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  Debmallya Chatterjee* et al./ (IJITR) INTERNATIONAL JOURNAL OF INNOVATIVE TECHNOLOGY AND RESEARCH VolumeNo.1, Issue No.4,June-July 2013, 283-291. ISSN 2320–5547  @ 2013  http://www.ijitr.com  All rights Reserved. Page |283 AStudy on The Comparison ofAHPAnd FuzzyAHPEvaluations ofPrivate Technical Institutions inIndia DEBMALLYA CHATTERJEE Research-Scholer,Department of Applied Mathematics,Indian School of Mines,Dhanbad, Jharkhand, India BANI MUKHERJEE Professor,Department of Applied Mathematics,Indian School of Mines,Dhanbad, Jharkhand, India  Abstract- The numbers of private technical institutions in India are increasing rapidly in the recent decade. Today thereare thousands of private self-financed technical institutions most   of which are compromising with their quality of education. Analytical hierarchy process(AHP)and its fuzzy extension(FAHP)aretwo oftheefficienttools by whichonecan evaluate such institutions. There are ample numbers of studies in literature that discussed the efficiencies of the AHPand FAHP separately. This present piece of work makes an attempt to study and quantify the difference, if any in theapplications of AHP and FAHP on the evaluation of self-financed private technical institutions in India.Key words: Analytical hierarchy process, Fuzzy analytical hierarchy process, technical institutions, comparative study. I.I NTRODUCTION : Technical education in India plays a vital role in thedevelopment of any nation. It not only includesengineering education but also contributes in thedevelopmental activities of the nation. Since the era of liberalization, globalization and privatization, therehas been a significant changein the field of technicaleducation in India[12]. The growth is significant andcan be seen from the Figure 1. Figure 1: Growth of technical institutions (2007-2012) Source:Report of the working group 2011-12, Dept.of Higher Education, Ministry of Human ResourceDevelopment, India.Out of numerous of private self-financing technicalinstitutions that have emerged, a few are offeringquality education but many of them arecompromising with the quality. The stakeholders areconfused in selecting a quality institution for their career development and prosperity. Because of lowquality institutions the graduated student has becomea suspect. This phenomenon raises the importantquestion: how to select a quality institution?The importance of using a tool like AHP or FAHP inmulti criteria decision making like evaluation of technical institutions in India has been the illustratedin many studies done by the researchersacrossdifferent field where they talked about capturingtangible and intangible factors as well([2];[5]; [7];[8];[9];[10]; [11]; [13]).Interestinglythe researchers in most of their studyinvolving FAHP opinioned that embedding fuzzymathematics with the classical AHP helped capturethe vagueness of human decision making and provided better precision ([1];[6]; [14]). However noexisting study illustrated the difference byquantifying it through the application of AHP andFAHP on the same problem.The following sectionsof this paper makes anattempt todemonstrate the detailed comparison between the resultsi.e. convergence and non-convergencein terms of the factor weights, sub factor weights and alternative scoresobtained in theevaluation of private self-financed technicalinstitutions using AHP and FAHP respectively. Anattempt is also made to find the statisticalsignificance of the correlation between the resultsobtained using the two different methods. II.METHODOLOGY  A.Selection of respondents for the study The analytical hierarchy process (AHP) and its fuzzyextension (FAHP) are both capable of handling amixture of subjective and objectivefeedbacks and because of this character requires consistent inputsfor efficacy. This character of both AHP and FAHPinvites ‘expert opinion’ for consistent evaluations of the factor weight.In this study twelve experts were selected fromacademia havingmore than fifteen years’ experiencein the field of engineering education and wereassociated with all the three technical institutions of Durgapur for some time in their career. Mostly the  Debmallya Chatterjee* et al./ (IJITR) INTERNATIONAL JOURNAL OF INNOVATIVE TECHNOLOGY AND RESEARCH VolumeNo.1, Issue No.4,June-July 2013, 283-291. ISSN 2320–5547  @ 2013  http://www.ijitr.com  All rights Reserved. Page |284 respondents were the Professors, DepartmentalHeads, Deans and Deputy Directors who haveworked in these institutes for some time in their career within the last ten years.The experts were requested to do pair wisecomparisons among factors, sub factors andalternative institutions and identify the level of importanceof one over the other. To do that a set of questionnaires were provided to the experts.  B.Identification of factors and subfactors for theevaluation Besides the identification of experts for the study theidentification of the factors and sub factors is also acritical task for the success of both AHP and FAHPmodels. The factors and sub factors in the performance evaluation of a self-financing technic   alinstitution (under AICTE) in India is available in theformat mentioned by National Board of accreditation(http://www.nba-india.org) under the banner of AllIndia Council for Technical education (AICTE).Since its inception in 1945, AICTE is in the processof improving the governance and after a lot of  permutations and combinations structured the set of criteria for the evaluation of a technical institution.Since this set of factors and sub factors are wellestablished and are evaluated in the NBAaccreditation process in India, the researcher in the present study relied on the same set of factors andsub factors with some modification / adjustmentsuitable for the study restricted to private self-financed technical institutions in India. The expertopinions were sought to shape the final selection or alteration of thefactors and sub factors for the study.The factors and corresponding sub factors identifiedfor the present study can be found in Table 1. Table 1: Factors and sub factors selected in the study FactorsSub FactorsCampusInfrastructureHostel, Transport/ canteen,Power backup, SecurityFacultyTeacher/ Student ratio,Qualification/ Experience of Faculty, Faculty retentionStudentAdmission, AcademicResult, PlacementAcademicAmbienceClassroom, Laboratory,LibraryTeaching LearningProcessSyllabuscoverage, Tutorial/remedial class, Use of Advance Teaching AidSupplementaryProcessAlumni, Co-curricular activity, Cultural activity,seminar/ workshop C.Identification of alternatives in the study This study is aimed to evaluate the private self-financing technical institutions in India and hence asample of three such institutions from Durgapur,West Bengal is taken for the study based onconvenience.Eight technical Institutions are functioning in the subdivision of Durgapur, West Bengal offeringB.Techin different specializations. Out of these eight, twoare government institutions and three private self-financed institutes emerged very recently and stillfighting to get students. The remaining three self-financed technical institutions are selected asalternatives in this study.This reason behind shortlisting these institutions isconsidered because all the three select institutionswere established on or before 2002, i.e. they have been providing engineering education for a decade or more andaround two thousand students graduatedfrom each of those institutions. Moreover all the threeshortlisted institutes are within ten kilometers fromthe nearest railway station and also admit studentsthrough the common West Bengal Joint EntranceExamination (WBJEE).The year of establishment is taken as main factor for short listing the alternatives as it indicates that all of them are in the growth phase and they survivedinfancy. Moreover, the government institutionswithin the sub division are not selected because theydo have a completely different pattern of funding and previous studies criticized the comparison of institutes having significant variation in funding. Thenames of the institutions are disguised as Alternative1, Alternative 2 and Alternative 3 for the smoothconduct of the study.  D.Construction of the detail hierarchy of the problem The design of the problem hierarchy is an essentialstep in common to both AHP and FAHP methods.This hierarchy help the researcher understand the problem andthe associated flow. The hierarchy in the problem of evaluating technical institutes isstructured keeping the objective at the top(performance evaluation of self-financed technicalinstitutions) through the intermediate levels (mainand sub-factors on which subsequent levels depend)to the bottom level (the list of three private self-financed technical institutions as alternatives).Figure 2 describes the hierarchy of this problem inwhich the objective is at the extreme left followed bythe factors andthen the sub factors of evaluation.Finally the alternatives to be evaluated are at the  Debmallya Chatterjee* et al./ (IJITR) INTERNATIONAL JOURNAL OF INNOVATIVE TECHNOLOGY AND RESEARCH VolumeNo.1, Issue No.4,June-July 2013, 283-291. ISSN 2320–5547  @ 2013  http://www.ijitr.com  All rights Reserved. Page |285 extreme right in the hierarchy. Instead of a top to bottom flow, the present hierarchy has a left to rightflow. Figure 2:   The detail hierarchy of the problem  E.Generation of factors weights and score for alternatives Once the hierarchy is established, the next step is todo pair wise comparisons between the factors and between the sub-factors within each factor consideredin the study. This pair wise comparison is done basedon the linguistic preference scale which can be non-fuzzy or fuzzy depending on the model of choice.These steps of computation vary significantly acrossclassical AHP and fuzzy AHP and can be seen fromthe studies by Chatterjee and Mukherjee ([3];[4]). III.RESULTS AND DISCUSSION  A.Comparison between factor weights To understand the difference or similarity betweenthe results obtained using AHP and FAHP methodsrespectively, let us start first with the factor weights.Figure 3 illustrates the weightsof the factors withrespect to the two methods considered in the study.From the figure one can see that the weights of thefactors ‘campus infrastructure’ and ‘teaching learning process’ are almost the same across the two methodswith slight differences in the other factors consideredin the present study. Interestingly the order of importance of the factors varies across the twomethods slightly. Where ‘faculty’ got the highestweight in AHP, ‘campus infrastructure’ got thehighest with respect to FAHP. Similar situationhappen in case of ‘academic ambience’ and ‘teachinglearning process’.However from Table 2 (SPSS output) it can be seenthat there exists a significant correlation with between the weights of the factorscorresponding to AHPand FAHP respectively.Though there are some differences in terms of weights of the factors across the results from the twomethods discussed, but the result of Table 2 indicatesthat the difference is not significant. Figure 3:Comparison of factor weightsTable 2:Correlation between the factor weights AHPFactor weightFAHPFactor weightAHP Factor weightPearsonCorrelation1.894 * Sig. (2-tailed).016 N66FAHP Factor weightPearsonCorrelation.894 * 1Sig. (2-tailed).016 N66*. Correlation is significant at the 0.05level (2-tailed).  B.Comparison between the sub factor weights Once the weights of the factors got compared it isimportant to see the comparison between the AHPsub factor weights and FAHP sub factor weightsunder eachfactor. From the Figure 4 one can witnessthat the trend is almost the same for the sub factorsunder ‘campus infrastructure’ in both AHP andFAHP results. However variations of weights are  Debmallya Chatterjee* et al./ (IJITR) INTERNATIONAL JOURNAL OF INNOVATIVE TECHNOLOGY AND RESEARCH VolumeNo.1, Issue No.4,June-July 2013, 283-291. ISSN 2320–5547  @ 2013  http://www.ijitr.com  All rights Reserved. Page |286 more in AHP in comparison to FAHP. In terms of importance also ‘hostel’ and ‘power backup’ are thetwo top sub factors that evolve in both models. Figure 4:Comparing between the sub factorweights under campus infrastructure Under the factor ‘faculty’ as well th   e weights of thesub factors follow similar trends in both AHP andFAHP methods. From Figure 5 one can easily see theimportance of ‘teacher/student ratio’ is highestthough numerically the AHP weight is slightly higher than the corresponding FAHP weight with respect toall the sub factors. Figure 5:Comparing between the sub factorweights under faculty Under the factor ‘student’ there has been no changein trends except the sub factor ‘placement’ where theAHP and FAHP weights differ significantly. In boththe AHP and FAHP models admission wasconsidered mostimportant among the other subfactors under ‘student’. Figure 6:Comparing between the sub factorweights under student From Figure 7 one can see that there is some amountof variation in sub factor weights under ‘academicambience’. Though both the AHP and FAHPweights of ‘library’ is less than the other counterparts, but the importance in the weights varysignificantly for laboratory and to some extent for classroom. Figure 7:Comparing between the sub factorweights under academic ambience Underteaching learning process there has been asignificant variation across the sub factor weightsobserved from Figure 8. Here apart from ‘syllabuscoverage’, the other two sub factor weights varied inthe fuzzy and non-fuzzy evaluations.
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