A fuzzy DEA model with undesirable fuzzy outputs and its application to the banking sector in India |
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| Affiliation: | 1. Instituto Superior Técnico, Universidade de Lisboa, Av. Prof. Dr. Aníbal Cavaco Silva, 2744-016 Porto Salvo, Portugal;2. INESC-ID Lisboa, Av. Prof. Dr. Aníbal Cavaco Silva, 2744-016 Porto Salvo, Portugal;1. Department of Energy, Politecnico di Milano, via Ponzio 34/3, 20133 Milan, Italy;2. Systems Science and the Energetic Challenge, European Foundation for New Energy-Electricité de France, Ecole Centrale Paris and Supelec, Paris, 92295 Chatenay-Malabry Cedex, France;3. Faculty of Engineering and Computing, Coventry University, Priory Street, Coventry, UK;1. Institute of Computing, University of Campinas, SP, Brazil;2. Dept. of Computer Engineering, Federal Technological University of Parana, PR, Brazil;3. IMMUNOCAMP Research and Development of Technology, SP, Brazil;4. Institute of Biology, University of Campinas, SP, Brazil;1. Communications Technologies Group (GTC), Aragón Institute of Engineering Research (I3A), University of Zaragoza, Spain;2. Hospital Management Research Unit, University of Zaragoza, Spain;1. Department of Engineering, University of Almería, 04120 Almería, Spain;2. Department of Informatics, University of Almería, 04120 Almería, Spain;3. Department of Applied Physics, University of Cordoba, Cordoba, Spain;4. Department of Cartographic Engineering, Geodesy and Photogrammetry, Polytechnic University of Madrid, 28040 Madrid, Spain |
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| Abstract: | Data envelopment analysis (DEA) is a widely used technique for measuring the relative efficiencies of decision making units (DMUs) with multiple inputs and multiple outputs. However, in real life applications, undesirable outputs may be present in the production process which needs to be minimized. The present study endeavors to propose a DEA model with undesirable outputs and further to extend it in fuzzy environment in view of the fact that input/output data are not always available in exact form in real life problems. We propose a fuzzy DEA model with undesirable fuzzy outputs which can be solved as crisp linear program for each α in (0, 1] using α-cut approach. Further, cross-efficiency technique is applied to increase the discrimination power of the proposed models and to rank the efficient DMUs at every α in (0, 1]. Moreover, for better understanding of the proposed methodology, we present a numerical illustration followed by an application to the banking sector in India. This is the first study which attempts to measure the performance of public sector banks (PuSBs) in India using fuzzy input/output data for the period 2009–2011. The results obtained from the proposed methodology not only depict the impact of undesirable output on the performance of PuSBs but also analyze efficiently the influence of the presence of uncertainty in the data over the efficiency results. The findings show that the efficiency results of many PuSBs vary with the variation in α during the selected period. |
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| Keywords: | Data envelopment analysis Fuzzy data envelopment analysis Undesirable outputs Rank efficient units Banking sector performance |
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