• A HYBRID APPROACH OF TOPSIS AND FUZZY GOAL PROGRAMMING FOR BI-LEVEL MODM PROBLEMS WITH FUZZY PARAMETERS

Abstract

In this paper, TOPSIS (technique for order preference by similarity to ideal solution) approach for solving bi-level multi-objective programming problems (BL-MOPP) with fuzzy parameters is proposed. These fuzzy parameters are assumed to be characterized as fuzzy numbers, reflecting the experts' imprecise or fuzzy understanding of the nature of parameters in the problem formulation process. Using the level sets of fuzzy parameters, the corresponding non fuzzy bi-level programming problem is introduced. The proposed approach for obtaining the satisfactory solution of the     BL-MOPP with fuzzy parameters includes the membership functions of the distance function from the positive ideal solution (PIS), the membership functions of the distance function from the negative ideal solution (NIS) and the membership functions of the upper level decision variables vector with possible tolerances. Also, a modified TOPSIS approach is presented in this paper. Illustrative numerical example is given to demonstrate the proposed TOPSIS and modified TOPSIS approach. Also, a comparison between the proposed TOPSIS and the modified TOPSIS approaches with existing Algorithms is given to clarify the powerful of the proposed approaches.