A parametric study of multiobjective NLP problems with fuzzy parameters in the objective functions

This paper deals with the stability of multiobjective nonlinear programming problems with ordinary and fuzzy parameters in the objective functions. These fuzzy parameters are characterized by fuzzy numbers. The existing results concerning the qualitative analysis of the notions (solvability set, stability sets of the first king and of the second kind) in parametric nonlinear programming problems are reformulated to study the stability of multiobjective nonlinear programming problems under the concept of α-pareto optimality. An algorithm for obtaining any subset of the parametric space which has the same corresponding α-pareto optimal solution is also present. An illustrative example is given to clarify the obtained results.