A fuzzy approach for multilevel multiobjective programming problems and the concept of generalized Λ-extreme points

In this paper, we focus on multilevel multiobjective programming problems where multiple decision makers in a hierarchical organization have their own multiple objective functions, and propose an interactive decision making method to obtain the satisfactory solution which reflects not only the hierarchical relationships between multiple decision makers but also their own preferences for their objective functions from among the generalized Lambda-extreme point set. The generalized Lambda-extreme point is defined by using Lambda-extreme points of each of the decision makers, which is an extended concept of Pareto optimal solutions in multiobjective programming problems. In order to obtain the satisfactory solution from among the generalized Lambda-extreme point set, an interactive fuzzy decision making method based on the hyperplane method is proposed.