Fuzzy Shapley Value of n-Person Cooperative Games with Fuzzy Worth

The fuzzy Shapley value of n-person cooperative games with fuzzy worth is discussed employing the representation theorem of fuzzy set.The α-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 α-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.