Fuzzy Data envelopment Analysis with SBM using α-level Fuzzy Approach

Qaiser Farooq Dar, Ahn Young Hyo, Gulbadian Farooq Dar, Shariq Ahmad Bhat, Arif Muhammad Tali, Yasir Hamid Bhat

Abstract


The applications of fuzzy analysis in data-oriented techniques are the challenging aspect in the field of applied operational research. The use of fuzzy set theoretic measure is explored here in the context of data envelopment analysis (DEA) where we are utilizing the fuzzy α-level approach in the three types of efficiency models. Namely, BCC models, SBM model and supper efficiency model in DEA. It was observed from the result that the fuzzy SBM model has good discrimination power over fuzzy BCC. On the other side, both the models fuzzy BCC and fuzzy SBM are not able to make the genuine ranking which is acceptable for all. So this weakness is overcome with the help of fuzzy super SBM model and all three models are applied to illustrate the types of decisions and solutions that are achievable when the data are vague and prior information is in imprecise.

           In this paper, we are considering that our inputs and outputs are not known with absolute precision in DEA and here, we using Fuzzy-DEA models based on an α-level fuzzy approach to assessing fuzzy data. 


Keywords


Fuzzy Set, Linear Parametrical Programming, Data Envelopment Analysis, Vague, Fuzzy Equalities, and Inequalities.

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DOI: http://dx.doi.org/10.18187/pjsor.v15i2.2051

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Title

Fuzzy Data envelopment Analysis with SBM using α-level Fuzzy Approach

Keywords

Fuzzy Set, Linear Parametrical Programming, Data Envelopment Analysis, Vague, Fuzzy Equalities, and Inequalities.

Description

The applications of fuzzy analysis in data-oriented techniques are the challenging aspect in the field of applied operational research. The use of fuzzy set theoretic measure is explored here in the context of data envelopment analysis (DEA) where we are utilizing the fuzzy α-level approach in the three types of efficiency models. Namely, BCC models, SBM model and supper efficiency model in DEA. It was observed from the result that the fuzzy SBM model has good discrimination power over fuzzy BCC. On the other side, both the models fuzzy BCC and fuzzy SBM are not able to make the genuine ranking which is acceptable for all. So this weakness is overcome with the help of fuzzy super SBM model and all three models are applied to illustrate the types of decisions and solutions that are achievable when the data are vague and prior information is in imprecise.

           In this paper, we are considering that our inputs and outputs are not known with absolute precision in DEA and here, we using Fuzzy-DEA models based on an α-level fuzzy approach to assessing fuzzy data. 


Date

2019-06-22

Identifier


Source

Pakistan Journal of Statistics and Operation Research; Vol. 15 No. 2, 2019



Print ISSN: 1816-2711 | Electronic ISSN: 2220-5810