A fuzzy evaluation approach with the quasi-ordered set: evaluating the efficiency of decision making units

摘要

This work proposes an inequality approach with the quasi-ordered set to evaluate the performances of decision making units (DMUs). In real world applications, input and output data are often imprecise and fluctuated. In this case, a fuzzy inequality approach is proposed to evaluate DMUs with fuzzy data. Fuzzy inequalities consist of fuzzy expressions of the production possibility set and the line segment joining the origin to the evaluated DMU. Moreover, under constant returns to scale, the production possibility set is spanned by all the DMUs without the evaluated DMU. Fuzzy efficiency is dependent upon whether the solution set of fuzzy inequalities is empty or not. The quasi-ordered set is used to distinguish the fuzzy efficiency. Finally, numerical examples are used to illustrate the approach.