Interactive Cutting-Plane Method for Multiobjective Programming with Fuzzy Parameters

This paper presents an interactive solution method for treating multi objective mathematical programming problems with fuzzy parameters in the objective functions and in the constraints. Theses fuzzy parameters are characterized by fuzzy numbers. For such problems, the concept of a-Pareto optimality introduced by extending the ordinary Pareto optimality based on the a-level sets of fuzzy numbers. The proposed solution method is based on cutting planes, which are based on local trade off ratios between the objective functions as prescribed by the decision maker at each iterate generated by the method. An illustrative numerical example is given to clarity this method.