An interactive fuzzy decision making method for decentralized multiobjective programming problems

The authors focus on decentralized multiobjective programming problems where multiple decision makers called the leader and the followers make decisions in their hierarchical positions and each of them have multiobjective functions. Under the cooperative relationships between the leader and the followers, the original problem is formally decomposed into the leader's multiobjective programming problem and the followers' ones. In order to deal with such multiobjective programming problems, extended Pareto optimal concepts are introduced, called the leader's Pareto optimal solutions and the corresponding followers' ones which are defined in membership function space. An interactive fuzzy decision making method is proposed to obtain a satisfactory solution which reflects not only their preferences but also their relationships in some sense. The numerical example illustrates the proposed method under the hypothetical interactions between the leader and the followers.