Decomposition of the fuzzy parametric space in multiobjective nonlinear programming problems

Abstract

This paper deals with a method for decomposing the fuzzy parametric space in multiobjective nonlinear programming problems using the generalized Tchebycheff norm. This approach is simpler than the corresponding one using the nonnegative weighted sum of objectives. Also, several results are introduced which relate two fuzzy programs with each other, one with fuzzy parameters in the constraints and the other with fuzzy parameters in both objective functions and constraints. These fuzzy parameters are characterized by fuzzy numbers. The existing results concerning the decomposition of parametric space in multiobjective convex programs using the generalized Tchebycheff norm are reformulated to study under the concept of α-pareto optimality. Such results make the study of the first type of problems rather simple. Three illustrated examples are presented in the paper which clarify the developed theory.