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).

<abstract><p>The fuzzy reinstatement labelling ($ FRL $) puts forward a reasonable method to rewind the acceptable degrees of arguments in fuzzy argumentation frameworks. The fuzzy labelling algorithm ($ FLAlg $) computes the $ FRL $ by infinitely approximating the limits of an iteration sequence. However, the $ FLAlg $ is unable to provide an exact $ FRL $, and its computation complexity depends on not only the number of arguments but also the accuracy. This brings a quick increase in complexity when higher accuracy is acquired. In this paper, through the in-depth study of the $ FLAlg $, we introduce an effective algorithm for decomposing $ FRL $ by strongly connected components. For simple fuzzy frameworks in the form of trees, odd cycles, and even cycles, the new algorithm provides an exact value of the limit. Therefore, by avoiding the infinite approximation process, it is independent of accuracy. And for complex frames, the new algorithm outputs an approximate value to the $ FLAlg $. It is more efficient because the number of arguments in the approximation process is usually reduced.</p></abstract>