Document Type: Research Paper
Department of Mathematics, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran.
Farhad Moradi, Islamic Azad University, Department of Mathematics, Sanandaj
Department of mathematics, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran.
One way to increase the discrimination ability in data envelopment analysis (DEA) is to use the pessimistic view in the performance evaluation. A traditional and usual approach to move from the optimistic to the pessimistic view is to expand the production possibility set. By expanding the production possibility set, the distance between each unit can be increased from the efficiency frontier, and then a smaller number of units are located on the boundary. On the other hand, in practical applications, we are confronted with imprecise inputs and outputs. Expressions of inputs and outputs as imprecise data can give us an opportunity to use it in order to increase the efficiency discrimination. Our view of the ambiguity in the data focus on fuzzy relation. We introduce a fuzzy monotonicity assumption and construct a fuzzy production possibility set (FPPS) with varying degrees of feasibility. Using the tolerance approach a nonsymmetric fuzzy linear programming model and subsequently, a parametric DEA model is constructed. By applying this model, it will be seen that, for a specific and small tolerance of constraints, The discrimination efficiency of the units increases. Finally, we propose a procedure for ranking of DMUs and employ it to rank Iranian national universities.