• A FUZZY GOAL PROGRAMMING ALGORITHM FOR SOLVING BI-LEVEL MULTI-OBJECTIVE LINEAR FRACTIONAL PROGRAMMING PROBLEMS

Abstract

This paper studies a fuzzy goal programming (FGP) approach for solving bi-level multi-objective linear fractional programming problem. This paper makes an extension work of Pramanik and Dey [International Journal of Computer Applications 25 (11) (2011), 34-40] which deals with bi-level linear fractional programming problem based on FGP approach. In proposed approach, firstly we construct the linear fractional membership functions for objective functions of both levels decision makers (DMs). Then we transform the linear fractional membership functions into equivalent linear membership functions at the individual best solution point by using first order Taylor series. Thereafter, multi-objective decision making models are formulated for both level DMs and FGP technique is used to identify the satisfactory solution for each level DM. We again transform the linear fractional membership functions for objective functions of both level DMs into equivalent linear membership functions at the satisfactory solution point. Since the objectives of the DMs are conflicting in nature, the preference bounds on the decision variables under the control of both level DMs are considered. Finally, FGP approach is utilized to solve the problem. An illustrative numerical example is solved in order to clarify the proposed approach.