Abstract
In this paper a generalized form called fuzzy games on augmenting systems with fuzzy characteristic functions is introduced, where the player payoffs are fuzzy numbers, and their participation levels are real numbers in [0, 1]. Based on the defined restriction difference on fuzzy numbers, the explicit expression of the Shapley value is provided, and an axiomatic system is researched. Meantime, some properties are discussed. In order to better understand fuzzy games on augmenting systems with fuzzy characteristic functions, we further introduce and investigate fuzzy games on augmenting systems with multilinear extension and fuzzy characteristic functions.