An efficient algorithm of fuzzy reinstatement labelling

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.