Inexact Discretionary Inputs in Data Envelopment Analysis
In this chapter, the relationship between fuzzy concepts and the efficiency score in Data envelopment analysis (DEA) is dealt with. A new DEA model for handling crisp data using fuzzy concept is proposed. In addition, the relationship between possibility
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Inexact Discretionary Inputs in Data Envelopment Analysis Majid Zerafat Angiz Langroudi
Abstract In this chapter, the relationship between fuzzy concepts and the efficiency score in Data envelopment analysis (DEA) is dealt with. A new DEA model for handling crisp data using fuzzy concept is proposed. In addition, the relationship between possibility sets and the efficiency score in the traditional crisp CCR model is presented. The relationship provides an alternative perspective of viewing efficiency. With the usage of the appropriate fuzzy and possibility sets to represent certain characteristics of the input data, many DEA models involving input data with various characteristics could be studied. Furthermore, based upon the proposed models, two nondiscretionary models are introduced in which some inputs or outputs, in a fuzzy sense, are inexact discretionary variables. For this purpose, a two-stage algorithm will be presented to treat the DEA model in the presence of an inexact discretionary variable. With this relationship, a new perspective of viewing and exploring other DEA models is now made possible. Keywords Data envelopment analysis Efficiency Non-discretionary variables
Fuzzy
Possibility distribution
1 Introduction Since its inception 48 years ago, the theory of fuzzy sets has advanced in a variety of ways and in many disciplines. Applications of fuzzy technology can be found in artificial intelligence, computer sciences, control engineering, decision theory, expert systems, logic, management sciences, operations research, robotics and others [1].
M. Z. A. Langroudi (&) School of Quantitative Sciences, Universiti Utara Malaysia, 06010 Sintok, Kedah, Malaysia 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_8, Springer-Verlag Berlin Heidelberg 2014
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M. Z. A. Langroudi
Sugeno [2] defined a fuzzy measure. Banon [3] shows that very many measures with finite universe, such as probability measures, belief functions, plausibility measures and so on, are fuzzy measures in the sense of Sugeno. In recent years, some specific interpretations of fuzzy set theory have been suggested. One of them is possibility theory. In the framework of fuzzy set theory, Zadeh [4] introduced the notion of a possibility distribution and the concept of a possibility measure, which is a special type of fuzzy measure proposed by Sugeno [2]. Possibility theory focuses primarily on imprecision. Possibility theory used to correspond, roughly speaking, to the min–max version of fuzzy set theory, that is, to fuzzy set theory in which the intersection is modeled by the min operator and the union by the max operator. This interpretation of possibility theory, however, is no longer correct. Rather, it has been developed into a well-founded and comprehensive theory. DEA researchers have begun using fuzzy concept for measuring efficiency and productivity of DMUs s
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