Fuzzy mix-efficiency in fuzzy data envelopment analysis and its application

Abstract

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 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 mix-efficiency 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 α-cut approach is used to evaluate the fuzzy input as well as fuzzy output mix-efficiencies 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. © 2014 Springer-Verlag Berlin Heidelberg.