A fuzzy inequality evaluation approach for measuring the relative efficiency

Evaluating the performances of a set of entities called decision making units (DMUs) which convert multiple inputs into multiple outputs has long been considered as a difficult task because one is dealing with complex economics. This work proposes an inequality approach to evaluate the performances of DMUs. Inequalities consist of expressions of the production possibility set and the line segments joining the evaluated DMU to the positive output-axes. However, in real-world application involving performance measurement, inputs and outputs are often imprecise and fluctuated. In this case, a fuzzy inequality approach is proposed to evaluate the performances. What is more, fuzzy relative efficiency is dependent upon the number of solutions. Furthermore, the minimal element is used to distinguish the fuzzy relative efficient DMUs. Finally, two numerical examples are used to illustrate the fuzzy approach and compare the results with those obtained with alternative fuzzy approaches.