Interactive Fuzzy Dual Decomposition Approach to Large-Scale Multi-Level Multi-Objective Programming Problems

In this paper, we focus on multi-level multiobjective programming problems with block angular structures where multiple decision makers in a hierarchical organization have their own multiple objective functions, and propose an interactive algorithm based on the dual decomposition 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. In the proposed algorithm, assuming that each of the decision makers has fuzzy goals for his/her objective functions, corresponding membership functions are elicited from the decision makers in their subjective manner. In order to deal with the fuzzy multi-level multiobjective programming problem, a new kind of Pareto optimality concept in membership spaces is defined and the concept of decision powers of multiple decision makers in a hierarchical decision structure are introduced. After each of the decision makers specifies his/her decision power and his/her reference membership values, the minimax problem is solved efficiently on the basis of the dual decomposition method, and the corresponding candidate of the satisfactory solution is obtained. If at least one of the decision makers is not satisfied with the current values of the membership functions, he/she updates his/her reference membership values and/or his/her decision