Abstract
In order to deal with multiobjective programming
problems, the concept of domination structures based on convex cones were introduced, which can be regarded as a generalization of Pareto optimal concept. Since domination structures are deeply related to the decision maker's preference in objective space, it seems to be very difficult for the decision maker to supply precise information that makes it possible to find a sharp borderline of a domination structure. From such a point of view, Takeda and Nishida proposed the concept of fuzzy domination structures based on fuzzy convex cones. In this paper, we first consider multiobjective programming problems with fuzzy domination
structures and define the solution concept using the alpha-level set for the fuzzy convex cone. After that, we focus on multilevel multiobjective programming problems with fuzzy domination structures where multiple decision makers in a hierarchical organization have their own multiple objective functions and their own fuzzy domination structures. After introducing the solution concept using the alpha-level sets for the fuzzy convex cones of multiple decision makers, we 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. An interactive process is demonstrated by means of an illustrative numerical example.
