New Frontier of Hybrid MCDM Model for ... - Waseda University

New Frontier of Hybrid MCDM Model for Creating the Best Global

Supply Chain Systems- with a Focus on

“Multiple Attribute Decision Making: Methods and Applications

Gwo-Hshiung TzengDistinguished Chair Professor

a Institute of Project ManagementDept. of Business and Entrepreneurial Administration

Kainan Universityb Institute of Management of Technology

National Chiao-Tung University

Keynote Speech in KESIDT 2011July 20-22, 2011

The University of Piraeus, Greece

Contents

� Introduction� Research Methods for Problems-Solving� Background� Research problems� Purposes� Research Methods� An empirical study example� Discussions� Concluding remarks

2

Basic ConceptsIdea in this topic includes: My new book for solving

the real problems existing interdependence and feedback dynamic problems. Combining DEMATEL with DANP hybrid MCDM model

DANP global influential weights --> local weights -->fuzzy integral for integration (information fusion in performance) of value function (non-additive/ super-additive) in Changeable space for achieving the aspiration level (the best) global supply chain systems in real world.

3

Which skills to write the high quality papers

Good story (hot topic and which problems in case study)

+Good research methods for problems-solving

(interdisciplinary systems)+

Good writing skills2011/7/21 4

Introduction

� The concepts of globalization and offshore sourcing have emerged and become prosperous in the past decades.

� The global supply chain management have already become one of the most significant issues in this era.

5

Introduction

� Modern globalized firms are leveraging both � Global manufacturing resources and � Logistics systems

� For pursuing � Higher quality� Lower cost and product differentiation� Mass customization

6

Introduction� But …

� How to � Evaluate and select components of a global supply chain and

� Define optimization strategies � by considering issues from the aspects of� Global manufacturing, � Logistics as well as � Marketing channel management

has become one of the most critical and difficult issue.

7

Introduction

� How the chosen intertwined � Global manufacturing, � Logistics and � Distribution system can be designed to achieve the aspiration level for satisfaction (Herbert Simon, 1978 Nobel Prize) of the global supply chain has few been addressed.[Herbert Simon, 1978 Nobel Prize: Humans do not solve problems by maximizing utility, but are “satisficers”, who set aspiration levels (that a solution must satisfy) when solving problems]

8

Which skills to write the high quality papers

Good story (hot topic and which problems in case study)

+Good research methods for problems-solving

(interdisciplinary systems)+

Good writing skills2011/7/21 9

Introduction

� The concepts of globalization and offshore sourcing have emerged and become prosperous in the past decades.

� The global supply chain management have already become one of the most significant issues in this era.

10

IntroductionConcept of Methods

� For achieving the aspiration level (the best) global supply chain systems in real world� DANP (DEMATEL-based ANP) for deriving global influential weights (for solving interdependence and feedback dynamic problems)

� Fuzzy integral for integrating (fusing information in performance matrix) of value function (non-additive/super-additive) in Changeable space [Kahneman, 2002 Novel Proze, from experiment]

11

Research Methods for Problems-Solving

� DEMATEL� ANP� DNP� Fuzzy Integral� Hybrid MCDM

Methods

12

Research Methods for Problems-Solving

13

i

Performance

Matrix(crisp/fuzzy)

DataProcessing/

Analysis

DataInvestigating /

Collecting

FutureProspecting/Forcasting

ExplorativeModel

Data Processing / Statistical and Multivariate Analysis Planning / Designing Evaluating / Choosing

Objects (InternalReal Situations):features/attributes/criteria/objectives/variables

ResponseOr

Perception

Personal / Social Attribute

Normative Models

PolicyStrategic

alternatives

Goal

w1 . . .wj . . . wn

MADM

Data Sets:

Crisp Sets

Fuzzy Sets

Grey Hazy Sets

Rough Sets

Data Mining

Statistical/Multivariate Analysis

Genetic AlgorithmsNeural Networks Logic Reasoning

Fuzzy Statistical/Multivariate Analysis

ARIMAGrey ForecastingBaysian Regression

Regression/Fuzzy Regression

Dimensions

Criteria

WeightingsAHP / Fuzzy AHPANP / Fuzzy ANP Entropy MeasureFuzzy IntegralDynamic WeightingNeural Networks Weighting

Non-Additive Types Fuzzy IntegralNeural Network + Fuzzy

Additive Types SAWTOPSIS,VIKORPROMETHEEELECTREGrey Relation

Normalizing

C1 . . .Cj . . . Cn

Single level+

Fuzzy+

Multi-level+

Multi-stage+

Dynamics+

Habitual Domain

MODM (GP, MOP,Compromisesolution, etc.)

+

De Novo Programming( including Fuzzy )

External EnvironmentMODM

Descriptive Model

MCDM

1

i

m

a

a

a

�

�

- DEA- Network DEA- MOP DEA- Fuzzy MOP DEA- MOP Network DEA

- ISM, Fuzzy ISM- DEMATEL, Fuzzy DEMATEL- Fuzzy Cognitive Map (FCM)- Formal Concept Analysis-Linear Structure Equation Model

(LISEM, or called “SEM”)- Input-Output Analysis

Data Mining Concepts of Intelligent Computation in Knowledge Economy

14

BackgroundA Quick Overview of Traditional MCDM Approaches

� Criteria weight calculations by AHP (assuming criteria independences) or

� ANP based weight derivations by a decision problem structure being derived arbitrarily (based on assumption, Saaty)

� TOPSIS which determines a solution with � The shortest distance from the ideal solution and � The farthest distance from the negative-ideal solution (cannot be used for ranking purpose)

Opricovic, S., Tzeng, G.H. (2004). Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPISIS, European Journal of Operational Research, Volume 156, Issue 2, 16 July 2004, Pages 445-455(Essential Science Indicatorssm to be one of the most cited papers in the field of Economics).

15

Background - Problems being Faced by Traditional MCDM Approaches

Alternatives being derived as is� Wrong assumptions on the independences between

the determinants� Vague correlations between criteria (such as, SEM,

etc.)� The lack of priorities of the alternatives� Compromise solutions being derived (e.g. by

TOPSIS) is not always the closest to the ideal (cannot be used for ranking purpose)

� “Rotten (decay, not good) apples versus rotten apples” situation

16

Purpose

� For satisfying the real world MCDM problems, the above mentioned problems should be corrected� A proposal of novel hybrid MCDM framework is essential in my books and my papers of our research group

17

Research Methods Combined DEMATEL Technique with a Hybrid

Novel MCDM Method for applying the real case

18

Define an Decision

Problem in objects

Define Determinants

Establish a Structure of

theDecision Problem

Calculate Compromise Ranking and Improving by

combing VIKOR and Influential

NRM

- Delphi- Brain-storming DEMATEL

- VIKOR-GRA (Grey

relation analysis- Fuzzy integral

Derive Strategies for

Achieving Aspiration

Levels

Derive Influential Weights of

Determinants

DANP(DEMATEL-based

ANP)

Improve and Select

Strategiesby the

Secondary Research

19

DEMATEL -Decision Making Trial and Evaluation Laboratory

New Methods

20

Introduction (1)� The DEMATEL method was developed by the Battelle

Geneva Institute to� Analyze complex world problems dealing mainly with

interactive man-model techniques in complex social systems (Gabus and Fontela, 1972) for improving traditional “Dynamic Systems” by Forester”, then we use this basic concepts for using to evaluate qualitative and factor-linked aspects of social problems

� We, also based on these concepts, develop a novel MCDM, such as Liou et al. (2007), Tzeng et al. (2007); Ou Yang, et al. (2008) and so on.

� The applicability of the method can be widespread� Industrial planning and improvement� Decision-making to urban planning and design� Regional environmental assessment� Analysis of world problems� Social network analysis, and � Others

21

Introduction (2)

� The DEMATEL method is based upon graph theory� Enabling us to plan and solve complex problems visually� We may divide multiple criteria into a cause and effect group, in order to better understand causal relationships and build influential network relationship map (NRM) in interdependence and feedback problems for improving the gaps of criteria to achieve aspiration levels in satisfaction. [Solving and treating the basic concepts proposed by Herbert Simon, 1978 Nobel Prize]

22

Relation Graphs (1)

� Directed, in-directed, and total relation graphs (also called digraphs) are more useful than directionless graphs� Digraphs (such as SEM model etc.) will demonstrate the

directed, in-directed and total relationships of sub-systems.

� A digraph typically represents a communication network, or a domination relationship between individuals, etc.

� Suppose a system contains a set of elements, , and particular pair-wise relationships are determined for modeling, with respect to a mathematical relationship, MR.

1 2{ , , , }nS s s s� �

23

Relation Graphs (2)

� Next, portray the relationship MR as a relation matrix that is indexed equally in both dimensions by elements from the set S by directed relation graph. Then, extract the case for which the number 0 (completely no influence) to 4 (extremely or very high influence) appears in the cell (i,j) by directedrelation graph, if the entry is a positive integral that has the meaning of:� the ordered pair (si, sj) is in the relationship MR;� it has the kind of relationship regarding that element

such that si causes element sj.

24

Relation Graphs (3)

� The number between factors is influence or influenced degree.

� The DEMATEL method can convert the relationship between the causes and effects of criteria into an intelligible structural model of the system

25

Relation Graphs (4)

Directed Relation Graph� The elements, S1, S2, S3

and S4 represent the factors that have relationships in the digraph.

� The number between factors is influence or influenced degree. � For example, an arrow from

S1 to S2 represents the fact that influences and its influenced degree is two.

s2

2

3

1

3s1

s4

s3

26

Definitions (1)

� Definition 1� The pair-wise comparison scale may be designated as eleven levels, where the scores, such as ‘completely no influence (0),’ ‘low influence (1),’ ‘medium influence (2),’ ‘high influence (3),’ and ‘very high influence (4),’ respectively (or 0, 1, 2, 3, 4 or 0, 1, 2,…, 10) represent the range from ‘no influence’ to ‘very high influence’.

27

Definitions (2)

� Definition 2� The initial direct relation/influence matrix A is an n�nmatrix obtained by pair-wise comparisons, in terms of influences and directions between the criteria, in which aij is denoted as the degree to which the ith criteria affects the jth criteria.

11 12 1

21 22 2

1 2

n

n

ij

n n nn

a a aa a a

aa a a

� ��

A

��

� � ��

i

j

i j

28

Definitions (3)� Definition 3

� The normalized direct relation/influence matrix N can be obtained through Equations (1) and (2) by normlization, in which all principal diagonal elements are equal to zero.

(1)where

(2)

In this case, N is called the normalized matrix.

Since

z�N A

1 11 11 max max ,max

n n

ij iji n j nj iz a a

� � � ��

� � � �

� ��

lim [0]h

h��N

29

Definitions (4)� Definition 4

� Then, the total relationship matrix T can be obtained using Equation (3), where I stands for the identity matrix.

��

�

�� If at least one row or column of summation, but not all, is

equal to 1, then and T is a total influence-related matrix; matrix N is a direct influence matrix and

� matrix stands for a indirect influence matrix. The (i,j) element tij of matrix T denotes the direct and indirect influences of factor i on factor j.

� � � ��

� ��

2

11

1

...

... [ ]

h

h

h

��

�

� � � �

� � � � � �

� �

T N N N

N I N N I N I N

= N I N I Nwhen (3) h��

1 10 1, 0 1and 0 1,

n n

ij ij ijj i

x d d� �

� � � � � �� lim [0]h

h��N

� �... h� � �2N N N

1then, ( - ) ,�T = N I Nwhere [ ] ,ij n nx ��N

lim [0]hh�� N

30

Definition (5)

� Definition 5� The row and column sums are separately denoted as vector r and vector c within the total-relation matrix T through Equations (4), (5), and (6).

(4)

(5)

(6)

where the vector r and vector c vectors denote the sums of the rows and columns, respectively.

[ ], , {1,2,..., }ijt i j n� �T

[ ], , {1,2,..., }ijt i j n� �T

11 1

[ ]n

i n ijj n

r t��

� ��

�r

11 1

[ ]n

j n iji n

c t��

��

�c

31

Definition 6

� Definition 6� Suppose ri denotes the row sum of the ith row of matrix T. Then, ri is the sum of the influences dispatching from factor i to the other all factors, both directly and indirectly. Suppose that cj denotes the jth column sum of the column of matrix T. Then, cj is the sum of the influences that factor j is received from the other all factors.

32

Definition 6 (Continued)

� Furthermore, when i=j (i.e., the sum of the row sum and the column sum (ri+cj) represents the index representing the strength of the influence, both dispatching and received), (ri+cj)is the degree of the central role that factor iplays in the problem.

� If (ri-cj) is positive, then factor primarily is dispatching influence upon the other factors; and if (ri-cj) is negative, then factor primarily is received influence from other factors (Tamura et al., 2002; Tzeng et al., 2007; etc.).

The impact-direction map for improving gaps in performance valuesChen, Y.C., Lien, H. P., Tzeng, G.H. (2010), Measures and evaluation for environment watershed plan using a novel hybrid MCDM model, Expert Systems with Applications, 37(2), 926-938

� Example 1: For improving wetland environments

1

2

5 6 7

(6.773, 0.640), gap: 4.78Humanity Environment

(7.286, 1.198), gap: 6.28Physical environment

(6.977, -1.506), gap: 4.68Ecological environment

(6.424, -0.332), gap: 4.85 Natural environment

0

-1

Liu, C. H., Tzeng, G.H., Lee, M.H. (2011), Strategies for improving cruise product sales in the travel agency- using hybrid MCDM models, The Service Industry Journal (Forthcoming).

� Example 2: Strategies for improving cruise product sales in the travel agency

Liu, C.H., Tzeng, G.H., Lee, M.H. (2011), Improving tourism policy implementation - the use of hybrid MCDM models, Tourism Management (Accepted)

� Example 3: For improving tourism policy implementation

Chen, F.H., Hsu,T.S., Tzeng , G.H. (2011), A Balanced Scorecard Approach to Establish a Performance Evaluation and Relationship Model for Hot Spring Hotels Based on a Hybrid MCDM Model Combining DEMATEL and ANP, International Journal of Hospitality Management, 30(4), 908-932.

p ppEstablish a Performance Evaluation and Relationship Model for Hot Spring Hotels

Chen, C.H. and Tzeng, G.H. (2011), Creating the Aspired Intelligent Assessment Systems for Teaching Materials, Expert Systems with Applications, 38(10), 12168-12179.

p g p gAssessment Systems for Teaching Materials: Case of Mandarin Chinese

38

Analytic Network Process(ANP) and DANP

(DEMATEL-based ANP)

DANP (DEMATEL-based ANP) based on DEMATEL technique to build network relationship map (NRP) for constructing Super-matrix using the basic concept of ANP to find the influential weights (called DANP)

Source: Tzeng (2006)

39

Introduction (1)

� The ANP method� A multi-criteria theory of measurement proposed by Saaty (1996).

� Provides a general framework to deal with � Decisions without making assumptions about the independence of higher-level elements from lower level elements

� About the independence of the elements within a level as in a hierarchy.

[i.e., between each dimension is dependent, but criteria within dimension are independent]

40

Introduction (2)� Compared with traditional MCDM methods,

ANP is a more reasonable tool for dealing with complex MCDM problems in the real world. � Traditional MCDM methods usually assume the independence between criteria.

� ANP extends AHP to deal with dependence in feedback and utilizes the super-matrix approach.

41

Introduction (3)� The ANP is a coupling of two parts.

� The first consists of a control hierarchy or network of criteria and subcriteria that control the interactions.

� The second is a network of influences among the elements and clusters. � The network varies from criterion to criterion � A different supermatrix of limiting influence is computed for each control criterion.

� Each of these super-matrices is weighted by the priority of its control criterion and the results are synthesized through addition for all the control criteria.

42

The Control Hierarchy (1)

� A control hierarchy is a hierarchy of criteria and subcriteria for which priorities are derived in the usual way with respect to the goal of the system being considered.� The criteria are used to compare the components of a system, and

� The subcriteria are used to compare the elements.

� The criteria with respect to which influence is presented in individual supermatrices are called control criteria.

43

The Control Hierarchy (2)Goal

Criteria

Subcriteria

Control Criteria

A possible different network under each subcriterion of the control hierarchy

GoalCriteria

Subcriteria

Control Criteria

A possible different network under each subcriterion of the control hierarchy

44

The Network (1)� A network connects the components of a

decision system. � According to size, there will be a system

that is made up of subsystems, with each subsystem made up of components, and each component made up of elements.

� The elements in each component interact or have an influence on some or all of the elements of another component with respect to a property governing the interactions of the entire system, such as energy, capital, or political influence.

45

The Network (2)

� Source component� Those components which no arrow enters are known as source components. E.g. C1 and C2.

� Sink component� Those from which no arrow leaves are known as sink component. E.g. C5.

� Transient component� Those components which arrows both enter and exit leave. E.g. C3 and C4.

Source Component

Source Component

SourceComponent

(Feedback loop)

SourceComponent

(Feedback loop)

Intermediate Component

(Transient State)


(Transient State)Sink Component(Absorbing State)Sink Component(Absorbing State)

IntermediateComponent

(Recurrent State)


(Recurrent State)

Outerdependence

Innerdependence loop

C1

C3

C4

C5

C2

Source Component

Source Component

SourceComponent

(Feedback loop)

SourceComponent

(Feedback loop)


(Transient State)




(Recurrent State)


(Recurrent State)

Source Component

Source Component

SourceComponent

(Feedback loop)

SourceComponent

(Feedback loop)


(Transient State)




(Recurrent State)


(Recurrent State)

Outerdependence


C1

C3

C4

C5

C2

46

The Network (3)� Cycle

� A cycle of components is formed when the components feed back and forth into each other. E.g. C3 and C4.

� Loop� A loop connect to a component itself and is inner dependent. E.g.. C2 and C4 have loops that connect them to themselves and are inner dependent.

� Outer dependent � Other connections represent dependence between components which are thus known to be outer dependent.

Source Component

Source Component

SourceComponent

(Feedback loop)

SourceComponent

(Feedback loop)


(Transient State)




(Recurrent State)


(Recurrent State)

Outerdependence


C1

C3

C4

C5

C2

Source Component

Source Component

SourceComponent

(Feedback loop)

SourceComponent

(Feedback loop)


(Transient State)




(Recurrent State)


(Recurrent State)

Source Component

Source Component

SourceComponent

(Feedback loop)

SourceComponent

(Feedback loop)


(Transient State)




(Recurrent State)


(Recurrent State)

Outerdependence


C1

C3

C4

C5

C2

47

The Network (4)A Typical Example

Source Component

Source Component

SourceComponent

(Feedback loop)

SourceComponent

(Feedback loop)


(Transient State)




(Recurrent State)


(Recurrent State)

Outerdependence


C1

C3

C4

C5

C2

Source Component

Source Component

SourceComponent

(Feedback loop)

SourceComponent

(Feedback loop)


(Transient State)




(Recurrent State)


(Recurrent State)

Source Component

Source Component

SourceComponent

(Feedback loop)

SourceComponent

(Feedback loop)


(Transient State)




(Recurrent State)


(Recurrent State)

Outerdependence


C1

C3

C4

C5

C2

48

The Super-matrix (1)

� A component of a decision network will be denoted by Ch, h =1,2,…,m, and assume that it has nh elements, which we denote by eh1,eh2 ,…, ehm.

� The influences of a given set of elements in a component on any element in the decision system are represented by a ratio scale priority vector derived from pair-wise comparisons of the relative importance of one criterion and another criterion with respect to the interests or preferences of the decision-makers.

49


� This relative importance value can be determined using a scale of 1 9 to represent equal importance to extreme importance.

� The influence of elements in the network on other elements in that network can be represented in the following supermatrix:

50


� A typical entry Wij in the supermatrix, is called a block of the supermatrix in the following form where each column of Wij is a principal eigenvector of the influence of the elements in the ith component of the network on an element in the jthcomponent. Some of its entries may be zero corresponding to those elements that have no influence.

51

The Supermatrix (4)

1

2

11

12

1

1

21

22

2

2

1

2

2

1 2

1 2

11 1 21 2 1

11 12 1

21 22 2

1 2

m

n

n

m

m

mn

m

m

n n m mn

m

m

m m mm

e

e

e

e

e

e

e

e

e

e e e e e e

� ��

�

C

C

C

C C C

W W W

W W W

W W W

W

�

�

� �

�

�

� � � �

�

�

��

�

New methodHybrid MCDM model

DEMATEL based Analytic Network Process (DANP)

53

�The DANP is proposed by Pro. Tzeng, which is composed of DEMATEL technique and ANP concept.

- DEMATEL-based Analytic Network Process (DANP) (1/14)

DEMATELANP

conceptDANP

2011/06/09

DEMATEL-based ANP = DANP

DEMATEL-based ANP = DANP54

�

- DEMATEL based Analytic Network Process (DANP) (2/14) -

2011/06/09


�

DEMATEL based Analytic Network Process (DANP) (3/14)

2011/06/09


�Step1: Calculate the direct-influence matrix by scores. Lead users and experts are asked to indicate the direct effect they believe a factor will have on factor , as indicated by . The matrix D of direct relations can be obtained.

�Step2: Normalize the direct-influence matrix based on the direct-influence matrix D by the equation:

1 1; min{1/ max ,1/ max }, , {1,2,..., }

n n

ij iji jj iN vD v d d i j n

� �

� � ��

2011/06/09



�Step3: Attaining the total-influence matrix T by calculating this equation:

�Step4: The row and column sums are separately denoted as and within the total-relation matrix through equations:

[ ], , {1,2,..., }ijt i j n� �T

11 1

[ ]n

i n ijj n

r t��

� ��

�r 1

1 1

[ ]n

j n iji n

c t��

� ��

�c

2 -1... ( - ) ,h� � � � �T N N N N I N

2011/06/09

when h��


58

Total relationship matrix T can be measured by criteria, shown as cT

1112

1 1

12

12

1

11 1 1 11

1 11 1 1

1

1

c cc

c c c

c

c

c c

� ��

�

�

�

�

�

� � ��

��

�

�

� �

� � ��

� � ��

cc

c m

cici

cim

cncn

cnmn

j n

m j jm n nmnj

i

i

n

D D Dc c c c c c

j nD

i ij inD

n nj nnD

T T T

T T T T

T T T


59

Step 5: Normalize with the total degree of effect and obtain

cT


1112

1 1

12

12

1

11 1 1 111

...11 1 1

1

1

cc

cc c

c c c

j nc

ij inC

n nj nn

� � �

� � ��

� � �

� ��

�

�

�

�

�

� � ��

�

�

� �

� � ��

� � ��

cc

c m

cici

cim

cncn

cnmn

j n

m j jm n nmj n

i

i

n

D D Dc c c c c c

D

D i

D

T

T T T

T T T

T T T

C�T


�According to the result of step 4� represents the index representing the strength of the influence, both dispatching and receiving, it is the degree of the central role that factor plays in the problem. �If is positive, then factor primarily is dispatching influence upon the strength of other factors; and if is negative, then factor primarily is receiving influence from other factors (Huang et al.,2007; Liou et al., 2007; Tamura et al., 2002).

( )i ir c�

( - )i ir c( - )i ir c

2011/06/09


Research Method61

�Now we call the total-influence matrix obtained by criteria and obtained by dimensions (clusters) from .� Then we normalize the ANP weights of dimensions (clusters) by using influence matrix .

C ij nxnt� �� T

DD ij nxn

t� �� T

CT

DT1 111 1

1

1

11 1 1 1 11

11 1

11

, , 1,...,

j m j

ij ijiji im

mjmjm mm

mD DD Dj m j

j

m mD DDD D

D i ij i iji ij imj j

mDDD D

m mjm mj mmj

t t t d t

d t d t i mt t t

d tt t t

�

� �

�

� � ��

�

� �

�

� ��

� ��

� �

T

2011/06/09



�Step 6: normalize the total-influence matrix and represent it as


DT

1 111

1

1

11 1 111 1 1 1 1 1

11

11

/ / /

/ / /

/ / /

j m

D D D

iji imD D D

mjm mmD D D

D D j nDj m

D i ij inD DD i i ij i im i

n nj nnDD Dm m mj m mm m

t t tt d t d t d

t t tt d t d t d

t t tt d t d t d

� � �

� � ��

� � �

� � � ��

� ��

� ��

� ��

T

2011/06/09


�Step 7: Calculate the unweighted supermatrix based on .

2011/06/09


1112

1 1

1

2

12

111 1 1 111

...11 1 1

' 1

1

( )c�

� ��

�

�

�

�

�

� � ��

�

�

� ��

� � ��

cc

c m

cc j

c jm

cncn

cnmn

i nm i im n nmi n

jj

j

n

D D Dc c c c c cD

i n

D j ij nj

n in nnD

T

W W W

W W W W

W W W

�cTW


�Step 8: Calculate the weighted supermatrix .

2011/06/09


11 11 1 1 1 1

1 1

1 1

i i n nD D D

j j ij ij nj njD D D D

n n in in nn nnD D D

t t t

t t t

t t t

� � �

� � � � �

� � �

� ��

� ��

� ��

� �

W W W

W T W W W W

W W W

�W


�Step 9: Limit the weighted super-matrix by raising it to a sufficiently large power g, as this equation, until the super-matrix has converged and become a long-term stable super-matrix to get the global priority influential vectors or called DANP influential weights.


lim ( )gg

�� W

2011/06/09

Fuzzy Integral

Hybrid MCDM ModelNon-additive/Super-additive

Based concept from Kahneman in 1969S[Kahneman, 2002 Novel Proze, from experiment]

Kahneman-Tversky (prospect theory)Von Neumann-Morgeustern (Expected utility model

Fishburn (bilateral independence)Keeney (Utility independence)

66

Fuzzy Integral (1)� Multiple attribute decision making

(MADM) involves � Determining the optimal alternative among multiple, conflicting, and interactive criteria (Chen and Hwang, 1992).

� Many methods, which are based on multiple attribute utility theory (MAUT), have been proposed to deal with the MCDM problems� E.g. the weighted sum and the weighted product methods

67

Fuzzy Integral (2)� The concept of MAUT

� To aggregate all criteria to a specific uni-dimension (called utility function) to evaluate alternatives.

� Therefore, the main issue of MAUT � To find a rational and suitable aggregation operator (fusion operator) which can represent the preferences of the decision-maker.

68

Fuzzy Integral (3)� Although many papers have been

proposed to discuss the aggregation operator of MAUT (Fishburn, 1970), the main problem of MAUT� The assumption of preferential independence (Hillier, 2001; Grabisch, 1995); but in real world, it is a non-additive/super-additive MAUT problem.

[Kahneman, 2002 Novel Proze, from his experiment, he also found ”it is a non-additive/super-additive MAUT problem” in 1960S] Von Neumann-Morgeustern

69

Fuzzy Integral (4)

� Preferential independence can be described as the preference outcome of one criterion over another criterion is not influenced by the remaining criteria.

� However, the criteria are usually interactive in the practical MCDM problems.

� In order to overcome this non-additive problem, the Choquet integral was proposed (Choquet, 1953; Sugeno, 1974).

70

Fuzzy Integral (5)

� The Choquet integral can represent a certain kind of interaction among criteria using the concept of redundancy and support/synergy.

71

Fuzzy Integral (6)

� In 1974, Sugeno introduced the concept of fuzzy measure and fuzzy integral � Generalizing the usual definition of a measure by� Replacing the usual additive property with a weaker requirement� I.e. the monotonicity property with respect to set

inclusion.

72

Fuzzy Integral (7)

73

Definition 3.2.1: Let X be a measurable set that is endowed with pro [0,1]�� perties of �-algebra, where � is all subsets of X. A fuzzy measure g defined on the measurable space ( , )X � is a set function g: , which satisfies the following properties: (1) ( ) 0, ( ) 1g g X� � � ; (2) for all ,A B�� , if A B then ( ) ( )g A g B�(monotonicity).

Fuzzy Integral (8)

74

As in the above definition, ( , , )X g� is said to be a fuzzy measure space. Furthermore, as a consequence of the monotonicity condition, we can obtain: ( )g A B! " max{ ( ), ( )}g A g B , and

( )g A B# � min{ ( ), ( )}g A g B .In the case where ( )g A B! =

max{ ( ), ( )}g A g B , the set function g is called a possibility measure (Zadeh 1978), and if

( )g A B# = min{ ( ), ( )}g A g B , g is called a necessity measure.

Fuzzy Integral (9)

75

Definition 3.2.2: Let 1

1i

n

i Ai

h a�

� $� be a simple

function, where1iA is the characteristic function of

the set , 1, ,iA i n�� $ $ $ ; the sets iA are pairwise

disjoint, and ( )iM A is the measure of iA . Then

the Lebesque integral of h is

1( )

n

i ii

h dM M A a�

$ � $�% .

Fuzzy Integral (10)

76

Definition 3.3.3 Let ( , , )X g� be a fuzzy

measure space. The Sugeno integral of a fuzzy

measure : [0,1]g �� with respect to a simple

function h is defined by ( ) ( )h x g x% � =

( ) ( )1( ( ) ( ))

n

i iih x g A

�& ' = ( )' 'max min , ( )i ii

a g A , where

( )( )ih x is a linear combination of a characteristic

function '1iA such that 1 2 nA A A* * $$ $ * ,and

' '{ | ( ) }i iA x h x a� " .

Fuzzy Integral (11)

77

Definition 3.3.4 Let ( , , )X g� be a fuzzy measure space. The Choquet integral of a fuzzy measure : [0,1]g �� with respect to a simple function h is defined by ( )h x dg$ +% , -1

1( ) ( ) ( )

n

i i ii

h x h x g A��

� $� , with the same notions as above, and (0)( ) 0h x � .

Fuzzy Integral (12)

78

Let g be a fuzzy measure which is defined on a

power set P(x) and satisfies the definition 3.3.1 as

above. The following characteristic is evidently,

, ( ),A B P X A B �. � # � / ( )g A B0 ! �

( ) ( )g A g B0 0� ( ) ( )g A g B0 00� , for 1 0� � � � .

Fuzzy Integral (13)

79

Set 1 2{ , , , }nX x x x� $ $ $ , the density of fuzzy

measure ({ })i ig g x0� can be formulated as

follows: 1 2({ , , , })ng x x x0 $ $ $ =1

n

ii

g�� +

1 2

1 2 1

1

1 1

n n

i ii i i

g g0�

� � �

$� � +

$ $ $ + 11 2

nng g g0 � $ $ $ $ $ =

1

1 (1 ) 1n

ii

g00 �

� $ �1 , for

1 0� � � � .

Fuzzy Integral (14)

80

Let h is a measurable set function defined on

the fuzzy measurable space ( , )X � , suppose

that 1 2( ) ( ) ( )nh x h x h x" " $ $ $ " , then the fuzzy

integral of fuzzy measure � �g $ with respect to

� �h $ can be defined as follows (Ishii & Sugeno,

1985; see Fig. 1).

Fuzzy Integral (15)

81

)( nxh

)( 1�nxh)()( 1 nn xhxh ��

)()( 21 xhxh �

)()( 32 xhxh �

)( nxh

)( 1�nHg

)( 2Hg

)( 1Hg

)( nHg

)( 3xh

)( 2xh

)( 1xh

1x 2x 3x 1�nx…nx

Figure 1 The concept of the Choquet integral

Fuzzy Integral (16)

82

h dg$% = ( ) ( )n nh x g H$ + 1[ ( ) ( )]n nh x h x� � 1( )ng H �$ +

$ $ $ + 1 2[ ( ) ( )]h x h x� 1( )g H$ = ( )nh x $

1[ ( ) ( )]n ng H g H �� + 1( )nh x � $ 1 2[ ( ) ( )]n ng H g H� �� +

$ $ $ + 1 1( ) ( )h x g H$ , where 1H = 1{ }x , 2H = 1 2{ , }x x ,

$ $ $ , nH = 1 2{ , , , }nx x x$ $ $ = X . In addition, if 00 �

and 1g = 2g = $ $ $ = ng then 1( )h x " 2( )h x "

( )nh x$ $ $ " is not necessary.

Fuzzy Measure with Variable Additivity Degree (1)

� A fuzzy measure with variable degree of additivity is proposed to overcome the above mentioned problems

83

Empirical Study

Creating The Best Global Supply Chain Systems

In real caseFor solving real problems

84

� Basic concept

85

Information/InternetService Providers

Suppliers Customers

Distribution in Global

Global Distribution

E-Era

Building the Global Win-Win Supply-Chain Systems in E-Era

86

Building the Global Win-Win Supply-ChainSystems in E-Erafor Business Competitiveness in E-Era

SuppliersManufacturing

Systems

Information platform and Information Flow

Money Flow

MRP

ERP

Max profit = PiQi - costs (M+P+W+T+…)Min priceMax qualityMax level of service

DRP (Distribution Requirements Planning

Max competitiveness

Customers

ISPInformation/Internet

Service Providers

For Satisfying Customer Needs

Global Distribution Distribution in Global

E nterpriseCustomers

... ...

Min negative environment impactsMin ecologicl impacts

Society

...

E-Era

Background (why this topic is the most significant issues?)

� The concept of globalization has been prosperous in the past decades

� Manufacturing as well as logistics have already become one of the most significant issues in global E-era,

(1) How can be the best global distribution in manufacturing systems for enterprise;

(2) How can satisfy the customer-needs in global logistics (physical distributions);

(3) How can minimize impact on negative environment, ecological, etc.

87

Research Problems� How we can evaluate, improve and select an

appropriate global manufacturing strategy by considering issues from both aspects of global � Manufacturing? as well as � Logistics? � Customers? How can satisfy the customers’ needs?

� How the chosen intertwined global manufacturing as well as logistics system is to be the best so that � The aspiration level of the global manufacturing

system can be achieved has few been addressed.

88

Research Purposes

� Resolve the above mentioned global manufacturing and logistics strategy selection as well as system reconfiguration issue for achieving win-win systems in aspired global manufacturing and logistics, and customers.

89

The Commercialization of DRAMManufacturing, Testing, Assembly and Distribution� The Dynamic Random Access Memory

(DRAM) is the most important components for serving as the main memory of electronic systems

� An example being modified from a real case will be presented for demonstrating effectiveness of the proposed fuzzy integral based hybrid MCDM methods

90

Case Design (1)

� A DRAM trading company usually needs to decide� The DRAM wafer source� The DRAM Manufacturing fabs

� Fab 1, Fab 2

� Assembly and test houses for DRAM dies and modules� Testing Houses A, B, and C

� Distribution channels� Channel W, X, Y

91Source of illustrations: computerhistory.org & digitaltrends.com

Case Design (2)

� Three combinations of SCs� Fab 1, Testing House A and Channel W (named as GSP 1)

� Fab 1, Testing House B and Channel X (named as GSP2)

� Fab 2, Testing House C and Channel Y (named as GSP3)

will be considered for handling some special low yield DRAM wafers (hard to test) in the down trend so that the wafers can be assembled, tested and shipped within the shortest time 92

Case Design (3)

93Source of illustrations: www.graphicsfactory.com & www.squint.com

DRAM Fab Assembly & TestHouse Channel

Fab 1

Fab 2

Testing House A

Testing House B

Testing House C

Channel W

Channel X

Channel Y

Case Design (4)

9494

Fab JFab C

Fab G

Fab TTestingHouse SZ

TestingHouse T

TestingHouse I

TestingHouse Sg

Fab U

MexicoPlant

C1

GMLS1

GMLS3

Fab JFab C

Fab G

Fab TTestingHouse SZ

TestingHouse T

TestingHouse I

TestingHouse Sg

Fab U

MexicoPlant

Fab 2

Fab 1

TestingHouse A

TestingHouse C

Channel Y

TestingHouse B

Channel W

Channel X

Decision Structure Derivations by Delphi (1)

� 16 determinants that are needed for selecting an intelligent global SC are reviewed by expert(s).

95

WaferFab

A&PHouse

MKT Chann

els

Criteria Derivations by Delphi and Brain-storming (2)� Wafer fab selection

� Wafer cost (c1)� Yield (c2)� Production control (c3)� Wafer quality (c4)� Defect density (c5)

� Testing house selection� Test systems and solutions

(c6)� Test programs, probe cards

and load boards (c7)

� Throughput maximization (c8)

� Lowest cost test solution provisions (c9)

� Full turnkey assembly and test solutions (c10)

� Channel selection� Sales capability (c11)� Relationships with system

houses (c12)� Brand (c13)� Finance capability (c14)� Technical support

capability (c15)� Technical support capability

(c16)

Prepared by Dr. Chi-Yo Huang 96

Source: test criteria from www.statschippac.com

Initial Influence Matrix A Derivationby Experts’ Opinions


0.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 3.000 1.000 2.000 1.000 1.000

5.000 0.000 4.000 5.000 1.000 2.000 3.000 2.000 3.000 3.000 1.000 2.000 2.000 1.000 3.000

4.000 1.000 0.000 1.000 1.000 1.000 1.000 4.000 1.000 1.000 1.000 2.000 1.000 1.000 1.000

1.000 1.000 1.000 0.000 1.000 4.000 4.000 4.000 3.000 2.000 1.000 3.000 3.000 1.000 3.000

5.000 5.000 3.000 5.000 0.000 4.000 4.000 4.000 3.000 2.000 2.000 3.000 2.000 1.000 3.000

1.000 1.000 1.000 1.000 1.000 0.000 1.000 4.000 5.000 5.000 2.000 2.000 3.000 1.000 3.000

A 1.000 1.000 1.000 1.000 1.000 5.000 0.000 5.000 5.000 5.000 1.000 2.000 2.000 1.000 3.000

1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.000 5.000 1.000 2.000 2.000 1.000 1.000 1.000

1.000 1.000 1.000 1.000 1.000 4.000 1.000 1.000 0.000 1.000 3.000 2.000 2.000 2.000 1.000

1.000 1.000 1.000 1.000 1.000 1.000 1.000 4.000 4.000 0.000 1.000 1.000 1.000 1.000 1.000

1.000 1.000 1.000 1.000 1.000 1.000 1.000 2.000 2.000 1.000 0.000 4.000 1.000 1.000 1.000

1.000 1.000 2.000 1.000 1.000 1.000 1.000 2.000 2.000 1.000 5.000 0.000 1.000 1.000 1.000

1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 4.000 4.000 0.000 2.000 1.000

1.000 1.000 1.000 1.000 1.000 1.000 1.000 2.000 1.000 1.000 3.000 4.000 3.000 0.000 3.000

1.000 2.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 4.000 4.000 4.000 1.000 0.000

Total Relational Matrix T Derivationby DEMATEL


0.027 0.043 0.044 0.045 0.038 0.053 0.046 0.062 0.064 0.050 0.103 0.066 0.073 0.041 0.050

0.160 0.044 0.130 0.152 0.058 0.113 0.116 0.133 0.155 0.126 0.107 0.129 0.112 0.064 0.124

0.115 0.047 0.027 0.049 0.042 0.058 0.050 0.130 0.075 0.055 0.072 0.090 0.059 0.045 0.054

0.067 0.060 0.063 0.042 0.053 0.145 0.126 0.162 0.151 0.102 0.100 0.141 0.124 0.059 0.117

0.179 0.160 0.126 0.171 0.047 0.174 0.152 0.198 0.186 0.128 0.149 0.173 0.132 0.075 0.144

0.064 0.058 0.059 0.060 0.051 0.055 0.061 0.152 0.181 0.151 0.115 0.115 0.117 0.057 0.108

0.069 0.062 0.063 0.065 0.055 0.165 0.044 0.183 0.196 0.163 0.101 0.121 0.105 0.061 0.116

0.052 0.046 0.048 0.049 0.041 0.062 0.049 0.046 0.153 0.055 0.091 0.091 0.059 0.046 0.054

0.055 0.049 0.051 0.051 0.044 0.123 0.052 0.076 0.058 0.062 0.117 0.099 0.084 0.068 0.060

0.052 0.046 0.047 0.049 0.041 0.061 0.049 0.129 0.136 0.033 0.069 0.069 0.058 0.045 0.054

0.051 0.045 0.048 0.048 0.040 0.057 0.048 0.087 0.091 0.053 0.049 0.129 0.056 0.043 0.052

0.054 0.047 0.069 0.050 0.042 0.059 0.050 0.091 0.094 0.055 0.151 0.053 0.058 0.045 0.054

0.053 0.047 0.050 0.050 0.042 0.058 0.050 0.071 0.072 0.055 0.135 0.136 0.037 0.066 0.055

0.056 0.051 0.053 0.053 0.045 0.062 0.053 0.095 0.078 0.059 0.124 0.144 0.106 0.027 0.100

0.058 0.071 0.055 0.055 0.045 0.063 0.054 0.076 0.079 0.060 0.143 0.144 0.125 0.049 0.038

Influence Diagram by DEMATEL

Prepared by Dr. Chi-Yo Huang 99Prepared by Dr. Chi- gYo Huang

DRAM Fab

TestingHouse

SalesChannel

Calculating the Influential Weights of Determinants by DANP

100

Determinant 1 2 3 4 5 6 7 8

Weights 5.76% 4.79% 5.14% 5.17% 4.06% 7.05% 5.28% 9.04%

Determinant 9 10 11 12 13 14 15

Weights 9.88% 6.35% 9.74% 9.70% 7.11% 4.73% 6.19%

Weight Derivations by Fuzzy Integral

� By assuming 0=1, we may derive c=0.7108 easily.

� The performance scores versus each alternative can be derived by using

101

Performance Scores versus Each Criteria

How to choose from various global supply chains from a DRAM trader’s perspective?� GSC 1: Good DRAM wafer price, terrible quality, good test

skills and medium sales management� GSC 2: Good DRAM wafer price, terrible quality, medium

test skills and best sales management� GSC 3: Medium DRAM wafer price, good wafer quality,

medium test skills and good sales channel management 102

CriteriaSupply Chain

5 2 4 2 2 5 5 3 4 5 5 3 3 2 25 2 4 2 2 4 4 5 3 4 4 5 4 4 53 4 2 4 4 3 3 4 4 3 4 4 3 5 3

c 3

GSC 1GSC 2GSC 3

c 1 c 2 c 15c 4 c 5 c 6 c 7 c 8 c 9 c 10 c 11 c 12 c 13 c 14

Performance Score Aggregationby the Fuzzy Integral

� The fuzzy integral technique was introduced for aggregating the performance scores

� By assuming 0=1, c can be derived as 0.7108

� The performance scores and results can be aggregated by the fuzzy integral as � GSC1 (2.417) > GSC3 (2.292) > GSC2 (2.278)which is different from the original results� GSC2 (3.927) > GSC1 (3.584) > GSC3 (3.567)

103

Discussions (1)

104

� In this research, a novel MCDM framework was proposed to address following problems and reached satisfactory results.� Designing a global supply chain is not easy. � No straightforward answers addressing how a global

manufacturing strategy should be designed to fit any business context.

� How a manufacturing strategy should be designed by considering factors being related to global logistics.

� Very few researches addressed this global manufacturing and logistics system design issue from the aspect of MCDM

� The results being derived by the novel hybrid method is different to the straight aggregation of DANP influential weights and performance scores

Discussions (2)

� Advantages of the novel MCDM framework� DANP to simply the difficulties in questionnaire collections

� Fuzzy integral to resolve the inconsistencies which occur when� Assuming the dependences of criteria while� Removing the assumptions of criteria independences when using traditional approaches for aggregating performance scores

105

Concluding Remarks

� This novel hybrid MCDM framework mainly advanced the SCM management and MCDM methods � The global supply chain can be improved and

selected by using the fuzzy integral based DANP approach for solving interdependence problem

� The fuzzy integral can be introduced to remove the inconsistencies when removing the dependences of criteria while using traditional approaches (additive) for aggregating performance scores

� The proposed analytic framework can be leveraged for resolving modern MCDM-nature problems.

106

The End

Thank you attentionEmail: [email protected]

[email protected]

Gwo-Hshiung Tzeng (Website)

http://www.knu.edu.tw/Distinguishedhttp://www.knu.edu.tw/lecturehttp://mcdm.ntcu.edu.tw/tzeng

http://sciencewatch.com/dr/erf/2009/09aprerf/09aprerfOpriET

http://www.knu.edu.tw/Distinguished/files/Published_in_Elsevier.mht

Tzeng, G.H., Huang, C.Y. (2011), Combined DEMATELtechnique with hybrid MCDM methods for creating the aspiredintelligent global manufacturing & logistics systems, Annals ofOperations Research (Forthcoming)

107

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