Abstract: The Gödel semantics in fuzzy argumentation frameworks covers several basic extension semantics, but does not further study the properties of each extension semantics. This brings some difficulties to the calculation and quick recognition of the semantic system. Through the in-depth study of the numerical properties of each extension semantics, this paper provides some solutions to the above problems. With the help of the basic properties of the Gödel t-norm, the numerical properties of the conflict-free set, the admissible extension, the complete extension, the preferred extension(the stable extension), and the grounded extension in the Gödel semantics are deduced one by one, and the algorithms of the grounded extension are given in fuzzy AFs without cycles and fuzzy AFs consisting of odd cycles or even cycles. These conclusions are the theoretical generalization of the semantic system. At the same time, the method of bypassing the definition and directly judging the extension semantics based on numerical values, as well as the algorithm of calculating the grounded extension from empty sets, are the development of the semantics in terms of algorithm and quick identification.

Key words: argumentation framework, fuzzy set, fuzzy argumentation framework, Gö, del semantics, Gö, del t-norm