Comparative Semantics of Fuzzy Argumentation under the Łukasiewicz t-Norm

Dung’s theory of argumentation frameworks (AF) has been applied in many fields of artificial intelligence. The arguments and attack relation are generally partly believed due to the uncertainty in the process of mining them. Fuzzy AFs catch uncertainty in AFs by associating fuzzy degrees with the arguments or the attacks. Among the various semantics of fuzzy AFs, the comparative semantics develops and defines Dung’s extensions in the form of fuzzy sets. However, the comparative semantic system only puts forward some basic concepts, and has not been deeply studied in terms of algorithms and properties. This paper studies the comparative semantics of fuzzy AFs based on the Łukasiewicz t-norm in a more in-depth and comprehensive manner. This work is not only a supplement and improvement to comparative semantic in theory, but also beneficial to the calculation and fast identification of its various extensions (based on the Łukasiewicz t-norm).