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In this paper, the concept of fuzzy share functions of cooperative fuzzy games with fuzzy characteristic functions is proposed. Players in the proposed cooperative fuzzy game do not need to know precise information about the payoff value. We generalize the axiom of additivity by introducing a positive fuzzy value function ∼μ on the class of cooperative fuzzy games in fuzzy characteristic function form. The so-called axiom of ∼μ-additivity generalizes the classical axiom of additivity by putting the weight ∼μ(∼υ) on the value of the game ∼υ. We show that any additive function ∼μ- determines a unique fuzzy share function satisfying the axioms of effcient shares, null player property, symmetry and ∼μ-additivity on the subclass of games on which ∼μ is positive and which contains all positively scaled unanimity games. Finally, we introduce the fuzzy Shapley share functions and fuzzy Banzhaf share functions for the cooperative fuzzy games with fuzzy characteristic functions. [ABSTRACT FROM AUTHOR]