Interval-valued least square prenucleolus of interval-valued cooperative games and a simplified method

The aim of this paper is to propose the concept of the interval-valued least square prenucleolus of interval-valued cooperative games and develop a direct and an effective simplified method for solving a special subclass of interval-valued cooperative games. In this method, through adding some conditions, the least square prenucleolus of cooperative games is proved to be a monotonic and non-decreasing function of coalitions’ values. Hence, the interval-valued least square prenucleolus of coalition size monotonicity-like interval-valued cooperative games can directly obtained via determining its lower and upper bounds by using the lower and upper bounds of the interval-valued coalitions’ payoffs, respectively. Thus, the proposed method may overcome the issues resulted from the Moore’s interval subtraction and the partial subtraction operator. Examples are used to illustrate the proposed method and comparison analysis is conducted to show its applicability and superiority. Moreover, some important properties of the interval-valued least square prenucleolus of coalition size monotonicity-like interval-valued cooperative games are discussed.