Some Approaches for Solving Fuzzy Data Envelopment Analysis Models

Abstract

In this thesis, flaws in the existing fuzzy CCR DEA model as well as in some of the existing methods for solving fuzzy CCR DEA model are pointed out. Also, to resolve the flaws new fuzzy CCR DEA model and new approaches for solving it are proposed. 1.2 Organization of the thesis The chapter wise summary of the thesis is as follows: Chapter 2 Hatami-Marbini et al. [40] proposed a method to solve fuzzy CCR DEA model for evaluating the best relative fuzzy efficiency of decision making units (DMUs). In this chapter, it is pointed that the product of fuzzy numbers, used by Hatami-Marbini et al. [40], in their proposed method, is incorrect and hence, the method, proposed by Hatami-Marbini et al. [40], is not valid. To resolve this flaw, the method proposed by Hatami Marbini et al. [40], is modified by using correct product of fuzzy numbers. Chapter 3 Wang et al. [106] replaced the crisp output data and crisp input data of the crisp CCR DEA model with fuzzy data and proposed two methods for solving this fuzzy CCR DEA model. In this chapter, it is pointed out that the fuzzy CCR DEA model, proposed by Wang et al.[106], is not valid and hence the methods, proposed by Wang et al. [106] for evaluating the fuzzy efficiency of DMUs, are also not valid. Also, a new fuzzy CCR DEA model as well as a method to solve this fuzzy CCR DEA model is proposed. Chapter 4 Wang and Chin [105] proposed an optimistic as well as pessimistic fuzzy CCR DEA model and an approach for solving it to evaluate the best relative fuzzy efficiency as well as worst relative fuzzy efficiency and hence, relative geometric crisp efficiency of DMUs. In this chapter, it is shown that the fuzzy CCR models, proposed by Wang and Chin [105], are ii not valid and hence cannot be used to evaluate the best relative fuzzy efficiency as well as worst relative fuzzy efficiency and hence, relative geometric crisp efficiency of DMUs. To resolve the flaws of the fuzzy CCR DEA model, proposed by Wang and Chin [105], new fuzzy CCR DEA models are proposed. Also, a new approach is proposed to solve the proposed fuzzy CCR DEA models for evaluating the relative geometric fuzzy efficiency of DMUs. Chapter 5 Puri and Yadav [83] proposed an optimistic as well as pessimistic intuitionistic fuzzy CCR DEA model and an approach to evaluate the best relative intuitionistic fuzzy efficiency as well as worst relative intuitionistic fuzzy efficiency and hence, relative geometric crisp efficiency of decision making units (DMUs). In this chapter, it is shown that the intuitionistic fuzzy CCR models, proposed by Puri and Yadav [83] are not valid and hence cannot be used to evaluate the best relative intuitionistic fuzzy efficiency as well as worst relative intuitionistic fuzzy efficiency and hence, relative geometric crisp efficiency of decision making units (DMUs). To resolve the flaws of the intuitionistic fuzzy CCR DEA model, proposed by Puri and Yadav [83], new intuitionistic fuzzy CCR DEA models are proposed. Also, a new approach is proposed to solve the proposed intuitionistic fuzzy CCR DEA models for evaluating the best relative intuitionistic fuzzy efficiency as well as worst relative intuitionistic fuzzy efficiency and hence, relative geometric crisp efficiency of DMUs. Chapter 6 Finally, in this chapter, some future directions has been suggested.