摘要
利用模糊集表现定理对具有模糊联盟值的n人合作博弈的模糊Shapley值重新进行研究.定义了具有模糊联盟值的n人合作博弈的α-博弈,并给出了其Shapley值定义及表达式.通过研究所有α-博弈的Shapley值之间的关系,验证了所有α-博弈的Shapley值构成一个集合套.利用模糊集表现定理和α-博弈Shapley值,定义了具有模糊联盟值的n人合作博弈的模糊Shapley值.实例研究表明,具有模糊联盟值的n人合作博弈的模糊Shapley值的有效性.
The fuzzy Shapley value of n-person cooperative games with fuzzy worth is discussed employing the representation theorem of fuzzy set. The a-games and its Shapley value of n-person cooperative game with fuzzy worth are defined and the expression of the Shapley value is formulated. The relationship among the Shapley values of all a-games is analyzed, and it is proved that the Shapley values structure a nest of sets. The fuzzy Shapley value of n-person cooperative game with fuzzy worth is redefined by means of the Shapley value of α-games and the representation theorem of fuzzy set. The fuzzy Shapley value of n-person cooperative game with fuzzy worth is proved effective by examples.
出处
《北京理工大学学报》
EI
CAS
CSCD
北大核心
2007年第8期740-744,共5页
Transactions of Beijing Institute of Technology
基金
国家自然科学基金资助项目(70471063)
