Generalized fuzzy data envelopment analysis methods

• We firstly revealed the necessity of sample decision making unit and improved the α-cut approach, the types of fuzzy number and the selected special point when evaluating Fuzzy DEA model.
• We proposed generalized fuzzy DEA methods.
• We proposed new evaluating methods based on vector for fuzzy DEA model.

The conventional data envelopment analysis (DEA) measures the relative efficiencies of a set of decision making units (DMUs) with exact values of inputs and outputs. In real-world problems, however, inputs and outputs typically have some levels of fuzziness. To analyze a DMU with fuzzy input/output data, previous studies provided the fuzzy DEA (FDEA) model and proposed an associated evaluating approach. Nonetheless, numerous deficiencies must be improved, including the α-cut approaches, types of fuzzy numbers, and ranking techniques. Moreover, a fuzzy sample DMU (SDMU) still cannot be evaluated for the FDEA model. Therefore, the present paper proposes a generalized FDEA model which can evaluate SDMU and the traditional FDEA model. Five evaluation methods are provided and these methods not only improve the types of FDEA model, the types of fuzzy number, the α-cut approach but also firstly propose a new evaluation method based on vector. At last related algorithm and ranking methods are provided to test our new methods. A numerical experiment is used to demonstrate and compare the results with those obtained using alternative approaches.

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