Computing crisp simulations for fuzzy labeled transition systems

Abstract

The problem of checking whether a state in a finite fuzzy labeled transition system (FLTS) crisply simulates another is one of the fundamental problems of the theory of FLTSs. This problem is of the same nature as computing the largest crisp simulation between two finite FLTSs. A naive approach to the latter problem is to crisp the given FLTSs and then apply one of the currently known best methods to the obtained crisp labeled transition systems. The complexity of the resulting algorithms is of order O (l (m + n) n), where l is the number of fuzzy values occurring in the specification of the input FLTSs, m is the number of transitions and n is the number of states of the input FLTSs. In the worst case, l can be m + n and O (l (m + n) n) is the same as O ((m + n) ²n). In this article, we design an efficient algorithm with the complexity O ((m + n) n) for computing the largest crisp simulation between two finite FLTSs. This gives a significant improvement. We also adapt our algorithm to computing the largest crisp simulation between two finite fuzzy automata.