A Direct Method of Interval Banzhaf Values of Interval Cooperative Games

Abstract

The goal of this paper is to develop a direct method for computing interval Banzhaf values for a class of interval cooperative games. In this method, it is proven that the Banzhaf values of the associated cooperative games of interval cooperative games are monotonic and non-decreasing functions of coalitions’ payoffs under weaker coalition monotonicity-like conditions. So the interval Banzhaf values can be explicitly obtained through using only the lower and upper bounds of the coalitions’ interval payoffs, respectively. The proposed method does not employ interval subtractions and hereby can effectively avoid the irrational issues such as irreversibility and uncertainty enlargement. We prove some important and desirable properties of the interval Banzhaf values and illustrate the applicability and validity of the proposed method with a numerical example.