Bi-Level Multi-Objective Absolute-Value Fractional programming Problems: A Fuzzy Goal Programming approach

Abstract

In this paper we propose a fuzzy goal programming method for obtaining a satisfactory solution to a bi-level multi-objective absolute-value fractional programming (BLMO-A-FP) problems. In the proposed approach, the membership functions for the de ned fuzzy goals of all objective functions at the two levels as well as the membership functions for vector of fuzzy goals of the decision variables controlled by upper level decision maker (ULDM) are developed in the model formulation of the problem. Then fuzzy goal programming technique is used for achieving highest degree of each of the membership goals by minimizing negative and positive deviational variables. The method of variable change on the under- and over-deviational variables of the membership goals associated with the fuzzy goals of the model is introduced to solve the problem eciently by using linear goal programming methodology. Theoretical results is illustrated with the help of a numerical.