Study Of Fuzzy-Ahp Model To Search The Criterion In The Evaluation

Debmallya Chatterjee et. al. / International Journal of Engineering Science and Technology Vol. 2(7), 2010, 2499-2510

1.6 Organisation of the Study

In order to develop a Fuzzy-AHP decision making model for the evaluation of private technical institutions, the piece of work is organized as follows. In the next section review of existing work is done. Then the methodology is introduced along with the stages of development of the model. After that an empirical study is conducted along wÅŸh its findings. Finally the paper ends with the conclusion.

1.7 . REVIEW OF EXISTING WORK

Among the different methodologies used, it has been observed that Fuzzy-AHP method was used extensively in decision making. The method was used to select the best bridge construction method among the alternatives avoiding the inconsistency there in [12]. In the literature, fuzzy-AHP has been widely used in solving many complicated decision making problems. Fuzzy-AHP and its extensions were developed in selecting the key capabilities in technology management [20]. The fuzzy AHP approach was used in the evaluation of computer integrated manufacturing alternatives. The same approach was used in the selection of the best location for a facility and in the evaluation of catering firms in Turkey [9]. Fuzzy Integrated Analytic Hierarchy Process Approach is used for Selecting Strategic Big-sized R&D Programs in the Sector of Energy Technology Development [17]. It is further used it in Multi-criteria Supplier Evaluation and vendor selection [3, 8]. Many researchers who have studied Fuzzy AHP provided evidences that it shows more efficiency in handling human judgments than the Classical AHP method [5, 6, 7, 10].

2. METHODOLOGY

2.1 Development of Fuzzy-AHP model in multicriteria decision making

2.1.1 Conceptual Hierarchy of Fuzzy –AHP model

Analytical Hierarchy Process starts by laying out the overall hierarchy of the decision making problem. The hierarchy is structured from the top (the overall goal of the problem) through the intermediate levels (criteria and sub-criteria on which subsequent levels depend) to the bottom level (the list of alternatives). Each criterion in the lower level of hierarchy is compared with respect to the criteria in the upper level of hierarchy. The criteria in the same level are compared using pair wise comparison. Fig 2.1 describes the hierarchy of a decision making problem.

Fig 2.1 Hierarchy of the Decision making problem

2.1.2 Fuzzy pair wise comparison method

Once the hierarchy is established, the pair wise comparison evaluation takes place. All the criteria on the same level of the hierarchy are compared to each of the criterion of the preceding (upper) level. A pair wise comparison is

Overall Goal

Criteria 1 Criteria 2 Criteria 3 Criteria 4

Alternative 1 Alternative 2 Alternative 3

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performed by using Fuzzy linguistic terms in the scale of 0 – 10 described by the Triangular Fuzzy Numbers in the Table 2.1.

Table 2.1

Fuzzy Importance scale with TFN

Verbal judgment Explanation Fuzzy number

Extremely Un-important (EXUI) A criterion is strongly inferior to another (0, 1, 2)

Un-important (UI) A criterion is slightly inferior to another (1, 2.5, 4)

Equally Important (EI) Two criteria contribute equally to the

object

(3, 5, 7)

Moderately Important (MI) Judgment slightly favor one criterion

over another

(6, 7.5, 9)

Extremely Important (EXI) Judgment strongly favor one criterion

over another

(8, 9, 10)

To reflect pessimistic, most likely and optimistic decision making environment, triangular fuzzy numbers with minimum value, most plausible value & maximum value are considered. Here the fuzzy comparison matrix is defined as

Where is the relative importance of each criteria in Pair wise comparison and are the minimum value, most plausible value & maximum value of the triangular fuzzy number. To simplify the calculation of element weight the fuzzy pair wise comparison matrix is broken into crisp matrices formed by taking the minimum values, most plausible values & maximum values from the triangular fuzzy numbers.

2.1.3 Generation of Criteria and Sub-Criteria weight

The Normalization of the Geometric Mean (NGM) method (Buckley et al, 1985) is applied to compute weights from the fuzzy pair wise comparison matrices which is given by

1

ini

ii

a

a

, where

1/

1

nn

i ijj

a a

1 2 1

21 2

31 3 2 3

1

1 ....

1 ..........................................(4 )

1 ...

.. .. 1

n

n

n

nn

a a

a aA

a a a

a

( , , )L M Ua a a ai j i j i j i j

, , ,L M Ui j i j i ja a a

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In the above equations, ia is geometric mean of criterion i. i ja is the comparison value of criterion i to criterion

j. i is the ith criterion's weight, where 0i and1

1n

ii

.

For group evaluation, it is required to aggregate evaluator’s opinions into one. Considering the evaluation given by

expert ( ) ( ) ( )( , , )i i i

i L M UE a a a the aggregate of all experts’ judgments can be calculated using average means

( ) ( ) ( )

1 1 1

1 1 1, , . . . . . . . . . . . . . ( 5 )

n n ni i i

L M Ui i i

A a a an n n

The final weight vector is generated by defuzzyfying the average [11]

( ) ( ) ( )

1 1 1( )

1 1 12

. . . . . . ( 6 )4

n n ni i i

L M Ui i i

i

a a an n n

w

The weight of ith sub criteria under kth main criteria is obtained by ( ) . . . . . . . . . . . . . . . . . . . . . . . . ( 7 )k k iw s

where kw is the kth main criteria weight and kis is the weight of ith sub criteria with respect to kth main criteria.

2.1.4 Calculation of overall score for alternatives

Once the weight of criteria, sub criteria are evaluated and are multiplied using equation (3) to obtain global weight of sub criteria, it is required to calculate the overall score of alternatives for their evaluation. The overall score of mth alternative is obtained by

1

. . . . . . . . . . . . . . . . . . . . . . . . ( 8 )N

m l m ll

A s a

where ls is the weight of lth sub criteria and m la is the weight of thm alternative with respect to lth sub

criteria.

2.2 Identification of Criteria and Sub Criteria for evaluating alternatives

One of the important steps of the proposed model is to determine all the important criteria and their relationship with the decision variables. This step is crucial because the selected criteria and sub criteria can influence the final choice. Here in this project the criteria and sub-criteria are selected based on the format mentioned by National Board of accreditation & through expert’s opinion. The alternatives taken are the private self financing technical institutions of Durgapur, West Bengal, India. The criteria and sub-criteria selected are described in Table 2.2

Criteria Sub Criteria

Campus Infrastructure Hostel, Transport/ canteen/ Internet, Power backup, Security

Faculty Teacher/ Student ratio, Qualification/ Experience of Faculty, Faculty retention

Student Admission, Academic Result, Placement Academic Ambience Classroom, Laboratory, Library Teaching Learning Process Syllabus coverage, Tutorial/ remedial class,

Use of Advance Teaching Aid Supplementary Process Alumni, Co-curricular activity, Cultural activity, seminar/

workshop

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2.3 Construction of the detailed hierarchy of the problem

The hierarchy is constructed taking all the criteria, sub-criteria and alternatives specific to the research problem. The hierarchy is structured from the top (performance evaluation of technical institutions) through the intermediate levels (main and sub-criteria on which subsequent levels depend) to the bottom level (the list of technical institutions).Figure 2.2 describes the hierarchy in detail.

Figure 2.2

Detailed hierarchy of the problem

3. RESULTS AND DISCUSSIONS

The detail of the steps of Fuzzy-AHP model described in section 2.1.2 to 2.1.4 are explained elaborately using the data collected from experts and the engineering students of Durgapur.

3.1 Illustration of the Fuzzy-AHP model

Once the hierarchy was established and a series of questions were asked to direct pair wise comparisons, each expert performed a pair wise comparison. Hence the main criteria weights from the first e éert’s judgment can be expressed in Table 3.1.

Evaluation of

Technical Inst.

FFaaccuullttyy

CCaammppuuss IInnffrraassttrruuccttuurree

SSttuuddeenntt

AAccaaddeemmiicc AAmmbbiieennccee

PPoowweerr bbaacckkuupp

SSeeccuurriittyy

HHoosstteell

Transport/ canteen

Qualification/ Experience

Faculty retention

AAccaaddeemmiicc RReessuulltt

PPllaacceemmeenntt

LLiibbrraarryy

AAddvv tteeaacchhiinngg aaiidd

DDIIAATTMM

BBCCRREECC

BBCCEETT

TTeeaacchhiinngg LLeeaarrnniinngg

LLaabboorraattoorryy

SSuupppplleemmeennttaarryy PPrroocceessss

Teacher/ Std ratio

CCllaassssrroooomm

AAddmmiissssiioonn

AAlluummnnii

CCoo--CCuurrrriiccuullaarr

CCuullttuurraall aaccttiivviittyy

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SSyyllllaabbuuss

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Table 3.1

First Expert’s judgment

Fuzzy weight of Main Criteria

( l m u )

Campus Infrastructure 0.4473 0.2470 0.2291

Faculty 0.5527 0.2808 0.2474

Student 0.0000 0.1777 0.1795

Academic Ambience 0.0000 0.1058 0.1220

Teaching Learning Process 0.0000 0.1132 0.1270

Supplementary Process 0.0000 0.0756 0.0950

Repeating the same procedure for all experts’ judgments following equation (5) in section 2.1.3 the global weights of the main criteria was obtained in Table 3.2

Table 3.2

Global weight of main criteria

Name of the Main Criteria Global weight of main criteria

( l m u )

Campus Infrastructure 0.3620 0.2433 0.2261

Faculty 0.3379 0.2075 0.1935

Student 0.0831 0.1766 0.1800

Academic Ambience 0.1098 0.1565 0.1609

Teaching Learning Process 0.0381 0.1064 0.1191

Supplementary Process 0.0692 0.1096 0.1203

The results indicate that the priority of campus infrastructure is the maximum followed by faculty of an institution. Following the same procedure the weights of the sub-criteria are calculated and the results are described below in Table 3.3.

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Table 3.3

Sub criteria weights

Weight of sub criteria

Sub criteria ( l m u )

Hostel 0.3880 0.2894 0.2752

Transport/ canteen etc 0.0002 0.2282 0.2299

Power backup 0.2189 0.2966 0.2886

Security 0.1894 0.1858 0.2064

Teacher/ student ratio 0.7133 0.4867 0.4458

Qualification/ exp of faculty 0.1174 0.2755 0.2940

Faculty retention 0.1693 0.2377 0.2602

Admission 0.5000 0.4336 0.3999

Academic result 0.0000 0.2569 0.2766

Placement 0.5000 0.3096 0.3235

Classroom 0.4354 0.3544 0.3291

Laboratory 0.3737 0.3272 0.3131

Library 0.0731 0.1589 0.1755

Syllabus coverage 0.1178 0.1595 0.1823

Tutorial/remedial class 0.5370 0.4621 0.4368

Use of Adv teaching aid 0.1157 0.2367 0.2576

Alumni Association 0.3473 0.3012 0.3056

Cultural activity 0.2807 0.2818 0.2883

Co-curricular activity 0.6033 0.4902 0.4527

Seminar/ workshop 0.1160 0.2280 0.2591

Further the sub-criteria weights are multiplied by the corresponding main criteria weights to obtain global weight of the sub-criteria as in Table 3.4.

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Table 3.4

Global weight of sub-criteria

Global weight of sub criteria

( l m u )

Hostel 0.1405 0.0704 0.0622

Transport/ canteen etc 0.0002 0.0555 0.0520

Power backup 0.0792 0.0722 0.0653

Security 0.0686 0.0452 0.0467

Teacher/ student ratio 0.2410 0.1010 0.0863

Qualification/ exp of faculty 0.0397 0.0572 0.0569

Faculty retention 0.0572 0.0493 0.0504

Admission 0.0415 0.0766 0.0720

Academic result 0.0000 0.0454 0.0498

Placement 0.0415 0.0547 0.0582

Classroom 0.0478 0.0555 0.0530

Laboratory 0.0410 0.0512 0.0504

Library 0.0080 0.0249 0.0282

Syllabus coverage 0.0129 0.0250 0.0293

Tutorial/remedial class 0.0204 0.0492 0.0520

Use of Adv teaching aid 0.0044 0.0252 0.0307

Alumni Association 0.0132 0.0320 0.0364

Cultural activity 0.0194 0.0309 0.0347

Co-curricular activity 0.0417 0.0537 0.0545

Seminar/ workshop 0.0080 0.0250 0.0312

The results of the global sub-criteria weights indicate that the priorities are highest in teacher student ratio followed by student hostel. Students feedbacks of three alternative technical institutions are collected with respect to each of the sub-criteria using Fuzzy linguistic preference scale and the corresponding weights are generated as described in Table 3.5.

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Table 3.5

Weights of alternatives

Weights of the Alternatives

BCREC DIATM BCET

( l m u ) ( l m u ) ( l m u )

Hostel 0.362 0.354 0.349 0.199 0.246 0.266 0.439 0.400 0.385

Transport/ canteen etc 0.271 0.297 0.306 0.490 0.427 0.401 0.239 0.276 0.293

Power backup 0.403 0.380 0.370 0.242 0.272 0.288 0.356 0.347 0.342

Security 0.713 0.474 0.444 0.117 0.246 0.264 0.169 0.281 0.293

Teacher/ student ratio 0.355 0.340 0.343 0.529 0.441 0.412 0.117 0.219 0.245

Qualification/ exp of faculty 0.339 0.340 0.343 0.331 0.330 0.329 0.331 0.330 0.329

Faculty retention 0.426 0.356 0.356 0.574 0.430 0.400 0.000 0.214 0.244

Admission 0.580 0.387 0.365 0.210 0.306 0.317 0.210 0.306 0.317

Academic result 0. 713 0.496 0.447 0.000 0.215 0.246 0.210 0.289 0.307

Placement 0.415 0.386 0.371 0.386 0.367 0.359 0.198 0.248 0.270

Classroom 0.625 0.477 0.434 0.117 0.243 0.267 0.259 0.280 0.299

Laboratory 0.655 0.439 0.405 0.123 0.250 0.275 0.223 0.311 0.320

Library 0.423 0.391 0.376 0.198 0.243 0.263 0.379 0.366 0.361

Syllabus coverage 0.309 0.289 0.278 0.280 0.274 0.269 0.256 0.259 0.258

Tutorial/remedial class 0.556 0.453 0.422 0.155 0.244 0.262 0.289 0.304 0.316

Use of Adv teaching aid 0. 790 0.474 0.432 0.117 0.246 0.270 0.169 0.281 0.299

Alumni Association 0.534 0.452 0.416 0.233 0.274 0.292 0.233 0.274 0.292

Cultural activity 0.167 0.289 0.303 0.667 0.479 0.440 0.167 0.232 0.258

Co-curricular activity 0.333 0.333 0.333 0.333 0.333 0.333 0.333 0.333 0.333

Seminar/ workshop 0.380 0.361 0.353 0.284 0.302 0.309 0.336 0.337 0.338

Fuzzy Score of alternative private technical institutions, namely BCREC, BCET and DIATM of Durgapur along with the final crisp score are expressed in table 3.6.

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Table 3.6

Global weights of alternatives

Final Score of the Alternatives

BCREC DIATM BCET

( l m u ) ( l m u ) ( l m u )

Hostel 0.051 0.025 0.022 0.028 0.017 0.017 0.062 0.028 0.024

Transport/ canteen etc 0.002 0.016 0.016 0.002 0.024 0.021 0.002 0.015 0.015

Power backup 0.032 0.027 0.024 0.019 0.020 0.019 0.028 0.025 0.022

Security 0.049 0.021 0.021 0.008 0.011 0.012 0.012 0.013 0.014

Teacher/ student ratio 0.085 0.034 0.030 0.127 0.045 0.036 0.028 0.022 0.021

Qualification/ exp of faculty 0.013 0.019 0.020 0.013 0.019 0.019 0.013 0.019 0.019

Faculty retention 0.024 0.018 0.018 0.033 0.021 0.020 0.000 0.011 0.012

Admission 0.024 0.030 0.026 0.009 0.023 0.023 0.009 0.023 0.023

Academic result 0.000 0.023 0.022 0.000 0.010 0.012 0.000 0.013 0.015

Placement 0.017 0.021 0.022 0.016 0.020 0.021 0.008 0.014 0.016

Classroom 0.030 0.026 0.023 0.006 0.013 0.014 0.012 0.016 0.016

Laboratory 0.027 0.022 0.020 0.005 0.013 0.014 0.009 0.016 0.016

Library 0.003 0.010 0.011 0.002 0.006 0.007 0.003 0.009 0.010

Syllabus coverage 0.004 0.007 0.008 0.004 0.007 0.008 0.003 0.006 0.008

Tutorial/remedial class 0.011 0.022 0.022 0.003 0.012 0.014 0.006 0.015 0.016

Use of Adv teaching aid 0.003 0.012 0.013 0.001 0.006 0.008 0.001 0.007 0.009

Alumni Association 0.007 0.014 0.015 0.003 0.009 0.011 0.003 0.009 0.011

Cultural activity 0.003 0.009 0.011 0.013 0.015 0.015 0.003 0.007 0.009

Co-curricular activity 0.014 0.018 0.018 0.014 0.018 0.018 0.014 0.018 0.018

Seminar/ workshop 0.003 0.009 0.011 0.002 0.008 0.010 0.003 0.008 0.011

Sum of Weights : 0.404 0.385 0.372 0.307 0.316 0.318 0.219 0.294 0.305

Defuzzified Weights: 0.387 0.315 0.279

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3.2 Findings and discussions

From the main and sub-criteria weights in the tables is can be inferred that there exists variation between the priorities of the main and sub criteria mentioned in the model. It is further observed that the priority of the main criteria “Campus Infrastructure” is highest followed by “Faculty”. In case of sub criteria the priority is highest for ”Hostel” under “Campus Infrastructure” , “Teacher student ratio” among “Faculty”, “Admission” and “placement” among “Student”, “Classroom” among “Academic ambience” and “Co-curricular activity” among “Supplementary process”. When it comes to the alternative technical institutions it is found that the Hostel of BCET, Teacher student ratio, Placement of BCREC and Cultural activity of DIATM are the best. Finally from the defuzzified final score of the alternative technical institutions it has been observed that the overall score of Dr. B. C. Roy engineering college is the highest followed by Durgapur Institute of Advanced Technology and Management and Bengal college of engineering and Technology.

4. CONCLUSIONS

Since nineties there is a sea change in the field of Technical Education in India. Lots of Private self financing Technical Institutions have emerged with a business orientation offering readymade courses. Few of them are truly worthy and offering quality education in India but many of them are managing with the quality. The stakeholders are in a state of utter confusion in choosing a quality Institution for their career development and prosperity. Agencies are giving contradictory judgments about the Institutions and thus confusing the stakeholders at the highest level. Previously no attempt was made to generate a model which would help the stakeholders in decision making. This paper presents a Fuzzy-AHP model to overcome stakeholders problem in evaluating Technical Institutions. In this model Triangular Fuzzy numbers are utilized in collecting human judgments through linguistic variables. Further Analytical Hierarchy Process was used in generating criteria weights and sub criteria weights for the evaluation of alternatives. Although for simplicity less number of alternatives are taken but this model can be used in evaluating a number of alternatives. Further this study is not limited to the evaluation of Technical Institutions; rather it can be used in multi-criteria decision making in any field of study.

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Study Of Fuzzy-Ahp Model To Search The Criterion In The Evaluation

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