Abstract
The paper presents a microcomputer implementation of a visual interactive method, called ‘FLIP’”, for solving multi-objective linear programming (MOLP) problems with fuzzy coefficients in the objective functions and on the both sides of the constraints. It is a modified version of the ‘FLIP’ method (cf.Czyzak,1990 and Slowinski,1990) which relies on a special comparison principle of fuzzy numbers in order to transform the fuzzy MOLP problem into an associate deterministic multi-objective linear fractional programming (MOLFP) problem. The modification consists in permitting a different interpretation of fuzzy objectives and constraints, which leads to an associate deterministic MOLP (instead of MOLFP) problem. The associate MOLP problem is then solved using an interactive sampling method. The efficient solutions of the associate MOLP problem are presented to the decision maker (DM) in terms of the original fuzzy objectives and constraints. The quality of these solutions can be evaluated by the DM from three following points of view: (a) scores of fuzzy objectives in relation to the goals, (b) possible dispersion of values of the fuzzy objectives due to uncertainty and (c) safety of solutions or risk of violation of the constraints. In order to support the evaluation, an appropriate graphical interface has been implemented.
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