基于风险偏好与满意度的区间值合作对策

Interval-valued Cooperative Games Based on Risk Preferences and Satisfaction

研究区间Shapley值一般是以超可加区间值合作对策或凸区间值合作对策为前提,但这限制了区间Shapley值的适用范围。本文以区间数的接受指标及局中人对风险的偏好水平为基础,提出了局中人满意度的概念,并利用满意度对区间值合作对策进行了探讨。通过计算区间值合作对策的局中人与联盟对其区间Shapley值的满意度,来判断区间Shapley值是否被局中人或联盟接受,形成的联盟是否稳定,拓展了区间值合作对策Shapley值的适用范围。同时,得到了当区间值合作对策满足一定条件时满意度的一些性质。

The study of interval Shapley value is usually based on superadditive interval-valued cooperation games or convex interval-valued cooperative games, limiting the scope of the application of the interval Shapley value. Based on acceptability index the fuzzy preference ordering for interval and the intensities of risk preferences for players, we discuss the concept of the players with degrees of satisfaction. In this paper, we find that the degree of satisfaction plays a key role of analyzing the interval-valued cooperative games. By calculating the degrees of satisfaction with the allocation for interval-valued cooperative games, we find it obvious to determine whether the allocation, including the interval Shapley value, is reasonable. And we can judge whether the coalitions of players who coordinate their actions is stable by using the degrees of satisfaction. The basis of this method is an extension of the application of the interval Shapley value. Furthermore, we get some useful properties when the interval-valued cooperative game is at particular situations.