Reference direction interactive method for solving multiobjective fuzzy programming problems

Abstract

A reference direction interactive method (called RDIM) is proposed in this paper for solving multiobjective fuzzy programming problems. The method combines the reference direction approach for multiobjective linear programming of Korhonen and Laakso (1986), "A visual interactive method for solving multiple criteria problems", European Journal of Operational Research 24, 277-287, with the interactive satisficing method of Sakawa and Yano (1989), "An interactive fuzzy satisficing method for multiobjective nonlinear programming problem with fuzzy parameters", Fuzzy Sets and Systems 30, 221-238. The proposed method is applicable to nonsymmetric linear as well as nonlinear mathematical models wherein the objectives are modeled as fuzzy goals and the satisfaction of fuzzy constraints is considered at different α-level sets of the fuzzy parameters involved. At each interactive phase the decision maker (DM) specifies a reference direction in the membership function space. A discrete parametric programming problem is then solved in this direction to provide the DM with a number of alternatives from amongst which he/she can select the most preferred solution on the basis of his/her preference structure. Illustrative examples taken from literature have been solved using the proposed method. © 1998 Elsevier Science B.V.