Interactive Fuzzy Decision Making for Hierarchical Multiobjective Linear Programming Problems Using Reference Membership Intervals

In this paper, we focus on hierarchical multiobjective linear programming problems where multiple decision makers in a hierarchical organization have their own multiple objective linear functions together with common linear constraints, and propose an interactive decision making method to obtain a satisfactory solution which reflects not only the hierarchical relationships between multiple decision makers but also their own preferences for their membership functions. In the proposed method, instead of Pareto optimal concept, a generalized Λ-extreme point concept is introduced. In order to obtain a satisfactory solution from among a generalized Λ-extreme point set, an interactive algorithm based on linear programming is proposed, and an interactive processes are demonstrated by means of an illustrative numerical example.