A New Approach to Solve Bi Level Multi Objective Fuzzy Goal Programming Problem

This paper presents a new fuzzy goal programming (FGP) approach for solving bi-level fuzzy multi-objective linear fractional goal programming (BLFMOLFGP) problems. In the proposed approach, first aspiration levels for the objective functions at two levels are determined. The membership functions for the defined fuzzy goals of the decision makers (DMs) objective functions at both levels as well as the membership functions for vector of fuzzy goals of the decision variables controlled by first-level decision maker are developed first in the model formulation of the problem. Then a fuzzy goal programming model is formulated to solve the BLFMOLFGP. Here in the achievement function the weighted sum of the under deviation variables involved in the goal constraint is minimized to achieve the highest degree (unity) of each of the defined membership goals. The Zimmerman's max min operator has been taken as a goal constraint having aspiration level 1 (unity). Illustrative numerical example is given to demonstrate the proposed algorithm.