Nonlinear Programming Models and Method for Interval-Valued Multiobjective Cooperative Games

The purpose of this paper is to develop a nonlinear programming method for solving a type of cooperative games in which there are multiple objectives and coalitions' values on objectives are expressed with intervals, which are called interval-valued multiobjective cooperative games for short. In this method, we define the concepts of interval-valued cores of interval-valued multiobjective cooperative games and satisfactory degrees of comparing intervals with inclusion and/or overlap relations. The interval-valued cores can be computed by developing a new two-phase method based on the auxiliary nonlinear programming models. The proposed method can seek cooperative chances under the situations of inclusion and/or overlap relations of intervals in which the traditional interval ranking method may not always assure that the interval-valued cores exist. The feasibility and applicability of the developed method are illustrated with a real example.