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.

The Boolean models of argumentation semantics have been established in various ways. These models commonly translate the conditions of extension-based semantics into some constraints of the models. The goal of this work is to explore a simple method to build Boolean models for argumentation. In this paper, the attack relation is treated as an operator, and its value is calculated by the values of its target and source arguments. By examining the values of the attacks, a Boolean model of conflict-free sets is introduced. This novel method simplifies the existing ways by eliminating the various constraints. The conflict-free sets can be calculated by simply checking the values of the attacks.