Fuzzy programming in multi-objective linear programming-A parametric approach

Zimmermann’s fuzzy approach to the compromise solution concept in the multiobjective linear programming problem is considered. It is shown that given a class of membership functions of fuzzy goals assigned to objective functions in the problem, wider than primarily proposed by Zimmermann, the use of classical linear programming methods to solve and analyse the problem is also possible. As a result of application of the method based on the parametric programming technique, one can obtain a fuzzy solution of the problem. This solution is a certain fuzzy subset of the set of weakly efficient solutions of the problem. The solution which belongs to this set to the highest degree is a maximizing one (in Bellman and Zadeh’s terminology). It may also be obtained by use of the usual non-parametric simplex method.