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 intervalvalued 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.