Fuzzy Mix-efficiency in Fuzzy Data Envelopment Analysis and Its Application
Data envelopment analysis (DEA) is a linear programming based non-parametric technique for evaluating the relative efficiencies of a homogeneous set of decision making units (DMUs) which utilize multiple inputs to produce multiple outputs. It consists of
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Fuzzy Mix-efficiency in Fuzzy Data Envelopment Analysis and Its Application Jolly Puri and Shiv Prasad Yadav
Abstract Data envelopment analysis (DEA) is a linear programming based nonparametric technique for evaluating the relative efficiencies of a homogeneous set of decision making units (DMUs) which utilize multiple inputs to produce multiple outputs. It consists of two types of DEA models: radial models and non-radial models. A radial model deals only with proportional changes of inputs/outputs and neglects the input/output slacks whereas a non-radial model deals directly with the input/output slacks. The slack based measure (SBM) model is a non-radial model that results into the SBM efficiency which can be further decomposed into radial, scale and mix-efficiency. The mix-efficiency is a measure to estimate how well the set of inputs are used (or outputs are produced) together. The conventional mixefficiency measure is limited to crisp input and output data which may not always be available in real life applications. However, in real life problems, data may be imprecise or fuzzy. In this chapter, we extend the idea of mix-efficiency to fuzzy environments and develop a concept of fuzzy mix-efficiency in fuzzy DEA. We provide both the input and output orientations of fuzzy mix-efficiency. The a-cut approach is used to evaluate the fuzzy input as well as fuzzy output mixefficiencies of each DMU. Further, a new method is provided for ranking the DMUs on the basis of fuzzy input and output mix-efficiencies. Moreover, to ensure the validity of the proposed methodology, we illustrate a numerical example and applied the proposed methodology to the banking sector in India.
Keywords Fuzzy DEA Fuzzy mix-efficiency Banking performance evaluation
Fuzzy ranking approach
J. Puri S. P. Yadav (&) Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee 247667, India e-mail: [email protected] J. Puri e-mail: [email protected]
A. Emrouznejad and M. Tavana (eds.), Performance Measurement with Fuzzy Data Envelopment Analysis, Studies in Fuzziness and Soft Computing 309, DOI: 10.1007/978-3-642-41372-8_6, Springer-Verlag Berlin Heidelberg 2014
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J. Puri and S. P. Yadav
1 Introduction Data envelopment analysis (DEA), initially developed by Charnes, Cooper and Rhodes [1], is basically a generalization of Farrell’s technical efficiency measure to multiple inputs and multiple outputs case [2]. It is a linear programming based non-parametric technique for evaluating the relative efficiencies of homogeneous decision making units (DMUs) which utilize multiple inputs to produce multiple outputs. It constructs a non-parametric piecewise frontier (surface) over the data and using this frontier it computes a maximal performance measure for each DMU relative to that of all other DMUs with the restriction that each DMU lies on the efficient frontier or is enveloped by the frontier. The DMUs which lie on the frontier are called the efficient DMUs. The efficiency value of an efficient DMU is equal
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