Collected from (Kannan et al. 2009)


proposed methodologies are not similar to the result reported in the literature. (Kannan et

al. 2009) tried to solve TPRLP selection by using Interpretive Structural Modeling (ISM)

& Fuzzy TOPSIS methodology. The proposed method suggests the cutting fluid alternative

A4 as the best cutting fluid, which is differ from ranking suggested by (Kannan et al. 2009)

ISM & Fuzzy TOPSIS. (Kannan et al. 2009) solved same TPRLP selection problem and

obtain the TPRLP alternative A14 as the best solution. Comparing with alterative A4 and

alternate A14 from the input matrix, alternatives A4 is better. But in the calculation,

different attribute weights lead to change in the ranking solution.

Further, 2nd

rank and 4th

rank are calculated by proposed methods doesn‘t match with

published results of Interpretive Structural Modeling (ISM) & fuzzy TOPSIS method

which is one of the hybrid methods. They are differed due to published method works with

different weight criteria calculation/ assumption/ expert opinion or same equation of

normalization/ without normalization. Other than this, ISM is not MADM technique, ISM

works with structural self-interaction matrix (SSIM), reachability matrix, partition

reachability matrix into different levels, convert reachability matrix into conical form,

drawing digraph and then convert into ISM model. Here, researcher tried to make hybrid

of ISM and Fuzzy TOPSIS which leads different ranking order.

4.12 Comparative Performance of Proposed MADM Techniques

162


Even proposed methodology F-SVNS EW-MADM works with calculating attribute

weight. Proposed methodologies works with minimum calculations, without calculating

any kind of relative importance of attributes, without need to resize the assignment matrix

and it is gifted to convert simple set or lingustic set to F-SVNS.





reverse logistics provider‘s selection for manufacturing environment which leads to

improve manufacturing function.

4.12 Comparative Performance of Proposed MADM Techniques

In the proposed methods work with the least amount of mathematical calculation are

required and further they do not require any kind of special computer programming.

Current methodologies are gifted with crisp set to SVNS conversion also. Another major

advantage of these methods is that they without introduction of any extra parameter such

as weight strategy with MADMs. For this reason the proposed methods are highly stable

for varying decision making problems.

With the comparison, one can understand that, there is some variation in ranking order

possible due to their different method and mathematical set practices even some of the

researcher work with their own attribute weight measures it leads to change the ranking

order.

Table 4.69 shows first ranking similarity in percentage of proposed methodologies with

published result. Table 4.69, it is observed in the current chapter that, the function of

MADM is to select the best alternative, which is more than 50% matched with published

result, which is satisfied here. In the implementation and validation of proposed

methodologies with other MADMs shows first rank obtained by the proposed method hold

good decision.


163

Table 4.69: First Ranking Similarity in Percentage of Proposed Methodologies with Published Results

Case

Example

No. of

Alternative

No. of Attributes

F-SVNS

N-MADM

Rank with

Published

Results

F-SVNS

EW-

MADM

Rank with

Published

Results

F-SVNS

ACC-

MADM

Rank with

Published

Results

#

Beneficial Non Beneficial 1st

Rank 1st

Rank 1st

Rank

1 5 3 1 2/2 2/2 2/2 A

100 100 100 B

2 5 4 2 6/6 6/6 6/6 A

100 100 100 B

3 6 2 4 5/7 5/7 5/7 A

71.43 71.43 71.43 B

4 4 2 4 1/3 1/3 1/3 A

33.33 33.33 33.33 B

5 8 5 1 2/3 2/3 2/3 A

66.67 66.67 66.67 B

6 27 2 2 2/4 2/4 2/4 A

50 50 50 B

7 6 3 2 6/6 6/6 6/6 A

100 100 100 B

8 15 4 2 1/7 4/7 1/7 A

14.29 57.14 14.29 B

9 5 0 4 6/6 6/6 6/6 A

100 100 100 B

10 18 4 1 2/3 2/3 2/3 A

66.67 66.67 66.67 B

11 15 4 3 0/1 0/1 0/1 A

0 0 0 B

Average of Rank Similarity in % 63.85 67.75 63.85 # Where, A = Rank similarity with published results, B= Rank similarity with published results in percentage

It is observed that in comparisons to other MADM methods the proposed methodologies

are very simple and easy to implement on manufacturing and supply chain environment in

presence of multi attribute. Hence, it may be quite helpful to the decision makers who may

not have a strong background on mathematics. In addition, in the most of the result

comparisons first choice or first ranking of result of the proposed method is consistent but

subsequent ranking is inconsistent. The inconsistency in such results occurs due to

following reason.

The technique which works with predetermined or calculated weight of criteria

except PSI methodology.

Some techniques add some parameter during calculation which affects the ranking

solution except PSI methodology.

164

The techniques differ in their approach or mathematical equations to selecting best

solution except PSI methodology.

There are wide verities of MADM techniques are available and it is difficult to answer the

question like

Which method is more superior?

Which method is more appropriate for what type of problem?

Does a decision change when using different methods?

Further existing MADMs of verity of complexity and possible solutions, confuses

practitioners hence practitioners seem to prefer simple and transparent method. So, in these

work alternative methodologies, work carried out to convert qualitative/ quantitative

information in crisp or linguistic set form to SVNS (work as human decision behavior) and

proves accurate ranking solution with comparative simple calculation and leads to accurate

solution. Here two of the proposed methodologies work without calculating/assuming

criteria weight.

The proposed methods prove the capability to solve diverse problems in manufacturing

and supply chain field. The proposed methods also prove their soundness of ranking in this

chapter by implemented in collected case examples in random eleven domains. After

implementation of proposed methodologies, the validation of the proposed methodologies

carried out with two phases: (i) different normalization equations and (ii) Spearman

correlation coefficient, for eleven case examples is carried out in Chapter 5.

Chapter 5: Sensitivity Analysis

165


5.1 Introduction

166

CHAPTER NO.5

Sensitivity Analysis

Sensitivity analysis is carried out for the model validation purpose. Here the validation of

proposed methodology is carried out with the help of sensitivity analysis. Brief

explanations of sensitivity analysis are as under. The sensitivity analysis is performed to

check the robustness of the model. It also helps in finding the best method among all

proposed methodologies.

5.1 Introduction

When numbers of decisions arise within problem, the review needed to carry out which is

known as sensitivity analysis (Higgins and Green 2011).

Purpose of Sensitivity Analysis: (Kumar et al. 2004) explained that sensitivity analysis

becomes widely popular for variety of purposes i.e. uncertainty validation, model

calibration and diagnostic evaluation, dominant control analysis and robust decision

making, screening, mapping and ranking purpose.

5.2 Classification of Sensitivity Analysis

(Kumar et al. 2004) tried to classify types of sensitivity analysis to check the consistency

of the proposed model as shown below.

(1) Perturbation and derivatives technique (Devenish et al. 2012) for calculating local

sensitivity

(2) Multiple starts perturbation methods: Elementary Effect Test for calculating global

sensitivity (Morris 1991)

(3) Correlation and Regression analysis methods

a. Spearman correlation coefficient/ partial rank correlation coefficient (for

nonlinear but monotonic relations of x and y) investigated by (Pastres et al.

1999).


167

b. Classification and Regression Tree (CART) which can handle non

numerical output (If input output relationship is nonlinear) (Hall et al.

2009), (Harper et al. 2011)

(4) Regional Sensitivity analysis/ Monte-Carlo filtering (Young et al. 1978),

(5) Variance based method: Fourier Amplitude Sensitivity Test (FAST) (Cukier et al.

1973)

(6) Density based method: Probability Density Function (PFA) (Kumar et al. 2004)

For MADM (Rao 2013) worked to find the best method using Spearman correlation

coefficient. With different normalization methods proposed methods are analyzed with the

help of Spearman correlation coefficient which is randomly selected.

5.3 Spearman Correlation Coefficient

The correlation rank calculation initially introduced by (Spearman 1904). (Zar 1972)

derived the equation for calculating correlation coefficient as shown in Equation. (5.1)

∑

…………………………………………………….………………… (5.1)

Where, shows the numbers of alternatives, and shows difference between two

ranks of each MADM for relative alternatives.

To evaluate the similarity of ranking order obtained by two approaches Spearman‘s

correlation test is used which allows ascertaining for similarity of two ranking

values.

Find the sensitivity of proposed methodologies; here work is carried to calculate the

Spearman correlation coefficient with respect to proposed MADM techniques

test with various normalization methods for identifying the best methodology.

5.4 Sensitivity Analysis of Proposed MADMs for Collected Case

Examples

Various matrix normalization approaches are shown in Table 5.1 collected from the

(Nirmal and Bhatt 2016a), (Sałabun 2013). This is helpful to solve the collected case

examples with different normalization for sensitivity purpose.

5.4 Sensitivity Analysis of Proposed MADMs for Collected Case Examples

168

TABLE 5.1: Various Normalization Approaches for Beneficial and Non-beneficial Values

Name of Normalization

Methods

Normalized Value

For Benefit Criteria For Non- Beneficial Criteria

Linear Scale Transformation,

Max Method (LSTMM) iMax

ij

ijX

XR

ij

iMinij

X

XR

Linear Scale Transformation

Max- Min Method (LSTMMM) ijij

ijij

ijMinXMaxX

MinXXR

ijij

ijij

ijMinXMaxX

XMaxXR

Linear Scale Transformation

Sum Method (LSTSM)

m

i

i

ij

ij

X

XR

1

m

i

i

ij

ij

X

XR

1

1

Vector Normalization Method

(VNM)*

m

i

ij

ij

ij

X

XR

1

2

m

i

ij

ij

ij

X

XR

1

2

1

Collected from the Source: (Maniya 2012) (Nirmal and Bhatt 2016a), (Sałabun 2013) [*Normalization

method is applied in the proposed methodologies]

Table 5.1 shows various normalizations are carried out with the relative beneficial and

non-beneficial attributes. Then for validation purpose the Spearman correlation coefficient

calculation is carried out. Average value of Spearman correlation coefficient nearer to

value 1; show that ranking methodology is the best among others. Table 5.2 shows

proposed methodologies with their relative normalization equation for validation purpose.

TABLE 5.2: Relative Normalization Equations for Proposed Methods

Method

Code Method Name Beneficial Equation (3.1)*

Non-Beneficial Equation

(3.2)*

M1 F-SVNS N-MADM with LSTMM

M2 F-SVNS N-MADM with LSTMMM

M3 F-SVNS N-MADM with LSTSM

∑

∑

M4 F-SVNS N-MADM with VNM Equation (3.1) unchanged Equation (3.2) unchanged

M5 F-SVNS EW-MADM with LSTMM


169

M6 F-SVNS EW-MADM with

LSTMMM

M7 F-SVNS EW-MADM with LSTSM

∑

∑

M8 F-SVNS EW-MADM with VNM Equation (3.1) unchanged Equation (3.2) unchanged

M9 F-SVNS ACC-MADM with LSTMM

M10 F-SVNS ACC-MADM with

LSTMMM

M11 F-SVNS ACC-MADM with LSTSM

∑

∑

M12 F-SVNS ACC-MADM with VNM Equation (3.1) unchanged Equation (3.2) unchanged

*Equation (3.1) and Equation (3.2) replaced with respective equation for validation

purpose.

5.4.1 Sensitivity Analysis of Proposed MADMs for Case Example 1: Material

Selection

A sensitivity analysis is performed with material selection example of section 4.1. To study

the effects of normalization methods on the ranking solutions are obtained with the

proposed methodologies using MATLAB coding Annexure–E[1-12]. The result of ranking

orders obtained using different normalization methods of proposed methodologies which is

method code M1 to M12 for Case example 1 for material selection. Fig. 5.1 shows chart of

relative ranking order and different material alternatives, which is solved with the help of

Methods M1 to M12. For validation purpose the methods are solved with MATLAB

coding. It shows material selection performance measures of three proposed

methodologies.


170

FIGURE 5.1: Effect of Normalization Methods on Material Selection Case Example 1

Result represented in Fig. 5.1 shows that there is a change in ranking order obtained using

M1 to M12. The result is also indicating the poorest alternatives A2 and A3 respectively.

But normalization methods suggested A4 alternative as the best choice except M2 and

M10 methods. It shows the change of performance with LSTMMM normalization method.

Testing of Spearman Rank Correlation Coefficient for Collective Case Example of

Material Selection

Sensitivity analysis is carried out with ranking comparison with Spearman rank correlation

coefficient. The case example 1: (material selection), The detail calculation steps of

individual spearman rank correlation coefficient are shown in Annexure-D [1]. Where,

each method‘s ranking solution is compared with other and spearman rank correlation

A1 A2 A3 A4 A5

M1 2 4 5 1 3

M2 3 4 5 2 1

M3 2 4 5 1 3

M4 2 4 5 1 3

M5 2 4 5 1 3

M6 3 4 5 1 2

M7 2 4 5 1 3

M8 2 3 5 1 4

M9 2 4 5 1 3

M10 3 4 5 2 1

M11 2 4 5 1 3

M12 2 4 5 1 3

0

1

2

3

4

5

6

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coefficient calculations are carried out. Here, Table 5.3 shows the result of the average

value of calculated Spearman rank correlation coefficient for material selection case

example, which is collected from Table I in Annexure-D [1].

TABLE 5.3: Average Spearman Rank Correlation Coefficient for Case Example of Material Selection

Method

Code Method Name

Average Spearman Rank Correlation

Coefficient

M1 F-SVNS N-MADM with LSTMM 0.9333

M2 F-SVNS N-MADM with LSTMMM 0.7417

M3 F-SVNS N-MADM with LSTSM 0.9333

M4 F-SVNS N-MADM with VNM 0.9333

M5 F-SVNS EW-MADM with LSTMM 0.9333

M6 F-SVNS EW-MADM with LSTMMM 0.8917

M7 F-SVNS EW-MADM with LSTSM 0.9333

M8 F-SVNS EW-MADM with VNM 0.8083

M9 F-SVNS ACC-MADM with LSTMM 0.9333

M10 F-SVNS ACC-MADM with LSTMMM 0.7417

M11 F-SVNS ACC-MADM with LSTSM 0.9333

M12 F-SVNS ACC-MADM with VNM 0.9333

The average value of spearman rank correlation coefficients are nearer to the value 1

except Method M2 and M10, which works with LSTSM normalization method. Average

obtained with the help of spearman rank correlation coefficients are also shows the fitness

of proposed methodologies. It is concluded from the calculation that proposed methods

with VNM shows better ranking solution.

5.4.2 Sensitivity Analysis of Proposed MADMs for Case Example 2: Machine Tool

Selection

A sensitivity analysis is performed with machine tool selection example of section 4.2. To

study the effects of normalization methods on the ranking solutions are obtained with the

proposed methodologies using MATLAB coding Annexure–E(1-12). The result of

ranking orders obtained using different normalization methods of proposed methodologies

which is method code M1 to M12 for Case example 2 for machine tool selection. Fig. 5.2

shows chart of relative ranking order and different machine tool alternatives, which is

solved with the help of Methods M1 to M12. The methods are solved with MATLAB

coding. It shows the machine tool selection performance measures of three proposed

methodologies.


172

Result represented in Fig. 5.2 shows that there is no change in 1st, 2

nd and 5

th ranking order

obtained using M1 to M12. Validation shows the better performance of proposed

methodologies in ranking solution.

FIGURE 5.2: The Effect of Normalization Methods on Machine Tool Selection Case Example 2


Machine Tool Selection


coefficient. The case example 2: (machine tool selection), The detail calculation steps of

individual spearman rank correlation coefficient are shown in Annexure-D (2). Where,




example, which is collected from Table II in Annexure-D [2].

A1 A2 A3 A4 A5

M1 4 5 3 2 1

M2 3 5 4 2 1

M3 4 5 3 2 1

M4 4 5 3 2 1

M5 4 5 3 2 1

M6 3 5 4 2 1

M7 4 5 3 2 1

M8 4 5 3 2 1

M9 4 5 3 2 1

M10 3 5 4 2 1

M11 4 5 3 2 1

M12 4 5 3 2 1

0

1

2

3

4

5

6

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TABLE 5.4: Average Spearman Rank Correlation Coefficient for Case Example of Machine Tool

Selection

Method

Code Method Name Average Spearman rank correlation













The average value of spearman rank correlation coefficients are nearer to the value 1.

Average obtained with the help of spearman rank correlation coefficients are also shows

the fitness of proposed methodologies. It is concluded from the calculation that proposed

methods with VNM shows better ranking solution.

5.4.3 Sensitivity Analysis of Proposed MADMs for Case Example 3: Rapid

Prototype Selection

A sensitivity analysis is performed with rapid prototype selection example of section 4.3.

To study the effects of normalization methods on the ranking solutions are obtained with

the proposed methodologies using MATLAB coding Annexure–E(1-12). The result of


which is method code M1 to M12 for Case example 3 for rapid prototype selection. Fig.

5.3 shows chart of relative ranking order and different rapid prototype alternatives, which

is solved with the help of Methods M1 to M12. The methods are solved with MATLAB

coding. It shows the rapid prototype selection performance measures of three proposed

methodologies.

Result represented in Fig. 5.3 shows that there is a minor change in ranking order obtained

using M1 to M12. But the 1st ranking solution A5 is recommended by M1 to M12. The

result is also indicating the 2nd

best alternative is A2. Form the ranking solution obtained

using M1 to M12 are indicated the soundness of proposed methodologies with 4 different

normalization methods.


174

FIGURE 5.3: Effect of Normalization Methods on Rapid Prototype Selection Case Example 3


Rapid prototype Selection


coefficient. The case example 3: (rapid prototype selection), the detail calculation steps of





example, which is collected from Table III in Annexure-D [3].

TABLE 5.5: Average Spearman Rank Correlation Coefficient for Case Example of Rapid Prototype

Selection

Method




A1 A2 A3 A4 A5 A6

M1 2 4 6 5 1 3

M2 2 3 6 4 1 5

M3 2 3 5 4 1 6

M4 2 3 5 4 1 6

M5 2 4 5 6 1 3

M6 2 3 6 4 1 5

M7 2 3 5 4 1 6

M8 2 3 5 4 1 6

M9 2 4 6 5 1 3

M10 2 3 6 4 1 5

M11 2 3 5 4 1 6

M12 2 3 5 4 1 6

0

1

2

3

4

5

6

7

Ra

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175












except Method M1, M5 and M9 which works with LSTMM normalization method. From

this one can understand the loss of information is possible when calculation through

LSTMM normalization methodology in proposed methods. So, this normalization method

is not feasible for SVNS MADM. Average obtained with the help of spearman rank

correlation coefficients are also shows the fitness of proposed methodologies. It is

concluded from the calculation that proposed methods with VNM shows better ranking

solution.

5.4.4 Sensitivity Analysis of Proposed MADMs for Case Example 4: NTMP

Selection

A sensitivity analysis is performed with NTMP selection example of section 4.4. To study


proposed methodologies using MATLAB coding Annexure–E(1-12). The result of


which is method code M1 to M12 for Case example 4 for NTMP selection. Fig. 5.4 shows

chart of relative ranking order and different NTMP alternatives, which is solved with the

help of Methods M1 to M12. The methods are solved with MATLAB coding. It shows the

NTMP selection performance measures of three proposed methodologies.

Result represented in Fig. 5.3 shows that there is a minor change between ranking orders

obtained using M1 to M12. Here, chart shows the 1st ranking and 2

nd ranking are in nearer

solutions. But the 1st ranking solution A1 is highly recommended except normalization

method LSTMM. It indicates that, the proposed methodology may loss the information

while normalizing through LSTMM for normalization of M1, M5 and M9. Normalization

works better for proposed methodologies except LSTMM.


176

FIGURE 5.4: Effect of Normalization Methods on NTMP Selection Case Example 4


NTMP Selection


coefficient. The case example 4: (NTMP selection), the detail calculation steps of





example, which is collected from Table IV in Annexure-D [4].

TABLE 5.6: Average of Spearman Rank Correlation Coefficient for Case Example of NTMP Selection

Method







A1 A2 A3 A4

M1 2 1 4 3

M2 1 2 4 3

M3 1 2 3 4

M4 1 2 3 4

M5 2 1 4 3

M6 2 1 4 3

M7 1 2 3 4

M8 1 2 3 4

M9 2 1 4 3

M10 1 2 4 3

M11 1 2 3 4

M12 1 2 3 4

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Ra

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177









except Method M1, M5, M9 with LSTMM and M6 which works with LSTMMM

normalization method. From the result one can understand the loss of information is

possible when calculation through LSTMM normalization methodology in proposed

methods. This is again proved that LSTMM doesn‘t feasible for SVNS MADM. Average


of proposed methodologies. It is concluded from the calculation that proposed methods

with VNM shows better ranking solution.

5.4.5 Sensitivity Analysis of Proposed MADMs for Case Example 5: AGV Selection

A sensitivity analysis is performed with AGV selection example of section 4.5. To study


proposed methodologies using MATLAB coding Annexure–E(1-12). The result of ranking


method code M1 to M12 for Case example 5 for AGV selection. Fig. 5.5 shows chart of

relative ranking order and different AGV alternatives, which is solved with the help of

Methods M1 to M12. The methods are solved with MATLAB coding. It shows the AGV

selection performance measures of three proposed methodologies.




solutions. But the 1st ranking solution A5 is highly recommended by LSTSM and VNM

normalization methods. Normalization works better for proposed methodologies except

LSTMM, LSTMMM.


178

FIGURE 5.5: Effect of Normalization Methods on AGV Selection Case Example 5


AGV Selection


coefficient. The case example 5: (AGV selection), the detail calculation steps of individual

spearman rank correlation coefficient are shown in Annexure-D (5). Where, each method‘s

ranking solution is compared with other and spearman rank correlation coefficient

calculations are carried out. Here, Table 5.7 shows the result of the average value of

calculated Spearman rank correlation coefficient for AGV selection case example, which is

collected from Table V in Annexure-D [5].

TABLE 5.7: Average of Spearman Rank Correlation Coefficient for Case Example of AGV Selection

Method








A1 A2 A3 A4 A5 A6 A7 A8

M1 3 4 8 1 2 5 7 6

M2 3 4 8 1 2 6 7 5

M3 3 4 8 2 1 6 7 5

M4 3 4 8 2 1 6 7 5

M5 3 4 8 2 1 5 7 6

M6 3 6 8 1 2 5 7 4

M7 3 4 8 2 1 6 7 5

M8 3 4 8 2 1 5 7 6

M9 3 4 8 1 2 5 7 6

M10 3 4 8 1 2 6 7 5

M11 3 4 8 2 1 6 7 5

M12 3 4 8 2 1 6 7 5

0

1

2

3

4

5

6

7

8

9

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179








except Method M1, M5, M9 with LSTMM and M6 which works with LSTMMM

normalization method. From the result one can understand the loss of information is

possible when calculation through LSTMM normalization methodology in proposed

methods. This is again proved that LSTMM doesn‘t feasible for SVNS MADM. Result

also shows that M6: F-SVNS EW-MADM with LSTMMM gives the poorest ranking.


the fitness of proposed methodologies. It is concluded from the calculation that proposed


5.4.6 Sensitivity Analysis of Proposed MADMs for Case Example 6: Robot Selection

A sensitivity analysis is performed with robot selection example of section 4.6. To study




method code M1 to M12 for Case example 6 for robot selection. Fig. 5.6 shows chart of

relative ranking order and different robot alternatives, which is solved with the help of

Methods M1 to M12. The methods are solved with MATLAB coding. It shows the robot

selection performance measures of three proposed methodologies.

.


180

FIGURE 5.6: Effect of Normalization Methods on Robot Selection Case Example 6

A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14 A15 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25 A26 A27

M1 10 6 20 2 26 21 11 12 22 5 25 27 4 3 19 18 13 24 8 1 14 7 16 17 23 15 9

M2 14 12 20 18 25 8 1 9 17 2 13 26 4 7 15 22 27 16 3 24 23 10 5 6 11 19 21

M3 8 15 23 19 22 10 2 6 18 4 14 26 5 1 16 20 27 17 3 25 24 12 7 9 13 21 11

M4 12 14 22 20 24 9 1 8 18 4 13 26 5 2 16 21 27 17 3 25 23 10 6 7 11 19 15

M5 10 8 20 2 26 12 11 14 24 7 23 27 6 5 19 17 22 25 3 1 18 9 13 15 21 16 4

M6 13 11 23 17 19 8 2 9 16 3 14 24 6 5 18 20 27 15 1 25 26 10 4 7 12 21 22

M7 8 15 23 19 22 10 2 6 18 4 14 26 5 1 16 20 27 17 3 25 24 12 7 9 13 21 11

M8 10 15 22 19 23 9 2 7 18 4 13 26 5 1 16 20 27 17 3 25 24 11 6 8 12 21 14

M9 10 6 20 2 26 21 11 12 22 5 25 27 4 3 19 18 13 24 8 1 14 7 16 17 23 15 9

M10 14 12 20 18 25 8 1 9 17 2 13 26 4 7 15 22 27 16 3 24 23 10 5 6 11 19 21

M11 8 15 23 19 22 10 2 6 18 4 14 26 5 1 16 20 27 17 3 25 24 12 7 9 13 21 11

M12 12 14 22 20 24 9 1 8 18 3 13 26 5 2 16 21 27 17 4 25 23 10 6 7 11 19 15

0

5

10

15

20

25

30

Ran

kin

g So

luti

on


181

Result represented in Fig. 5.6 shows that there is a visible change in ranking orders

obtained with different normalization techniques. Here, focus is carried only on the 1st

ranking solution and with the observation; alternative A7, A14 and A20 are the

recommended solution. Now from the previous case examples validation M1, M5 and M9

solve with the help of for LSTMM normalization method gives the poor ranking solution,

again here also A20 is ranked at 24th

/ 25th

by other normalization methods. The 27th

ranking order is obtained, which is one of the poor ranking solutions with LSTMM

normalization method. The VNM normalization approach works better for the better

solution


Robot Selection


coefficient. The case example 6: (Robot selection), the detail calculation steps of




value of calculated Spearman rank correlation coefficient for robot selection case example,

which is collected from Table VI in Annexure-D [6].

TABLE 5.8: Average of Spearman Rank Correlation Coefficient for Case Example of Robot Selection

Method














In this case example the input matrix having 27 alternatives so, it may consider as a

milestone example. The average value of spearman rank correlation coefficients are nearer

to the value 1 except Method M1, M5, M9 with LSTMM and M6 which works with

LSTMMM normalization method. From the result one can understand the loss of


182

information is possible when calculation through LSTMM normalization methodology in

proposed methods. This is again proved that LSTMM doesn‘t feasible for SVNS MADM.


the fitness of proposed methodologies. One can easily conclude from the average value

that VNM > LSTSM > LSTMMM > LSTMM. It is concluded from the calculation that

proposed methods with VNM shows better ranking solution.

5.4.7 Sensitivity Analysis of Proposed MADMs for Case Example 7: Metal

Stamping Layout Selection

A sensitivity analysis is performed with metal stamping layout selection example of

section 4.7. To study the effects of normalization methods on the ranking solutions are

obtained with the proposed methodologies using MATLAB coding Annexure–E(1-12).

The result of ranking orders obtained using different normalization methods of proposed

methodologies which is method code M1 to M12 for Case example 7 for metal stamping

layout selection. Fig. 5.7 shows chart of relative ranking order and different metal

stamping layout alternatives, which is solved with the help of Methods M1 to M12. The

methods are solved with MATLAB coding. It shows the metal stamping layout selection

performance measures of three proposed methodologies.

FIGURE 5.7: Effect of Normalization Methods on Metal Stamping Layout Selection Case Example 7

A1 A2 A3 A4 A5 A6

M1 3 2 1 5 6 4

M2 2 3 1 5 6 4

M3 3 2 1 5 6 4

M4 3 2 1 5 6 4

M5 3 2 1 5 6 4

M6 1 3 2 5 6 4

M7 3 2 1 5 6 4

M8 2 3 1 5 6 4

M9 3 2 1 5 6 4

M10 2 3 1 5 6 4

M11 3 2 1 5 6 4

M12 3 2 1 5 6 4

01234567

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Result represented in Fig. 5.7 shows that there is a similar ranking order obtained using M1

to M12. But the 1st ranking solution A3 is recommended by M1 to M12 excluding M6. The

result is also indicating the 5th

and 6th

ranking are found similar with M1 to M12 for the

poorer solution. Form the ranking solution obtained using M1 to M12 are indicated the

soundness of proposed methodologies with 4 different normalization methods except F-

SVNS EW-MADM with LSTMMM. Here also, The VNM normalization approach works

better for the better solution.


Metal Stamping Layout Selection


coefficient. The case example 7: (Metal stamping layout selection), the detail calculation

steps of individual spearman rank correlation coefficient are shown in Annexure-D (7).

Where, each method‘s ranking solution is compared with other and spearman rank

correlation coefficient calculations are carried out. Here, Table 5.9 shows the result of the

average value of calculated Spearman rank correlation coefficient for metal stamping

layout selection case example, which is collected from Table VII in Annexure-D [7].

TABLE 5.9: Average of Spearman Rank Correlation Coefficient for Case Example of Metal Stamping

Layout Selection

Method















except Method M6 which works with LSTMMM normalization method. From the result

one can understand the loss of information is possible when calculation through

LSTMMM normalization methodology in proposed methods. This is again proved that

LSTMMM doesn‘t feasible for SVNS MADM. Result also shows that M6: F-SVNS EW-


184

MADM with LSTMMM gives the poorest ranking. Average obtained with the help of

spearman rank correlation coefficients are also shows the fitness of proposed

methodologies. It is concluded from the calculation and past case validation history proved

that proposed methods with VNM shows better ranking solution.

5.4.8 Sensitivity Analysis of Proposed MADMs for Case Example 8: Electro

Chemical Machining Programming Selection

A sensitivity analysis is performed with ECM program selection example of section 4.8.

To study the effects of normalization methods on the ranking solutions are obtained with

the proposed methodologies using MATLAB coding Annexure–E(1-12). The result of


which is method code M1 to M12 for Case example 8 for ECM program selection. Fig. 5.8

shows chart of relative ranking order and different metal stamping layout alternatives,

which is solved with the help of Methods M1 to M12. The methods are solved with

MATLAB coding. It shows the ECM program selection performance measures of three

proposed methodologies.

FIGURE 5.8: Effect of Normalization Methods on ECM Programming Selection Case Example 8

A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14 A15

M1 8 3 12 11 14 13 1 4 2 10 5 15 6 7 9

M2 6 2 11 14 13 12 3 5 4 7 1 15 9 8 10

M3 3 5 11 13 14 12 4 6 1 8 2 15 9 10 7

M4 5 4 11 14 13 12 3 6 2 8 1 15 10 9 7

M5 7 4 13 11 14 12 5 2 1 10 6 15 3 8 9

M6 6 4 11 14 13 12 5 3 2 7 1 15 8 10 9

M7 3 5 11 13 14 12 4 6 1 8 2 15 9 10 7

M8 3 5 11 14 13 12 4 6 1 8 2 15 9 10 7

M9 8 3 12 11 14 13 1 4 2 10 5 15 6 7 9

M10 6 2 11 14 13 12 3 5 4 7 1 15 9 8 10

M11 3 5 11 13 14 12 4 6 1 8 2 15 9 10 7

M12 5 4 11 14 13 12 3 6 2 8 1 15 10 9 7

0

2

4

6

8

10

12

14

16

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Result represented in Fig. 5.8 shows that there is a visible change in 1st ranking order

obtained with the help of different normalization techniques. Here, focus is carried only on

the 1st ranking solution and with the observation; alternative A7, A9 and A11 are the

recommended solution by various methods and approaches. Now from the previous case

examples validation one can conclude that LSTMM normalization method gives the poor

ranking solution, again here also A7 is concluded that LSTMM is not appropriate for

SVNS-MADM. The proposed methodologies with respective normalization for poorest

ranking solution same conclusion found. Here also, the VNM normalization approach

proves better for the better solution.


Electro Chemical Machining Programming Selection


coefficient. The case example 8: (ECM Programming selection), the detail calculation




average value of calculated Spearman rank correlation coefficient for ECM program

selection case example, which is collected from Table VIII in Annexure-D [8].

TABLE 5.10: Average of Spearman Rank Correlation Coefficient for Case Example of ECM


Method














In this case example the input matrix having 27 alternatives so, it may consider as a

milestone example. The average value of spearman rank correlation coefficients are nearer

to the value 1 except Method M1, M5, M9 with LSTMM and M6 which works with


186

LSTMMM normalization method. From the result one can understand the loss of

information may possible when calculation through LSTMM normalization methodology

in proposed methods. This is again proved that LSTMM doesn‘t feasible for SVNS

MADM. Average obtained with the help of spearman rank correlation coefficients are also

shows the fitness of proposed methodologies. One can easily conclude from the average

value that VNM > LSTSM > LSTMMM > LSTMM. It is concluded from the calculation

and from the previous case example validation that, proposed methods with VNM show

better ranking solution.

5.4.9 Sensitivity Analysis of Proposed MADMs for Case Example 9: Cutting Fluid

(Coolant) Selection

A sensitivity analysis is performed with cutting fluid (coolant) selection example of section

4.9. To study the effects of normalization methods on the ranking solutions are obtained

with the proposed methodologies using MATLAB coding Annexure–E(1-12). The result of


which is method code M1 to M12 for Case example 9. Fig. 5.9 shows chart of relative

ranking order and different metal stamping layout alternatives, which is solved with the

help of Methods M1 to M12. The methods are solved with MATLAB coding. It shows the

cutting fluid (coolant) selection performance measures of three proposed methodologies.

Result represented in Fig. 5.9 shows that there is no change in first ranking order obtained

using M1 to M12. But the 1st ranking solution A5 is recommended by M1 to M12. The

result is also indicating the 2nd

best alternative is A2 .While proposed methodologies also

gave the poorest rank to A1. Form the ranking solution obtained using M1 to M12 are

indicated the soundness of proposed methodologies with 4 different normalization

methods.


187

FIGURE 5.9: Effect of Normalization Methods on Cutting Fluid (Coolant) Selection Case Example 9


Cutting Fluid (Coolant) Selection


coefficient. The case example 9: cutting fluid (coolant) selection, the detail calculation




average value of calculated Spearman rank correlation coefficient for cutting fluid

(coolant) selection case example, which is collected from Table IX in Annexure-D [9].

TABLE 5.11: Average of Spearman Rank Correlation Coefficient for Case Example of Cutting Fluid

(Coolant) Selection

Method









A1 A2 A3 A4 A5

M1 5 4 2 3 1

M2 5 4 2 3 1

M3 5 4 2 3 1

M4 5 4 2 3 1

M5 5 4 2 3 1

M6 5 4 2 3 1

M7 5 4 2 3 1

M8 3 5 2 4 1

M9 5 4 2 3 1

M10 5 4 2 3 1

M11 5 4 2 3 1

M12 5 4 2 3 1

0

1

2

3

4

5

6

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The average value of spearman rank correlation coefficients are calculated are nearer to the

value equal to 0.9750 except Method M8 which is F-SVNS EW-MADM with VNM

method. In this case example in given input matrix all four criteria are non- beneficial.

From the result conclude that proposed methodology M8 with VNM normalization not

perform good for ranking solution. Fig. 5.9 also shows that the result obtained by the

proposed methods and with different ranking solution gives same 1st ranking to alternative

A5 and likewise for other alternatives ranking solution. Average obtained with the help of


methodologies. It is concluded from the calculation and past case validation history proved

that proposed methods with VNM shows better ranking solution for F-SVNS N-MADM

and F-SVNS ACC-MADM.

5.4.10 Sensitivity Analysis of Proposed MADMs for Case Example 10: Supplier

Selection

A sensitivity analysis is performed with supplier selection example of section 4.10. To




method code M1 to M12 for Case example 10 for supplier selection. Fig. 5.10 shows chart

of relative ranking order and different supplier selection alternatives, which are solved with

the help of Methods M1 to M12. The methods are solved with MATLAB coding. It shows

the supplier selection performance measures of three proposed methodologies.


189

FIGURE 5.10: Effect of Normalization Methods on Supplier Selection Case Example 10




solutions. But the 1st ranking solution A10 is highly recommended except normalization

method LSTMM. It indicates that, the proposed methodology may loss the information

during normalizing through LSTMM for normalization of M1, M5 and M9. Normalization

works better for proposed methodologies except LSTMM.


Supplier Selection


coefficient. The case example 10: (Supplier selection), the detail calculation steps of

individual spearman rank correlation coefficient are shown in Annexure-D [10]. Where,



value of calculated Spearman rank correlation coefficient for supplier selection case

example, which is collected from Table X in Annexure-D[10].

A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14 A15 A16 A17 A18

M1 4 12 13 17 2 1 18 10 11 5 3 9 7 15 6 14 8 16

M2 6 14 11 18 2 4 17 8 9 1 3 5 7 16 12 10 13 15

M3 8 10 13 18 3 2 17 12 11 1 6 9 7 14 4 15 5 16

M4 8 11 13 18 3 2 17 12 10 1 4 9 7 16 5 14 6 15

M5 5 12 13 17 1 2 18 10 11 4 3 9 6 16 7 14 8 15

M6 4 12 11 17 2 7 16 8 9 1 3 6 5 18 14 10 15 13

M7 8 10 13 18 3 2 17 12 11 1 6 9 7 14 4 15 5 16

M8 8 10 13 18 3 2 17 12 11 1 5 9 7 15 4 14 6 16

M9 4 12 13 17 2 1 18 10 11 5 3 9 7 15 6 14 8 16

M10 6 14 11 18 2 4 17 8 9 1 3 5 7 16 12 10 13 15

M11 8 10 13 18 3 2 17 12 11 1 6 9 7 14 4 15 5 16

M12 8 11 13 18 3 2 17 12 10 1 4 9 7 16 5 14 6 15

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TABLE 5.12: Average of Spearman Rank Correlation Coefficient for Case Example of Supplier

Selection

Method















except Method M6 which works with LSTMMM normalization method. From the result

one can understand the loss of information is possible when calculation through

LSTMMM normalization methodology in proposed methods. This is again proved that

LSTMMM doesn‘t feasible for SVNS MADM. Result also shows that M6: F-SVNS EW-

MADM with LSTMMM gives the poorest ranking. Average obtained with the help of


methodologies and better result obtained with VNM> LSTMM> LSTSM> LSTMMM. It

is concluded from the calculation and past case validation history proved that proposed


5.4.11 Sensitivity Analysis of Proposed MADMs for Case Example 11: TPRLP

Selection

A sensitivity analysis is performed with supplier selection example of section 4.12. To




method code M1 to M12 for Case example 11 for TPRLP selection. Fig. 5.11 shows chart

of relative ranking order and different reverse logistics provider‘s selection alternatives,

which are solved with the help of Methods M1 to M12. The methods are solved with


191

MATLAB coding. It shows the reverse logistics provider‘s selection performance

measures of three proposed methodologies.

FIGURE 5.11: Effect of Normalization Methods on Third Party Reverse Logistic Provider Selection

Case Example 11

Result represented in Fig. 5.11 shows that there is a similar ranking order obtained using

M1 to M12. But the 1st ranking solution A3 is recommended by M1 to M12 excluding M6.

Form the ranking solution obtained using M1 to M12 are indicated the soundness of

proposed methodologies with 4 different normalization methods except F-SVNS EW-

MADM with LSTMMM. Here also, The VNM normalization approach works for the

better solution.


Reverse Logistics Providers selection


coefficient. The case example 11: (Reverse logistics provider‘s selection), the detail

calculation steps of individual spearman rank correlation coefficient are shown in

Annexure-D [11]. Where, each method‘s ranking solution is compared with other and

spearman rank correlation coefficient calculations are carried out. Here, Table 5.13 shows

the result of the average value of calculated Spearman rank correlation coefficient for

A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14 A15

M1 2 4 14 1 8 15 9 5 11 10 6 3 12 7 13

M2 4 7 15 1 6 14 11 3 9 12 5 2 10 8 13

M3 6 7 15 1 5 14 12 3 11 9 4 2 10 8 13

M4 5 7 15 1 6 14 12 3 11 9 4 2 10 8 13

M5 2 4 14 1 8 15 9 5 11 10 6 3 12 7 13

M6 3 7 15 2 6 14 11 4 9 12 5 1 10 8 13

M7 6 7 15 1 5 14 12 3 11 9 4 2 10 8 13

M8 6 7 15 1 5 14 12 3 11 9 4 2 10 8 13

M9 2 4 14 1 8 15 9 5 11 10 6 3 12 7 13

M10 4 7 15 1 6 14 11 3 9 12 5 2 10 8 13

M11 6 7 15 1 5 14 12 3 11 9 4 2 10 8 13

M12 5 7 15 1 6 14 12 3 11 9 4 2 10 8 13

02468

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5.5 Outcome of Sensitivity Analysis

192

reverse logistic provider‘s selection case example, which is collected from Table XI in

Annexure-D [11].

TABLE 5.13: Average of Spearman Rank Correlation Coefficient for Case Example of TPLP Selection

Method














With 15 different alternatives proposed methodology, The average value of spearman rank

correlation coefficients are nearer to the value 1 except Method M5 which works with

LSTMM normalization method. From the result one can understand the loss of information

is possible when calculation through LSTMM normalization methodology in proposed

methods. This is again proved that LSTMM doesn‘t feasible for SVNS MADM. Average


of proposed methodologies and better result obtained with VNM> LSTMMM> LSTSM>

LSTMM. It is concluded from the calculation and past case validation history proved that

proposed methods with VNM shows better ranking solution.


Here, in this chapter sensitivity analysis is performed to study the effect various

normalization method on final ranking using Three new approaches for MADMs

investigated (i) Fuzzy Single Valued Neutrosophic Set Novel MADM (F-SVNS N-

MADM), (ii) Fuzzy Single Valued Neutrosophic Set Entropy Weight based MADM (F-

SVNS EW-MADM) and (iii) Fuzzy Single Valued Neutrosophic Set Advanced

Correlation Coefficient MADM (F-SVNS ACC-MADM).

Sensitivity analysis is carried out with the help of Spearman correlation coefficient

equation for ranking solution. Results of sensitivity analysis are performed with the help of


193

Spearman correlation coefficient equation. Different normalization equations applied on

the different case examples are collected from various peer reviewed books/ books with

proposed methodologies and various normalization methods. The flow of chapter is as

shown in Fig. 5.12.

Figure 5.12: Flow of Sensitivity Analysis for Proposed Methodologies

There is some difference in the ranking order obtained using proposed methods while

considering different normalization methods, but there is no more change in the final

selection or decisions suggested by the proposed methodologies except normalization

through LSTMM. The results show that normalization through LSTMM may loss the input

data at the normalization stage.

In addition, there is a deviation in the ranking orders but there is no deviation in the final

choice or decision or selection except Normalization method LSTMM. During

normalization process using LSTMM, Some attributes measures will get zero value which

is not desirable because it reveals loss of information during normalization. These results

prove that use of LSTMM MADM method may not desirable.

Average of Case examples Average Spearman Rank Correlation Coefficient:

For finding the best method among proposed methodologies with different normalization

methods, work is carried to calculate the average value of M1 to M12 with collected case

examples from Table 5.3 to Table 5.13. The average value of spearman rank correlation

coefficients are nearer to the value 1. Conclusion validation of the proposed methodology

using sensitivity analysis is as shown in Table 5.14. ANNEXURE-D [12] shows the

detailed calculations for average of Spearman correlation coefficient.

Eleven Collected Case

Examples

Four different Normalization

methods

Three Proposed Methodology

Sensitivity Analysis through

Spearman correlation coefficient

Find the Best Method among

Proposed Methodologies


194

TABLE 5.14: Conclusion Validation of the Proposed Methodology using Sensitivity Analysis

M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 M12

(A) 0.9333 0.7417 0.9333 0.9333 0.9333 0.8917 0.9333 0.8083 0.9333 0.7417 0.9333 0.9333

(B) 0.9750 0.9250 0.9750 0.9750 0.9750 0.9250 0.9750 0.9750 0.9750 0.9250 0.9750 0.9750

(C) 0.7810 0.9190 0.8952 0.8952 0.7190 0.9190 0.8952 0.8952 0.7810 0.9190 0.8952 0.8952

(D) 0.7667 0.8333 0.8333 0.8333 0.7667 0.7667 0.8333 0.8333 0.7667 0.8333 0.8333 0.8333

(E) 0.9643 0.9722 0.9762 0.9762 0.9683 0.9127 0.9762 0.9683 0.9643 0.9722 0.9762 0.9762

(F) 0.4958 0.8072 0.8319 0.8313 0.5887 0.7933 0.8319 0.8339 0.4958 0.8072 0.8319 0.8312

(G) 0.9714 0.9571 0.9714 0.9714 0.9714 0.8714 0.9714 0.9571 0.9714 0.9571 0.9714 0.9714

(H) 0.8926 0.9280 0.9372 0.9429 0.8438 0.9354 0.9372 0.9354 0.8926 0.9280 0.9372 0.9429

(I) 0.9758 0.9750 0.9750 0.9750 0.9750 0.9750 0.9750 0.7258 0.9750 0.9750 0.9750 0.9750

(J) 0.9243 0.8559 0.9104 0.9317 0.9345 0.7774 0.9104 0.9233 0.9243 0.8559 0.9104 0.9317

(K) 0.9315 0.9640 0.9625 0.9693 0.9315 0.9577 0.9625 0.9625 0.9315 0.9640 0.9625 0.9693

Average 0.8738 0.8980 0.9274 0.9304 0.8734 0.8841 0.9274 0.8926 0.8737 0.8980 0.9274 0.9304

[Where, M1: F-SVNS-N-MADM with LSTMM, M2: F-SVNS-N-MADM with LSTMMM, M3: F-SVNS-N-

MADM with LSTSM, M4: F-SVNS-N-MADM with VNM, M5: F-SVNS-EW-MADM with LSTMM, M6:

F-SVNS-EW-MADM with LSTMMM, M7: F-SVNS-EW-MADM with LSTSM, M8: F-SVNS-EW-MADM

with VNM, M9: F-SVNS-ACC-MADM with LSTMM, M10: F-SVNS-ACC-MADM with LSTMMM, M11:

F-SVNS-ACC-MADM with LSTSM, M12: F-SVNS-ACC-MADM with VNM. and Alternatives (A)

Material Selection, (B) Machine Tool Selection (C) Rapid Prototype selection, (D) NTMP Selection, (E)

AGV Selection (F) Robot Selection (G) Metal Stamping Layout Selection (H) Electro Chemical Machining

process (I) Cutting Fluid Selection (J) Supplier Selection (K) Reverse Logistics Providers Selection]

Above Table 5.14, where the row indicates the collected case examples 1 to 11 and the

column indicate proposed methodologies with normalization methods. From the average

values from the conclusion From Table 5.14 insight M4 F-SVNS N-MADM with VNM

and M12 F-SVNS ACC-MADM with VNM give better solutions among proposed

methodologies with relative normalization methods and average result is nearest to value 1.

From the validation with different normalization approaches and comparisons with

different MADM techniques conclude that M4 F-SVNS N-MADM works with less

calculation and accurate ranking solution compared to M12 F-SVNS ACC-MADM. From

the detail calculation steps from Chapter 3 Point 3.1 and Point 3.3 also concluded F-SVNS

N-MADM is less calculative techniques for selecting compared to F-SVNS ACC-MADM

with MADM approach to improving performance in manufacturing and supply chain

function.

Chapter 6: Conclusion and Future Scope

195


196

CHAPTER NO.6

Conclusion and Future Scope

Multi Attribute Decision Making (MADM) is the recognized branch of decision making.

The various researchers work to investigate new more accurate MADM since last 3

decades. A major criticism of MADM is that different techniques may yield different

ranking solution when applied to the same problem and there are several limitations of

existing MADMs with various mathematical set theories practices. Here, fundamental

research is carried out and the work focuses on resolving the issues and limitations of

existing MADM techniques.

The thesis compiled with three new methodologies which belong to SVNS.

Decision making is the process of selection of alternative from the set of various criteria, to

meet the objective. The single valued Neutrosophic set (SVNS) is an ideal set of

Neutrosophic theory, which includes the information in degree of truthness, degree of

indeterminacy and degree of falsehood. Three new approaches for MADMs investigated (i)

Fuzzy Single Valued Neutrosophic Set Novel MADM (F-SVNS N- MADM), (ii) Fuzzy

Single Valued Neutrosophic Set Entropy Weight Based MADM (F-SVNS EW-MADM)

and (iii) Fuzzy Single Valued Neutrosophic Set Advanced Correlation Coefficient MADM

(F-SVNS ACC-MADM); which works with conversion on crisp/ fuzzy set into single

valued Neutrosophic set.

The proposed methodologies are implemented in manufacturing and supply chain

published case examples from various peer reviewed journals and books with same input

information for material selection, machine tool selection, rapid prototype selection,

nontraditional machining process selection, AGV selection, robot selection, metal

stamping layout selection, ECM program selection, coolant (cutting fluid) selection,

supplier selection, third party reverse logistics providers selection. Validation of three

methodologies with various normalization shows that the proposed methodologies give

more efficient, more accurate and less calculative results than other MADM‘s. The


197

validation shows that the Fuzzy Single Valued Neutrosophic Set Novel MADM with

Vector Normalization Method gives more accurate results all proposed methodologies.

The positive corner of two methodologies (F-SVNS N-MADM and F-SVNS ACC-

MADM) among three is that they give the solution without calculating attributes weight

which is uniqueness in MADM by considering SVNS mathematical set. The same set

theory is applied to third novel F-SVNS entropy weight MADM methodology, where

attribute weight is calculated with the help of entropy weight method. It also shows the

better ranking solution.

In sensitivity analysis and comparisons with other MADM approaches conclude that

among proposed three techniques F-SVNS N-MADM with VNM normalization approach

gives the less calculation and better solution with uncertainty, indeterminate, imprecise and

inconsistent information by considering degree of truth, indeterminacy and falsehood

simultaneously. The better ranking solution shows that the proposed methodology name F-

SVNS N- MADM gives more effective strategic decision of ranking for improving

performance of manufacturing and supply chain function. The likely area of the proposed

methodologies works with crisp/ lingustic information and then convert them in to F-

SVNS form and gives better solutions.

6.1 Actual Contribution by the Thesis

The thesis is with remarkable contribution of novel MADM method where conversion of

information in crisp / lingustic set (exact thinking) to Single Valued Neutrosophic Set

(SVNS) (Human behavioral thinking) is carried out, which is having the information in

degree of truthness, degree of indeterminacy and degree of falsehood, which leads to

improve the ranking solution. F-SVNS N-MADM is work without calculating the attribute

weight and gives more accurate ranking solution with less calculation and also tried to

eliminate the limitations of existing MADMs. Other than this, thesis also contributes

following important points.

Primary Understanding of the existing MADMs with their steps and advantages.

Primary Understanding of existing mathematical set used for MADMs with their

advantages.

6.1 Actual Contribution by the Thesis

198

Identified and tried to collect and solve random eleven domains where, best

selection process one of the keys to improve performance of manufacturing and

supply chain. The names of eleven domains are as under.






o Robot selection





o Third party reverse logistics providers (TPRLP) selection

Identified the research gap in terms of limitation/ drawback of existing MADMs

and affiliated mathematical set theories.

Investigated three new different F-SVNS Multi Attribute Decision Making (F-

SVNS-MADM) techniques that work with/ without calculating attribute weight.

o Fuzzy-Single Valued Neutrosophic Set Novel MADM (F-SVNS-N-

MADM)

o Fuzzy Single Valued Neutrosophic Set Entropy Weight based MADM (F-

SVNS EW-MADM)

o Fuzzy Single Valued Neutrosophic Set SVNS Advance Correlation

Coefficient MADM (F-SVNS-ACC-MADM)

Implemented and validated the proposed methodologies in eleven domains through

random case example collected in each domain with peer reviewed journal/ book.

Studied and explored the general ranking solution of proposed MADMs with

published ranking results and found that the proposed methods works with high

ranking capacity as compared to other MADM

Testing and analyzing sensitivity analysis to check the soundness of proposed

MADMs solutions with same case examples of eleven domains through (i)

different normalization methods and (ii) spearman correlation coefficient.


199

Investigated ―F-SVNS N-MADM‖ as the best MADM among the proposed

methods through average of all eleven domain spearman correlation coefficient

sensitivity analysis and which works with less calculation.

Identified the F-SVNS N-MADM is relatively simple, systematic and effective than

other existing MADM‘s.

Validation and sensitivity of proposed methodology is carried out with three

phases, (i) Checking and comparing with published ranking solution of existing

MADMs. This is covered in chapter 4 by implementing random eleven selection

domains of manufacturing and supply chain management (ii) evaluate the effect of

different normalization technique by implementing random eleven selection

domains (as mansion above) (iii) sensitivity is carried out through Spearman

ranking correlation coefficient.

6.2 Advantages of Proposed methodology

• Proposed methodology is gifted to convert decision maker‘s crisp data/ fuzzy

(linguistic) information into SVNS form, which makes more efficient ranking solution.

These conversions have the following hidden benefits as follows. This leads to improve

the ranking solution.

Able to identify the degree of truthness

Able to identify the degree of indeterminacy

Able to identify the degree of falsity

• The decision making under inconsistent, incomplete and indeterminate information.

• The proposed methodology gives more efficient ranking of the best alternative with

less computation.

• During calculation and normalization there is no loss of information; no single attribute

becomes zero.

• For better comparison with another validated MADM, information is collected for

input matrix data from the peer reviewed journals/ books in crisp/ linguistic set

information.

6.3 Future Scope

200

6.3 Future Scope

The proposed methodologies can give better solution in hybrid MADM.

The proposed methodologies can also give the better ranking solution in MAGDM.

Single valued neutrosophic set with interval data can incorporate with the proposed

MADM for advancement in the result.

Mathematical set theory advancement gives insight for MADM and MAGDM.

Decision support system gives better performance in industrial application

Hybrid approach with other theories, like SVNS and Linear programming, SVNS

and DEA, SVNS and OLAP, SVNS mathematical Programming, also gives better

solution.

If MADM embedded with SVNS and Artificial Intelligence (AI), it will be helpful

not only for the selection methodology but also for the various industrial area of

application.

Work can be implemented in other various selection methodologies which include

medical healthcare, structural, building and town planning, oil refineries and

various industrial applications.

SVNS perform very well if provided with web platform.

List of References

201

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[1] Collected Case Example 1: Material Selection

222

APPENDIX-A: F-SVNS N-MADM Detailed

Calculations


Step 8. Calculate the alternative weight

Calculate the alternative weight with the Equation (3.5) is as shown in Table 4.5 i.e.

consider the alternative weight of First alternatives calculated as {

} { }

{ } {

} .



The alternatives rank is given according to alternative weight in descending order,

. Alternatives ranking orders is


[2] Collected Case Example 2: Machine Tool Selection




} { }

{ } {

} { } {

}



APPENDIX-A: F-SVNS N-MADM Detailed Calculations

223


. Alternatives ranking order is


[3] Collected Case Example 3: Rapid Prototype Selection




} { }

{ } {

} { } {

}




. Alternatives ranking

order is as shown in Table 4.17

[4] Collected Case Example 4: Non Traditional Machining Process

Selection




} { }

{ } {

} { } {

}


[5] Collected Case Example 5: Automated Guided Vehicle (AGV) Selection

224





[5] Collected Case Example 5: Automated Guided Vehicle (AGV)

Selection




} { }

{ } {

} { } {

}




Alternatives ranking order is as shown

in Table 4.29

[6] Collected Case Example 6: Robot Selection




} { }

{ } {

}


225




.

Alternatives ranking order is


[7] Collected Case Example 7: Metal Stamping Layout Selections




} { }

{ } {

} { }




Alternatives ranking order


[8] Collected Case Example 8: ECM Programme Selection


[9] Collected Case Example 9: Cutting Fluid (Coolant) Selection

226



} { }

{ } {

} { } {

}




.







} { }

{ } {

}







227

[10] Collected Case Example 10: Supplier Selection




} { }

{ } {

} { }






[11] Collected Case Example 11: Third Party Logistic Provider’s

Selection




} { }

{ } {

} { } {

} { }



228

The alternatives rank is given according to alternative weight in descending order

.



APPENDIX -B: F-SVNS EW-MADM Detailed Calculations

229

APPENDIX -B: F-SVNS EW-MADM Detailed

Calculations


Step 8. Calculate the entropy value for attribute

Calculate the attribute value with the Equation (3.6) is as shown in Table 4.6. i.e. consider

calculation of the entropy value for attribute A1.

{ } {

} { } {

} { }


Step 9. Calculate the entropy weight of attribute


i.e. consider calculation of the alternative entropy value for attribute A1.

*

+

The same calculation is also is carried out for to .

Where,∑



{ }

{ }

{ }

{ }




230






Calculate the attribute value with the Equation (3.6) is as shown in Table 4.12

i.e. consider calculation of the entropy value for attribute A1.

⁄ { } {

} { } {

} { }





*

+


Where,∑



{ }

{ } {

} {

} { }

{ }


231










⁄ { } {

} { } {

} { } {

}





*

+


Where,∑



{ }

{ } {

[4] Collected Case Example 4: Non Traditional Machining Process Selection

232

} {

} { }

{ }




. Alternatives ranking order


[4] Collected Case Example 4: Non Traditional Machining Process

Selection




⁄ { } {

} { } {

}





*

+


Where,∑


233


Find the alternative weight 1by Equation (3.8) is as shown in Table 4.24

{ }

{ } {

} {

} { }

{ }






[5] Collected Case Example 5: AGV Selection




⁄ { } {

} { } {

} { } {

} { } {

}






234

*

+


Where,∑



{ }

{ } {

} {

} { }

{ }




.

Alternatives ranking order is as shown

in Table 4.30





⁄ { } {

} { } {

} { } {

} { } {

} { } {

} { } {


235

} { } {

} { } {

} { } {

} { } {

} { } {

} { } {

} { } {

} { }





*

+


Where,∑



{ }

{ } {

} {

}




[7] Collected Case Example 5: Metal Stamping Layout Selection

236

.



[7] Collected Case Example 5: Metal Stamping Layout Selection




⁄ { } {

} { } {

} { } {

}





*

+


Where,∑



{ }

{ } {


237

} {

} { }




Alternatives ranking order


[8] Collected Case Example 8: Electro Chemical Machining Programme

Selection




⁄ { } {

} { } {

} { } {

} { } {

} { } {

} { } {

} { } {

} { }





*

+


238


Where,∑



{ }

{ } {

} {

} { }

{ }




.

Alternatives ranking orders as






⁄ { } {

} { } {

} { }




239



*

+


Where,∑



{ }

{ } {

} {

}




lternatives ranking order is






⁄ { } {

} { } {

} { } {

} { } {

} { } {


240

} { } {

} { } {

} { } {

} { } {

}





*

+


Where,∑



{ }

{ } {

} {

} { }





as shown in Table

4.60


241

[11] Collected Case Example 11: Third Party Logistics Provider’s

(TPLP) Selection




⁄ { } {

} { } {

} { } {

} { } {

} { } {

} { } {

} { } {

} { }





*

+


Where,∑



[11] Collected Case Example 11: Third Party Logistics Provider‘s (TPLP) Selection

242

{ }

{ } {

} {

} { }

{ } {

}




lternatives

ranking order is


APPENDIX -C: F-SVNS ACC-MADM Detailed Calculations

243

APPENDIX -C: F-SVNS ACC-MADM Detailed

Calculations


Step 8. Calculate the Advance Correlation Coefficient function of Alternatives



W (Aj)

[

{

{ } { } { } { }

}

{(

{ } { } { } { }

) (

)}

]

W (Aj)








Find the Correlation Advance Coefficient function for each alternative with Equation (3.9)



244

W (Aj)

[

{

{ } { } { } { } { } { } }

{

(

{ } { } { } { } { } { } )

(

)

}

]

W (Aj)










W (Aj)

[

{

{ } { } { } { } { } { } }

{

(

{ } { } { } { } { } { } )

(

)

}

]


245

W (Aj)






[4] Collected Case Example 4: NTMP Selection




W (Aj)

[

{

{ } { } { } { } { } { } }

{

(

{ } { } { } { } { } { } )

(

)

}

]

W (Aj)




. Alternatives ranking orders is



246





W (Aj)

[

{

{ } { } { } { } { } { } }

{

(

{ } { } { } { } { } { } )

(

)

}

]

W (Aj)











247

W (Aj)

[

{

{ } { } { } { }

}

{(

{ } { } { } { }

) (

)}

]

W (Aj)




.



[7] Collected Case Example 7: Metal Stamping Layout Selections





248

W (Aj)

[

{

{ } { } { } { } { } }

{

(

{ } { } { } { } { } )

(

)

}

]

W (Aj)





consider as last rank; is as shown in Table 4.43


. Alternatives ranking order







249

W (Aj)

[

{

{ } { } { } { } { } { } }

{

(

{ } { } { } { } { } { } )

(

)

}

]

W (Aj)










W (Aj)

[

{

{ } { } { } { }

}

{(

{ } { } { } { }

) (

)}

]


250

W (Aj)










W (Aj)

[

{

{ } { } { } { } { } }

{

(

{ } { } { } { } { } )

(

)

}

]

W (Aj)







251

[11] Collected Case Example 11: Third Party Logistic Provider’s

Selection




W (Aj)

[

{

{ } { } { } { } { } { } { } }

{

(

{ } { } { } { } { } { } { } )

(

)

}

]

W (Aj)




. Alternatives

ranking order is


[1] Sensitivity Analysis for Material Selection for Proposed Methodology (Case Example 1)

252

APPENDIX -D: Spearman Correlation Coefficient

Detailed Calculations

[1] Sensitivity Analysis for Material Selection for Proposed Methodology

(Case Example 1)

The value of between and is derived by Equation (5.1)

Similar steps are carried out to calculate the value of for to to to

to to to to to to to

Similar steps are carried out to calculate the value of for to .

TABLE I: Spearman Rank Correlation Coefficient for Collective Case Example of Material Selection

M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 M12

M1 1.0000 0.7000 1.0000 1.0000 1.0000 0.9000 1.0000 0.9000 1.0000 0.7000 1.0000 1.0000

M2 0.7000 1.0000 0.7000 0.7000 0.7000 0.9000 0.7000 0.4000 0.7000 1.0000 0.7000 0.7000

M3 1.0000 0.7000 1.0000 1.0000 1.0000 0.9000 1.0000 0.9000 1.0000 0.7000 1.0000 1.0000

M4 1.0000 0.7000 1.0000 1.0000 1.0000 0.9000 1.0000 0.9000 1.0000 0.7000 1.0000 1.0000

M5 1.0000 0.7000 1.0000 1.0000 1.0000 0.9000 1.0000 0.9000 1.0000 0.7000 1.0000 1.0000

M6 0.9000 0.9000 0.9000 0.9000 0.9000 1.0000 0.9000 0.7000 0.9000 0.9000 0.9000 0.9000

M7 1.0000 0.7000 1.0000 1.0000 1.0000 0.9000 1.0000 0.9000 1.0000 0.7000 1.0000 1.0000

M8 0.9000 0.4000 0.9000 0.9000 0.9000 0.7000 0.9000 1.0000 0.9000 0.4000 0.9000 0.9000

M9 1.0000 0.7000 1.0000 1.0000 1.0000 0.9000 1.0000 0.9000 1.0000 0.7000 1.0000 1.0000

M10 0.7000 1.0000 0.7000 0.7000 0.7000 0.9000 0.7000 0.4000 0.7000 1.0000 0.7000 0.7000

M11 1.0000 0.7000 1.0000 1.0000 1.0000 0.9000 1.0000 0.9000 1.0000 0.7000 1.0000 1.0000

M12 1.0000 0.7000 1.0000 1.0000 1.0000 0.9000 1.0000 0.9000 1.0000 0.7000 1.0000 1.0000

Average 0.9333 0.7417 0.9333 0.9333 0.9333 0.8917 0.9333 0.8083 0.9333 0.7417 0.9333 0.9333

[2] Sensitivity Analysis for Machine Tool Selection for Proposed

Methodology (Case Example 2)


APPENDIX -D: Spearman Correlation Coefficient Detailed Calculations

253




TABLE II: Spearman Rank Correlation Coefficient for Collective Case Example of Machine Tool

Selection

M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 M12

M1 1.0000 0.9000 1.0000 1.0000 1.0000 0.9000 1.0000 1.0000 1.0000 0.9000 1.0000 1.0000

M2 0.9000 1.0000 0.9000 0.9000 0.9000 1.0000 0.9000 0.9000 0.9000 1.0000 0.9000 0.9000

M3 1.0000 0.9000 1.0000 1.0000 1.0000 0.9000 1.0000 1.0000 1.0000 0.9000 1.0000 1.0000

M4 1.0000 0.9000 1.0000 1.0000 1.0000 0.9000 1.0000 1.0000 1.0000 0.9000 1.0000 1.0000

M5 1.0000 0.9000 1.0000 1.0000 1.0000 0.9000 1.0000 1.0000 1.0000 0.9000 1.0000 1.0000

M6 0.9000 1.0000 0.9000 0.9000 0.9000 1.0000 0.9000 0.9000 0.9000 1.0000 0.9000 0.9000

M7 1.0000 0.9000 1.0000 1.0000 1.0000 0.9000 1.0000 1.0000 1.0000 0.9000 1.0000 1.0000

M8 1.0000 0.9000 1.0000 1.0000 1.0000 0.9000 1.0000 1.0000 1.0000 0.9000 1.0000 1.0000

M9 1.0000 0.9000 1.0000 1.0000 1.0000 0.9000 1.0000 1.0000 1.0000 0.9000 1.0000 1.0000

M10 0.9000 1.0000 0.9000 0.9000 0.9000 1.0000 0.9000 0.9000 0.9000 1.0000 0.9000 0.9000

M11 1.0000 0.9000 1.0000 1.0000 1.0000 0.9000 1.0000 1.0000 1.0000 0.9000 1.0000 1.0000

M12 1.0000 0.9000 1.0000 1.0000 1.0000 0.9000 1.0000 1.0000 1.0000 0.9000 1.0000 1.0000

Average 0.9750 0.9250 0.9750 0.9750 0.9750 0.9250 0.9750 0.9750 0.9750 0.9250 0.9750 0.9750

[3] Sensitivity Analysis for Rapid Prototype Selection for Proposed

Methodology (Case Example 3)




Similar steps are carried out to calculate the value of for to

[4] Sensitivity Analysis for NTMP Selection for Proposed Methodology (Case Example 4)

254

TABLE III: Spearman Rank Correlation Coefficient for Collective Case Example of Rapid Prototype

Selection

M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 M12

M1 1.0000 0.8286 0.6571 0.6571 0.9429 0.8286 0.6571 0.6571 1.0000 0.8286 0.6571 0.6571

M2 0.8286 1.0000 0.9429 0.9429 0.7143 1.0000 0.9429 0.9429 0.8286 1.0000 0.9429 0.9429

M3 0.6571 0.9429 1.0000 1.0000 0.6000 0.9429 1.0000 1.0000 0.6571 0.9429 1.0000 1.0000

M4 0.6571 0.9429 1.0000 1.0000 0.6000 0.9429 1.0000 1.0000 0.6571 0.9429 1.0000 1.0000

M5 0.9429 0.7143 0.6000 0.6000 1.0000 0.7143 0.6000 0.6000 0.9429 0.7143 0.6000 0.6000

M6 0.8286 1.0000 0.9429 0.9429 0.7143 1.0000 0.9429 0.9429 0.8286 1.0000 0.9429 0.9429

M7 0.6571 0.9429 1.0000 1.0000 0.6000 0.9429 1.0000 1.0000 0.6571 0.9429 1.0000 1.0000

M8 0.6571 0.9429 1.0000 1.0000 0.6000 0.9429 1.0000 1.0000 0.6571 0.9429 1.0000 1.0000

M9 1.0000 0.8286 0.6571 0.6571 0.9429 0.8286 0.6571 0.6571 1.0000 0.8286 0.6571 0.6571

M10 0.8286 1.0000 0.9429 0.9429 0.7143 1.0000 0.9429 0.9429 0.8286 1.0000 0.9429 0.9429

M11 0.6571 0.9429 1.0000 1.0000 0.6000 0.9429 1.0000 1.0000 0.6571 0.9429 1.0000 1.0000

M12 0.6571 0.9429 1.0000 1.0000 0.6000 0.9429 1.0000 1.0000 0.6571 0.9429 1.0000 1.0000

Average 0.7810 0.9190 0.8952 0.8952 0.7190 0.9190 0.8952 0.8952 0.7810 0.9190 0.8952 0.8952

[4] Sensitivity Analysis for NTMP Selection for Proposed Methodology

(Case Example 4)





TABLE IV: Spearman Rank Correlation Coefficient for Collective Case Example of NTMP Selection

M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 M12

M1 1.0000 0.8000 0.6000 0.6000 1.0000 1.0000 0.6000 0.6000 1.0000 0.8000 0.6000 0.6000

M2 0.8000 1.0000 0.8000 0.8000 0.8000 0.8000 0.8000 0.8000 0.8000 1.0000 0.8000 0.8000

M3 0.6000 0.8000 1.0000 1.0000 0.6000 0.6000 1.0000 1.0000 0.6000 0.8000 1.0000 1.0000

M4 0.6000 0.8000 1.0000 1.0000 0.6000 0.6000 1.0000 1.0000 0.6000 0.8000 1.0000 1.0000

M5 1.0000 0.8000 0.6000 0.6000 1.0000 1.0000 0.6000 0.6000 1.0000 0.8000 0.6000 0.6000

M6 1.0000 0.8000 0.6000 0.6000 1.0000 1.0000 0.6000 0.6000 1.0000 0.8000 0.6000 0.6000

M7 0.6000 0.8000 1.0000 1.0000 0.6000 0.6000 1.0000 1.0000 0.6000 0.8000 1.0000 1.0000

M8 0.6000 0.8000 1.0000 1.0000 0.6000 0.6000 1.0000 1.0000 0.6000 0.8000 1.0000 1.0000


255

M9 1.0000 0.8000 0.6000 0.6000 1.0000 1.0000 0.6000 0.6000 1.0000 0.8000 0.6000 0.6000

M10 0.8000 1.0000 0.8000 0.8000 0.8000 0.8000 0.8000 0.8000 0.8000 1.0000 0.8000 0.8000

M11 0.6000 0.8000 1.0000 1.0000 0.6000 0.6000 1.0000 1.0000 0.6000 0.8000 1.0000 1.0000

M12 0.6000 0.8000 1.0000 1.0000 0.6000 0.6000 1.0000 1.0000 0.6000 0.8000 1.0000 1.0000

Average 0.7667 0.8333 0.8333 0.8333 0.7667 0.7667 0.8333 0.8333 0.7667 0.8333 0.8333 0.8333

[5] Sensitivity Analysis for AGV Selection for Proposed Methodology

(Case Example 5)


(

*




TABLE V: Spearman Rank Correlation Coefficient for Collective Case Example of AGV Selection

M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 M12

M1 1.0000 0.9762 0.9524 0.9524 0.9762 0.9048 0.9524 0.9762 1.0000 0.9762 0.9524 0.9524

M2 0.9762 1.0000 0.9762 0.9762 0.9524 0.9286 0.9762 0.9524 0.9762 1.0000 0.9762 0.9762

M3 0.9524 0.9762 1.0000 1.0000 0.9762 0.9048 1.0000 0.9762 0.9524 0.9762 1.0000 1.0000

M4 0.9524 0.9762 1.0000 1.0000 0.9762 0.9048 1.0000 0.9762 0.9524 0.9762 1.0000 1.0000

M5 0.9762 0.9524 0.9762 0.9762 1.0000 0.8810 0.9762 1.0000 0.9762 0.9524 0.9762 0.9762

M6 0.9048 0.9286 0.9048 0.9048 0.8810 1.0000 0.9048 0.8810 0.9048 0.9286 0.9048 0.9048

M7 0.9524 0.9762 1.0000 1.0000 0.9762 0.9048 1.0000 0.9762 0.9524 0.9762 1.0000 1.0000

M8 0.9762 0.9524 0.9762 0.9762 1.0000 0.8810 0.9762 1.0000 0.9762 0.9524 0.9762 0.9762

M9 1.0000 0.9762 0.9524 0.9524 0.9762 0.9048 0.9524 0.9762 1.0000 0.9762 0.9524 0.9524

M10 0.9762 1.0000 0.9762 0.9762 0.9524 0.9286 0.9762 0.9524 0.9762 1.0000 0.9762 0.9762

M11 0.9524 0.9762 1.0000 1.0000 0.9762 0.9048 1.0000 0.9762 0.9524 0.9762 1.0000 1.0000

M12 0.9524 0.9762 1.0000 1.0000 0.9762 0.9048 1.0000 0.9762 0.9524 0.9762 1.0000 1.0000

Average 0.9643 0.9722 0.9762 0.9762 0.9683 0.9127 0.9762 0.9683 0.9643 0.9722 0.9762 0.9762

[6] Sensitivity Analysis for Robot Selection for Proposed Methodology

(Case Example 6)


[7] Sensitivity Analysis for Metal Stamping Layout Selection for Proposed Methodology (Case Example 7)

256

(

)




TABLE VI: Spearman Rank Correlation Coefficient for Collective Case Example of Robot Selection

M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 M12

M1 1.0000 0.3089 0.3742 0.3364 0.9145 0.2723 0.3742 0.3474 1.0000 0.3089 0.3742 0.3382

M2 0.3089 1.0000 0.9225 0.9719 0.4328 0.9695 0.9225 0.9542 0.3089 1.0000 0.9225 0.9725

M3 0.3742 0.9225 1.0000 0.9799 0.5122 0.9243 1.0000 0.9933 0.3742 0.9225 1.0000 0.9792

M4 0.3364 0.9719 0.9799 1.0000 0.4713 0.9548 0.9799 0.9939 0.3364 0.9719 0.9799 0.9994

M5 0.9145 0.4328 0.5122 0.4713 1.0000 0.4054 0.5122 0.4872 0.9145 0.4328 0.5122 0.4689

M6 0.2723 0.9695 0.9243 0.9548 0.4054 1.0000 0.9243 0.9499 0.2723 0.9695 0.9243 0.9536

M7 0.3742 0.9225 1.0000 0.9799 0.5122 0.9243 1.0000 0.9933 0.3742 0.9225 1.0000 0.9792

M8 0.3474 0.9542 0.9933 0.9939 0.4872 0.9499 0.9933 1.0000 0.3474 0.9542 0.9933 0.9933

M9 1.0000 0.3089 0.3742 0.3364 0.9145 0.2723 0.3742 0.3474 1.0000 0.3089 0.3742 0.3382

M10 0.3089 1.0000 0.9225 0.9719 0.4328 0.9695 0.9225 0.9542 0.3089 1.0000 0.9225 0.9725

M11 0.3742 0.9225 1.0000 0.9799 0.5122 0.9243 1.0000 0.9933 0.3742 0.9225 1.0000 0.9792

M12 0.3382 0.9725 0.9792 0.9994 0.4689 0.9536 0.9792 0.9933 0.3382 0.9725 0.9792 1.0000

Average 0.4958 0.8072 0.8319 0.8313 0.5887 0.7933 0.8319 0.8339 0.4958 0.8072 0.8319 0.8312

[7] Sensitivity Analysis for Metal Stamping Layout Selection for

Proposed Methodology (Case Example 7)





257


TABLE VII: Spearman Rank Correlation Coefficient for Collective Case Example of Metal Stamping

Layout Selection

M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 M12

M1 1.0000 0.9429 1.0000 1.0000 1.0000 0.8286 1.0000 0.9429 1.0000 0.9429 1.0000 1.0000

M2 0.9429 1.0000 0.9429 0.9429 0.9429 0.9429 0.9429 1.0000 0.9429 1.0000 0.9429 0.9429

M3 1.0000 0.9429 1.0000 1.0000 1.0000 0.8286 1.0000 0.9429 1.0000 0.9429 1.0000 1.0000

M4 1.0000 0.9429 1.0000 1.0000 1.0000 0.8286 1.0000 0.9429 1.0000 0.9429 1.0000 1.0000

M5 1.0000 0.9429 1.0000 1.0000 1.0000 0.8286 1.0000 0.9429 1.0000 0.9429 1.0000 1.0000

M6 0.8286 0.9429 0.8286 0.8286 0.8286 1.0000 0.8286 0.9429 0.8286 0.9429 0.8286 0.8286

M7 1.0000 0.9429 1.0000 1.0000 1.0000 0.8286 1.0000 0.9429 1.0000 0.9429 1.0000 1.0000

M8 0.9429 1.0000 0.9429 0.9429 0.9429 0.9429 0.9429 1.0000 0.9429 1.0000 0.9429 0.9429

M9 1.0000 0.9429 1.0000 1.0000 1.0000 0.8286 1.0000 0.9429 1.0000 0.9429 1.0000 1.0000

M10 0.9429 1.0000 0.9429 0.9429 0.9429 0.9429 0.9429 1.0000 0.9429 1.0000 0.9429 0.9429

M11 1.0000 0.9429 1.0000 1.0000 1.0000 0.8286 1.0000 0.9429 1.0000 0.9429 1.0000 1.0000

M12 1.0000 0.9429 1.0000 1.0000 1.0000 0.8286 1.0000 0.9429 1.0000 0.9429 1.0000 1.0000

Average 0.9714 0.9571 0.9714 0.9714 0.9714 0.8714 0.9714 0.9571 0.9714 0.9571 0.9714 0.9714

[8] Sensitivity Analysis for Electro Chemical Machining Process Selection

for Proposed Methodology (Case Example 8)


(

)




TABLE VIII: Spearman Rank Correlation Coefficient for Collective Case Example of ECM


M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 M12

M1 1.0000 0.8893 0.8500 0.8679 0.9357 0.8714 0.8500 0.8393 1.0000 0.8893 0.8500 0.8679

M2 0.8893 1.0000 0.9179 0.9607 0.8000 0.9607 0.9179 0.9214 0.8893 1.0000 0.9179 0.9607

M3 0.8500 0.9179 1.0000 0.9786 0.8107 0.9464 1.0000 0.9964 0.8500 0.9179 1.0000 0.9786

[9] Sensitivity Analysis for Cutting Fluid (Coolant) Selection for Proposed Methodology (Case Example 9)

258

M4 0.8679 0.9607 0.9786 1.0000 0.7821 0.9571 0.9786 0.9821 0.8679 0.9607 0.9786 1.0000

M5 0.9357 0.8000 0.8107 0.7821 1.0000 0.8571 0.8107 0.8000 0.9357 0.8000 0.8107 0.7821

M6 0.8714 0.9607 0.9464 0.9571 0.8571 1.0000 0.9464 0.9500 0.8714 0.9607 0.9464 0.9571

M7 0.8500 0.9179 1.0000 0.9786 0.8107 0.9464 1.0000 0.9964 0.8500 0.9179 1.0000 0.9786

M8 0.8393 0.9214 0.9964 0.9821 0.8000 0.9500 0.9964 1.0000 0.8393 0.9214 0.9964 0.9821

M9 1.0000 0.8893 0.8500 0.8679 0.9357 0.8714 0.8500 0.8393 1.0000 0.8893 0.8500 0.8679

M10 0.8893 1.0000 0.9179 0.9607 0.8000 0.9607 0.9179 0.9214 0.8893 1.0000 0.9179 0.9607

M11 0.8500 0.9179 1.0000 0.9786 0.8107 0.9464 1.0000 0.9964 0.8500 0.9179 1.0000 0.9786

M12 0.8679 0.9607 0.9786 1.0000 0.7821 0.9571 0.9786 0.9821 0.8679 0.9607 0.9786 1.0000

Average 0.8926 0.9280 0.9372 0.9429 0.8438 0.9354 0.9372 0.9354 0.8926 0.9280 0.9372 0.9429

[9] Sensitivity Analysis for Cutting Fluid (Coolant) Selection for






TABLE IX: Spearman Rank Correlation Coefficient for Collective Case Example of Cutting Fluid

Selection

M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 M12

M1 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.7097 1.0000 1.0000 1.0000 1.0000

M2 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.7000 1.0000 1.0000 1.0000 1.0000

M3 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.7000 1.0000 1.0000 1.0000 1.0000

M4 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.7000 1.0000 1.0000 1.0000 1.0000

M5 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.7000 1.0000 1.0000 1.0000 1.0000

M6 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.7000 1.0000 1.0000 1.0000 1.0000

M7 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.7000 1.0000 1.0000 1.0000 1.0000

M8 0.7000 0.7000 0.7000 0.7000 0.7000 0.7000 0.7000 1.0000 0.7000 0.7000 0.7000 0.7000

M9 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.7000 1.0000 1.0000 1.0000 1.0000

M10 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.7000 1.0000 1.0000 1.0000 1.0000

M11 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.7000 1.0000 1.0000 1.0000 1.0000

M12 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.7000 1.0000 1.0000 1.0000 1.0000

Average 0.9758 0.9750 0.9750 0.9750 0.9750 0.9750 0.9750 0.7258 0.9750 0.9750 0.9750 0.9750


259

[10] Sensitivity Analysis for Supplier Selection for Proposed Methodology

(Case Example 10)


(

)




TABLE X: Spearman Rank Correlation Coefficient for Collective Case Example of Supplier Selection

M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 M12

M1 1.0000 0.8535 0.9298 0.9484 0.9917 0.7647 0.9298 0.9422 1.0000 0.8535 0.9298 0.9484

M2 0.8535 1.0000 0.7606 0.8246 0.8803 0.9587 0.7606 0.7936 0.8535 1.0000 0.7606 0.8246

M3 0.9298 0.7606 1.0000 0.9856 0.9319 0.6450 1.0000 0.9959 0.9298 0.7606 1.0000 0.9856

M4 0.9484 0.8246 0.9856 1.0000 0.9587 0.7255 0.9856 0.9938 0.9484 0.8246 0.9856 1.0000

M5 0.9917 0.8803 0.9319 0.9587 1.0000 0.8101 0.9319 0.9463 0.9917 0.8803 0.9319 0.9587

M6 0.7647 0.9587 0.6450 0.7255 0.8101 1.0000 0.6450 0.6863 0.7647 0.9587 0.6450 0.7255

M7 0.9298 0.7606 1.0000 0.9856 0.9319 0.6450 1.0000 0.9959 0.9298 0.7606 1.0000 0.9856

M8 0.9422 0.7936 0.9959 0.9938 0.9463 0.6863 0.9959 1.0000 0.9422 0.7936 0.9959 0.9938

M9 1.0000 0.8535 0.9298 0.9484 0.9917 0.7647 0.9298 0.9422 1.0000 0.8535 0.9298 0.9484

M10 0.8535 1.0000 0.7606 0.8246 0.8803 0.9587 0.7606 0.7936 0.8535 1.0000 0.7606 0.8246

M11 0.9298 0.7606 1.0000 0.9856 0.9319 0.6450 1.0000 0.9959 0.9298 0.7606 1.0000 0.9856

M12 0.9484 0.8246 0.9856 1.0000 0.9587 0.7255 0.9856 0.9938 0.9484 0.8246 0.9856 1.0000

Average 0.9243 0.8559 0.9104 0.9317 0.9345 0.7774 0.9104 0.9233 0.9243 0.8559 0.9104 0.9317

[11] Sensitivity Analysis for Third Party Reverse Logistics Selection for



[12] Conclusion validation of the proposed methodology using Sensitivity analysis

260

(

)




TABLE XI: Spearman Rank Correlation Coefficient for Collective Case Example of Reverse Logistics

Providers selection

M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 M12

M1 1.0000 0.9250 0.8929 0.9143 1.0000 0.9286 0.8929 0.8929 1.0000 0.9250 0.8929 0.9143

M2 0.9250 1.0000 0.9643 0.9714 0.9250 0.9929 0.9643 0.9643 0.9250 1.0000 0.9643 0.9714

M3 0.8929 0.9643 1.0000 0.9964 0.8929 0.9500 1.0000 1.0000 0.8929 0.9643 1.0000 0.9964

M4 0.9143 0.9714 0.9964 1.0000 0.9143 0.9607 0.9964 0.9964 0.9143 0.9714 0.9964 1.0000

M5 1.0000 0.9250 0.8929 0.9143 1.0000 0.9286 0.8929 0.8929 1.0000 0.9250 0.8929 0.9143

M6 0.9286 0.9929 0.9500 0.9607 0.9286 1.0000 0.9500 0.9500 0.9286 0.9929 0.9500 0.9607

M7 0.8929 0.9643 1.0000 0.9964 0.8929 0.9500 1.0000 1.0000 0.8929 0.9643 1.0000 0.9964

M8 0.8929 0.9643 1.0000 0.9964 0.8929 0.9500 1.0000 1.0000 0.8929 0.9643 1.0000 0.9964

M9 1.0000 0.9250 0.8929 0.9143 1.0000 0.9286 0.8929 0.8929 1.0000 0.9250 0.8929 0.9143

M10 0.9250 1.0000 0.9643 0.9714 0.9250 0.9929 0.9643 0.9643 0.9250 1.0000 0.9643 0.9714

M11 0.8929 0.9643 1.0000 0.9964 0.8929 0.9500 1.0000 1.0000 0.8929 0.9643 1.0000 0.9964

M12 0.9143 0.9714 0.9964 1.0000 0.9143 0.9607 0.9964 0.9964 0.9143 0.9714 0.9964 1.0000

Average 0.9315 0.9640 0.9625 0.9693 0.9315 0.9577 0.9625 0.9625 0.9315 0.9640 0.9625 0.9693

[12] Conclusion validation of the proposed methodology using Sensitivity

analysis

Average of Spearman Correlation Coefficient M1 with collected random sample selection



261










[12] Conclusion validation of the proposed methodology using Sensitivity analysis

262


APPENDIX - E: Investigated MADM‘s MATLAB Coding

263

APPENDIX - E: Investigated MADM’s MATLAB

Coding

The MATLAB coding solutions for three proposed methodologies with different

normalization methods are as under. For example purpose the input crisp information is

collected from material selection collected case example. Coding sign [1 1 0 1]; here 1

shows the beneficial attribute while 0 shows the non-beneficial attribute. It shows that A1,

A2 and A4 are beneficial attribute, while A3 is non-beneficial attribute. The coding is

carried out for accuracy reason. The coding is applied for each collected case examples

during validation through different normalization methods for chapter 5. Here, MATLAB

coding is demonstrated for Case Example 1 as sample.

[1] MATLAB Coding for M1: F- SVNS N- MADM with LST-MM

clear all

clc

Mat = [ 1650 58.5 2.3 0.5;

1000 45.4 2.1 0.335;

350 21.7 2.6 0.335;

2150 64.3 2.4 0.5;

700 23 1.71 0.59];

MatS = [1 1 0 1];

sz = size(Mat);

nr = sz(1);

nc = sz(2);

MatT = [];

Mat1 = [];

Mat2 = []; test=[];

[1] MATLAB Coding for M1: F- SVNS N- MADM with LST-MM

264

Mat3 = [];

for i=1:nc

if MatS(i) == 1

Mat1 = [Mat1 max(Mat(:,i))];

test=[];

for j=1:nr

test = [test; Mat(j,i)/Mat1(i)];

end

Mat2 = [Mat2 test];

test=[];

for j=1:nr

test = [test; Mat2(j,i) (1-Mat2(j,i)) (1-Mat2(j,i))];

end

Mat3 = [Mat3 test];

MatT = [MatT 1 0 0];

elseif MatS(i) == 0

Mat1 = [Mat1 min(Mat(:,i))];

test=[];

for j=1:nr

test = [test; Mat1(i)/Mat(j,i)];

end

Mat2 = [Mat2 test];

test=[];

for j=1:nr

test = [test; (1-Mat2(j,i)) Mat2(j,i) Mat2(j,i)];

end

Mat3 = [Mat3 test];


265


end

end

MatFinal = [];

for i=1:nr

MatFinal = [MatFinal; sum(Mat3(i,:).*MatT)];

end

MatFinal

[MM Rank] = sort(MatFinal,1,'descend');

[2] MATLAB Coding for M2: F- SVNS N- MADM with LST-MMM

clear all

clc

Mat = [ 1650 58.5 2.3 0.5;

1000 45.4 2.1 0.335;

350 21.7 2.6 0.335;

2150 64.3 2.4 0.5;

700 23 1.71 0.59];

MatS = [1 1 0 1];

sz = size(Mat);

nr = sz(1);

nc = sz(2);

MatT = [];

[2] MATLAB Coding for M2: F- SVNS N- MADM with LST-MMM

266

Mat1 = [];

Mat2 = []; test=[];

Mat3 = [];

for i=1:nc

if MatS(i) == 1

mx = max(Mat(:,i));

mn = min(Mat(:,i));

test=[];

for j=1:nr

test = [test; (Mat(j,i)-mn)/(mx-mn)];

end

Mat2 = [Mat2 test];

test=[];

for j=1:nr


end

Mat3 = [Mat3 test];


elseif MatS(i) == 0

mx = max(Mat(:,i));

mn = min(Mat(:,i));

test=[];

for j=1:nr

test = [test; (mx-Mat(j,i))/(mx-mn)];

end

Mat2 = [Mat2 test];

test=[];


267

for j=1:nr


end

Mat3 = [Mat3 test];


end

end

MatFinal = [];

for i=1:nr


end

MatFinal


[3] MATLAB Coding for M3: F- SVNS N- MADM with LST-SM

clear all

clc

Mat = [ 1650 58.5 2.3 0.5;

1000 45.4 2.1 0.335;

350 21.7 2.6 0.335;

2150 64.3 2.4 0.5;

700 23 1.71 0.59];

MatS = [1 1 0 1];

sz = size(Mat);

nr = sz(1);

nc = sz(2);

[3] MATLAB Coding for M3: F- SVNS N- MADM with LST-SM

268

MatT = [];

Mat1 = [];

Mat2 = []; test=[];

Mat3 = [];

for i=1:nc

if MatS(i) == 1

Mat1 = [Mat1 sum(Mat(:,i))];

test=[];

for j=1:nr


end

Mat2 = [Mat2 test];

test=[];

for j=1:nr


end

Mat3 = [Mat3 test];


elseif MatS(i) == 0


test=[];

for j=1:nr

test = [test; 1-Mat(j,i)/Mat1(i)];

end

Mat2 = [Mat2 test];


269

test=[];

for j=1:nr


end

Mat3 = [Mat3 test];


end

end

MatFinal = [];

for i=1:nr


end

MatFinal


[4] MATLAB Coding for M4: F- SVNS N- MADM with VNM

clear all

clc

Mat = [ 1650 58.5 2.3 0.5;

1000 45.4 2.1 0.335;

350 21.7 2.6 0.335;

2150 64.3 2.4 0.5;

700 23 1.71 0.59];

MatS = [1 1 0 1];

sz = size(Mat);

nr = sz(1);

[4] MATLAB Coding for M4: F- SVNS N- MADM with VNM

270

nc = sz(2);

MatT = [];

Mat1 = [];

Mat2 = []; test=[];

Mat3 = [];

for i=1:nc

if MatS(i) == 1

v1=0;

for j=1:nr

v1 = v1 + Mat(j,i)^2;

end

Mat1 = [Mat1 sqrt(v1)];

test=[];

for j=1:nr


end

Mat2 = [Mat2 test];

test=[];

for j=1:nr


end

Mat3 = [Mat3 test];


elseif MatS(i) == 0

v1=0;

for j=1:nr

v1 = v1 + Mat(j,i)^2;


271

end


test=[];

for j=1:nr


end

Mat2 = [Mat2 test];

test=[];

for j=1:nr


end

Mat3 = [Mat3 test];


end

end

MatFinal = [];

for i=1:nr


end

MatFinal


[5] MATLAB Coding for M5: F- SVNS EW- MADM with LST- MM

clear all

clc

Mat = [ 1650 58.5 2.3 0.5;

[5] MATLAB Coding for M5: F- SVNS EW- MADM with LST- MM

272

1000 45.4 2.1 0.335;

350 21.7 2.6 0.335;

2150 64.3 2.4 0.5;

700 23 1.71 0.59];

MatS = [1 1 0 1];

sz = size(Mat);

nr = sz(1);

nc = sz(2);

MatT = []; MatT2=[];

Mat1 = [];

Mat2 = []; test=[];

Mat3 = [];

for i=1:nc

if MatS(i) == 1


test=[];

for j=1:nr


end

Mat2 = [Mat2 test];

test=[];

for j=1:nr


end

Mat3 = [Mat3 test];



273

MatT2 = [MatT2 ones(nr,1)];

elseif MatS(i) == 0


test=[];

for j=1:nr


end

Mat2 = [Mat2 test];

test=[];

for j=1:nr


end

Mat3 = [Mat3 test];


MatT2 = [MatT2 ones(nr,1)*2];

end

end

Ej=[];

for j=1:nc

Ej = [Ej; 1 - 1/nr*sum((Mat3(:,(j-1)*3+1)+Mat3(:,j*3)).*abs(2*Mat3(:,(j-1)*3+2)-1))];

end

Wj=[];

for j=1:nc

Wj = [Wj; (1-Ej(j))/sum(1-Ej)];

end

MatFinal5 = [];

for i=1:nr

[6] MATLAB Coding for M6: F- SVNS EW- MADM with LST- MMM

274

MM=[];

for j=1:nc

MM = [MM Wj(j)*(sum(Mat3(i,(j-1)*3+1:j*3).*MatT((j-1)*3+1:j*3)))];

end

MatFinal5 = [MatFinal5; sum(MM)];

end

MatFinal5

[MM Rank5] = sort(MatFinal5,1,'descend');

[6] MATLAB Coding for M6: F- SVNS EW- MADM with LST- MMM

clear all

clc

Mat = [ 1650 58.5 2.3 0.5;

1000 45.4 2.1 0.335;

350 21.7 2.6 0.335;

2150 64.3 2.4 0.5;

700 23 1.71 0.59];

MatS = [1 1 0 1];

sz = size(Mat);

nr = sz(1);

nc = sz(2);


Mat1 = [];

Mat2 = []; test=[];

Mat3 = [];


275

for i=1:nc

if MatS(i) == 1

mx = max(Mat(:,i));

mn = min(Mat(:,i));

test=[];

for j=1:nr


end

Mat2 = [Mat2 test];

test=[];

for j=1:nr


end

Mat3 = [Mat3 test];



elseif MatS(i) == 0

mx = max(Mat(:,i));

mn = min(Mat(:,i));

test=[];

for j=1:nr


end

Mat2 = [Mat2 test];

test=[];

for j=1:nr


[7] MATLAB Coding for M7: F- SVNS EW- MADM with LST- SM

276

end

Mat3 = [Mat3 test];



end

end

Ej=[];

for j=1:nc


end

Wj=[];

for j=1:nc

Wj = [Wj; (1-Ej(j))/sum(1-Ej)];

end

MatFinal6 = [];

for i=1:nr

MM=[];

for j=1:nc


end


end

MatFinal6



clear all


277

clc

Mat = [ 1650 58.5 2.3 0.5;

1000 45.4 2.1 0.335;

350 21.7 2.6 0.335;

2150 64.3 2.4 0.5;

700 23 1.71 0.59];

MatS = [1 1 0 1];

sz = size(Mat);

nr = sz(1);

nc = sz(2);


Mat1 = [];

Mat2 = []; test=[];

Mat3 = [];

for i=1:nc

if MatS(i) == 1


test=[];

for j=1:nr


end

Mat2 = [Mat2 test];

test=[];

for j=1:nr


end


278

Mat3 = [Mat3 test];



elseif MatS(i) == 0


test=[];

for j=1:nr


end

Mat2 = [Mat2 test];

test=[];

for j=1:nr


end

Mat3 = [Mat3 test];



end

end

Ej=[];

for j=1:nc


end

Wj=[];

for j=1:nc

Wj = [Wj; (1-Ej(j))/sum(1-Ej)];

end


279

MatFinal7 = [];

for i=1:nr

MM=[];

for j=1:nc


end


end

MatFinal7


[8] MATLAB Coding for M8: F- SVNS EW- MADM with VNM

clear all

clc

Mat = [ 1650 58.5 2.3 0.5;

1000 45.4 2.1 0.335;

350 21.7 2.6 0.335;

2150 64.3 2.4 0.5;

700 23 1.71 0.59];

MatS = [1 1 0 1];

sz = size(Mat);

nr = sz(1);

nc = sz(2);


[8] MATLAB Coding for M8: F- SVNS EW- MADM with VNM

280

Mat1 = [];

Mat2 = []; test=[];

Mat3 = [];

for i=1:nc

if MatS(i) == 1

v1=0;

for j=1:nr

v1 = v1 + Mat(j,i)^2;

end


test=[];

for j=1:nr


end

Mat2 = [Mat2 test];

test=[];

for j=1:nr


end

Mat3 = [Mat3 test];



elseif MatS(i) == 0

v1=0;

for j=1:nr

v1 = v1 + Mat(j,i)^2;

end



281

test=[];

for j=1:nr


end

Mat2 = [Mat2 test];

test=[];

for j=1:nr


end

Mat3 = [Mat3 test];



end

end

Ej=[];

for j=1:nc


end

Wj=[];

for j=1:nc

Wj = [Wj; (1-Ej(j))/sum(1-Ej)];

end

MatFinal8 = [];

for i=1:nr

MM=[];

for j=1:nc


end


[9] MATLAB Coding for M9: F- SVNS CC- MADM with LST-MM

282

end

MatFinal8


[9] MATLAB Coding for M9: F- SVNS CC- MADM with LST-MM

clear all

clc

Mat = [ 1650 58.5 2.3 0.5;

1000 45.4 2.1 0.335;

350 21.7 2.6 0.335;

2150 64.3 2.4 0.5;

700 23 1.71 0.59];

MatS = [1 1 0 1];

sz = size(Mat);

nr = sz(1);

nc = sz(2);


Mat1 = [];

Mat2 = []; test=[];

Mat3 = [];

for i=1:nc

if MatS(i) == 1



283

test=[];

for j=1:nr


end

Mat2 = [Mat2 test];

test=[];

for j=1:nr


end

Mat3 = [Mat3 test];



elseif MatS(i) == 0


test=[];

for j=1:nr


end

Mat2 = [Mat2 test];

test=[];

for j=1:nr


end

Mat3 = [Mat3 test];



end

end

[10] MATLAB Coding for M10: F- SVNS CC- MADM with LST-MMM

284

MatFinal9 = [];

for i=1:nr

MatFinal9 = [MatFinal9; sum(Mat3(i,:).*MatT)];

end

MatTT=[]; MatTT2=[];

for j=1:nr

MatTT = [MatTT; MatT];

end

MatFinal1 = sum((Mat3.*MatTT).^2,2);

MatFinal1b = sum(MatT2,2);

MatFinal1_max = max(MatFinal1b, MatFinal1b);

MatFinal9_2 = MatFinal9./MatFinal1_max;

MatFinal9

MatFinal9_2


[MM Rank9b] = sort(MatFinal9_2,1,'descend');


clear all

clc

Mat = [ 1650 58.5 2.3 0.5;

1000 45.4 2.1 0.335;

350 21.7 2.6 0.335;

2150 64.3 2.4 0.5;

700 23 1.71 0.59];


285

MatS = [1 1 0 1];

sz = size(Mat);

nr = sz(1);

nc = sz(2);


Mat1 = [];

Mat2 = []; test=[];

Mat3 = [];

for i=1:nc

if MatS(i) == 1

mx = max(Mat(:,i));

mn = min(Mat(:,i));

test=[];

for j=1:nr


end

Mat2 = [Mat2 test];

test=[];

for j=1:nr


end

Mat3 = [Mat3 test];



elseif MatS(i) == 0


286

mx = max(Mat(:,i));

mn = min(Mat(:,i));

test=[];

for j=1:nr


end

Mat2 = [Mat2 test];

test=[];

for j=1:nr


end

Mat3 = [Mat3 test];



end

end

MatFinal10 = [];

for i=1:nr


end


for j=1:nr


end





287


MatFinal10

MatFinal10_2



[11] MATLAB Coding for M11: F- SVNS CC- MADM with LST-SM

clear all

clc

Mat = [ 1650 58.5 2.3 0.5;

1000 45.4 2.1 0.335;

350 21.7 2.6 0.335;

2150 64.3 2.4 0.5;

700 23 1.71 0.59];

MatS = [1 1 0 1];

sz = size(Mat);

nr = sz(1);

nc = sz(2);


Mat1 = [];

Mat2 = []; test=[];

Mat3 = [];

for i=1:nc

if MatS(i) == 1

[11] MATLAB Coding for M11: F- SVNS CC- MADM with LST-SM

288


test=[];

for j=1:nr


end

Mat2 = [Mat2 test];

test=[];

for j=1:nr


end

Mat3 = [Mat3 test];



elseif MatS(i) == 0


test=[];

for j=1:nr


end

Mat2 = [Mat2 test];

test=[];

for j=1:nr


end

Mat3 = [Mat3 test];




289

end

end

MatFinal11 = [];

for i=1:nr


end


for j=1:nr


end





MatFinal11

MatFinal11_2



[12] MATLAB Coding for M12: F- SVNS CC- MADM with VNM

clear all

clc

Mat = [ 1650 58.5 2.3 0.5;

1000 45.4 2.1 0.335;

350 21.7 2.6 0.335;

[12] MATLAB Coding for M12: F- SVNS CC- MADM with VNM

290

2150 64.3 2.4 0.5;

700 23 1.71 0.59];

MatS = [1 1 0 1];

sz = size(Mat);

nr = sz(1);

nc = sz(2);


Mat1 = [];

Mat2 = []; test=[];

Mat3 = [];

for i=1:nc

if MatS(i) == 1

v1=0;

for j=1:nr

v1 = v1 + Mat(j,i)^2;

end


test=[];

for j=1:nr


end

Mat2 = [Mat2 test];

test=[];

for j=1:nr


end

Mat3 = [Mat3 test];


291



elseif MatS(i) == 0

v1=0;

for j=1:nr

v1 = v1 + Mat(j,i)^2;

end


test=[];

for j=1:nr


end

Mat2 = [Mat2 test];

test=[];

for j=1:nr


end

Mat3 = [Mat3 test];



end

end

MatFinal12 = [];

for i=1:nr


end


292

for j=1:nr


end





MatFinal12

MatFinal12_2



List of Publications

293

List of Publications

National Conference:

1. Paper published and presented on title “Supplier Evaluation and Selection

Methods in Supply Chain: A Fresh Review” 4th National Conference on Recent

Advances in Manufacturing (RAM-2014) on 26th

-28th

, June, 2014 with ISBN No.

978-93-5156-755-4, page no. 346-351 at SVNIT, Surat.

International Conference:

1. Paper published and presented on title “New Integrated Multi-Attribute Decision

Making Approach for Supplier Selection”, 4th Biennial Supply Chain

International Conference 2014 on 18-19, Dec, 2014, at IIM, Bangalore.

2. Paper published and presented on title “Implementation and Validation of Multi

Attribute Decision Making Technique for Supplier Selection in Supply Chain

Management”, 4th IIMA International Conference on Advanced Data Analysis,

Business Analytics, available in IIM E-Repository, at IIM Ahmedabad.

3. Paper published and presented on title ―Implementation and Validation of

COPRAS- Multi Attribute Decision Making Methodology for Robot

Selection”, 57th

National Convention of Indian Institution of Industrial Engineering

& 3rd

International Conference on Industrial Engineering on December, 2015 with

ISBN no. 978-93-84935-56-6, page no. 665-669 at SVNIT, Surat.

4. Paper published and presented on title ―Supplier Selection by Integrated MCDM

Model for Sustainable Manufacturing Environment”, 57th

National Convention

of Indian Institution of Industrial Engineering & 3rd

International Conference on

Industrial Engineering on December, 2015 with ISBN no. 978-93-84935-56-6, page

no. 483-487 at SVNIT, Surat.

5. Paper published and presented on title “The Learning from Literature Analysis

for Health Care Assessment and Health Care Waste Management using Multi

Attribute Decision Making Techniques”, 2nd IIMA International Conference

on Advances in Healthcare Management Services December 10-11, 2016 at IIM

Ahmedabad.

294

National Journal

1. "Supplier Evaluation and Selection Methods in Supply Chain Management- A

Review" in Industrial Engineering Journal IIIE, Industrial Engineering Journal

Navi Mumbai Jan, 2015, Vol 7, Issue 1, ISSN: 0970-2555, page no 30-38.

2. “Selecting a Material for an Electroplating Process using “TOPSIS - Multi

Attribute Decision Making” Industrial Engineering Journal, IIIE Navi Mumbai,

September, 2015, Vol. 8, Issue 9, ISSN 0970-2555, page no 25-28.

International Contributory Book

1. Title of Chapter “Selection of Material Handling Automated Guided Vehicle

using Fuzzy Single Valued Neutrosophic Set - Entropy based Novel Multi

Attribute Decision Making Technique: Implementation and Validation”, Title

of Book “New Trends in Neutrosophic Theories and Application” Editors:

Florentin Smarandache and Surapati Pramanik Publisher of the BOOK: Europa

Nova, Brussels, USA Year 2016, ISSN: 978-1-59973-498-9, page no. 105-112.

2. Title of Chapter “Development of Fuzzy- Single Valued Neutrosophic MADM

Technique for Improving Performance of Manufacturing and Supply Chain

Functions”, (2019), Title of a Book “Fuzzy Multi Criteria Decision Making

using Neutrosophic Set (Studies in Fuzziness and Soft Computing)”, Editors:

Prof. Cengiz Kahraman & Prof. Irem Otay Publisher of the BOOK: Springer

International Publishing, ISBN: 978-3-030-00045, DOI:

https://doi.org/10.1007/978-3-030-00045-5

Encyclopedia

1. N. P. Nirmal, “Encyclopedia of Neutrosophic Researchers- 2nd

Volume” Editor

and founder- ‗Florentin Smarandache‘, 2018, ISBN: 978-1-59973-468-2, page no.

83-84.

https://doi.org/10.1007/978-3-030-00045-5

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