Abstract
There are numerous models for solving the efficiency evaluation in data envelopment analysis (DEA) with fuzzy input and output data. However, because of the limitation of those strategies, they cannot be implemented for solving fully fuzzy DEA (FFDEA). Furthermore, in real-world problems with imprecise data, fuzziness is not sufficient to consider, and the reliability of the information is also very vital. To overcome these flaws, this paper presented a new method for solving the fully fuzzy DEA model where all parameters are Z-numbers. The new approach is primarily based on crisp linear programming and has a simple structure. Moreover, it is proved that the only existing method to solve FFDEA with Z-numbers is not valid. An example is also presented to illustrate the efficiency of our proposed method and provide an explanation for the content of the paper.
Highlights
Data envelopment analysis (DEA) is a linear programming method for measuring the relative efficiencies of homogeneous decision-making units (DMUs) without knowing production functions [1,2]
To remove the mentioned shortcoming, we proposed an improved model for fully fuzzy DEA with Z-numbers
Step 3: Using Definition 11, the fully fuzzy DEA model of Step 2 can be transformed into the following model: s
Summary
Data envelopment analysis (DEA) is a linear programming method for measuring the relative efficiencies of homogeneous decision-making units (DMUs) without knowing production functions (i.e., just by utilizing input and output information) [1,2]. To obtain the efficiencies of DMUs as fuzzy numbers, they converted the proposed fuzzy DEA models into three linear programming (LP) models. Puri and Yadav [31] applied the α-cut approach and provided a cross-efficiency technique for a fuzzy DEA model with undesirable fuzzy outputs. Because of the limitations of the above methods, they cannot be implemented for solving fully fuzzy DEA (FFDEA), where all the inputs and outputs, as well as the decision variables, are fuzzy numbers. Hatami-Marbini et al [44] utilized a fully fuzzy linear programming problem presented by an FFDEA model.
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