a. ebrahimnejad

The present study evaluates the performance of decision-making units from two optimistic and pessimistic perspectives in the fuzzy environment based on data envelopment analysis with the common set of weights approach. In the proposed method, first, two fuzzy virtual decision-making units namely the fuzzy ideal decision-making unit and the fuzzy anti-ideal decision-making unit are introduced and their efficiencies are estimated. Then, based on the common set of weights technique, the fuzzy worst and the fuzzy best efficiency of units are computed. Finally, based on the fuzzy relative closeness index, the triangular fuzzy efficiency of all units is calculated. The important advantages of the proposed method are the logical comparison between units based on a common weight, preventing the flexibility of their weight, and more differentiation power among them. To analyze and illustrate the proposed method, the performance of 30 non-life insurance companies involving triangular fuzzy numbers in Iran is evaluated.

Generally exploring the exact solution of linear programming problems in which all variables and parameters are  Z-numbers, is either not possible or difficult. Therefore, a few numerical methods to find the numerical solutions do act an  important role in these problems. In this paper, we concentrate on introducing a new numerical method to solve such  problems based on the ranking function. After proving the necessary theories, for more illustrations and the correctness  of the topic, some theoretical and practical examples are also provided. Finally, the results obtained from the proposed  method have been compared with some existing methods.