Solving generalized DEA/AR model with fuzzy data and its application to evaluate the performance of manufacturing enterprises

Abstract

The use of conventional data envelopment analysis (DEA) models in real-world problems are limited because of some restrictions that must be considered in the model such as imprecise or vague data in inputs and outputs, and additional information or assumptions. One way to handle this problem is by using fuzzy DEA with assurance regions (FDEA/AR) models. There is a common approach in almost all the suggested methods for solving FDEA/AR models. However, in this paper, we show that in some DEA/AR models applying this approach can be led to inappropriate results. Four theorems are given to provide some sufficient conditions for a DMU to be the DEA/AR efficient. These theorems can be used to check the accuracy of the presented methods for solving FDEA/AR models, too. Moreover, a new method for solving a generalized FDEA/AR model that includes established DEA models such as CCR model (Charnes et al. 1978), BCC model (Banker et al. 1984), FG model (Fare and Grosskopf 1985), and ST model (Seiford and Thrall 1990) is proposed. These models are constant, variable, non-decreasing, and non-increasing returns to scale models, respectively. The proposed method is applied to evaluate the performance of manufacturing enterprises.