摘要
通过对经典合作对策上Banzhaf函数的描述,给出了模糊合作对策上Banzhaf函数的定义.讨论了两类模糊合作对策上Banzhaf函数的存在性和唯一性,并给出了它们的具体表达形式.探讨了所给Banzhaf函数的模糊零元,个人理性,单调性,非负性.研究了模糊联盟与其模糊支撑关于Banzhaf函数之间的关系,最后通过算例来说明所给模糊合作对策上的Banzhaf指标.
In this paper, the definition of the Banzhaf function for fuzzy cooperative games is proposed by ex- tending the description of the Banzhaf function for classical cooperative games. The existence and uniqueness of the Banzhaf functions for two kinds of fuzzy cooperative games are discussed. The specific expressions of the Banzhaf functions are given. Meantime, the given Banzhaf functions＇ fuzzy null player, individual ra- tionality, monotonicity and non negative are studied. The relationship between fuzzy coalition and its fuzzy supporter for the Banzhaf function is researched. Finally, a numerical examples is offered to illustrate the Banzhaf indices of the discussed fuzzy cooperative games.
出处
《系统工程学报》
CSCD
北大核心
2012年第1期1-8,共8页
Journal of Systems Engineering
基金
国家自然科学基金资助项目(70771010
70801064
71071018)
