Distribution-based limited fuzzy bisimulations for nondeterministic fuzzy transition systems

Bisimulation techniques have been adopted and developed in fuzzy transition systems (FTSs) to compare their behavior. Recently, distribution-based bisimulation has been introduced to nondeterministic fuzzy transition systems (NFTSs) to measure the similarity between two distributions which can be regarded as generalized states. However, the new bisimulation does not consider the similarity of states. In terms of limited approximate bisimilarity, in this article, a notion of distribution-based k-limited bisimulation is proposed for NFTSs, which can measure the similarity between two distributions in the neighboring subgraphs (subsystems) and take the similarity of states into account, where k is a natural number. This article discusses some properties of limited bisimulation and the nonexpansiveness of typical parallel composition operators with respect to the limited bisimulation which makes compositional verification possible. Then a fixed point characterization of the limited bisimulation is investigated and an algorithm is given to compute the degree of k-limited similarity between two distributions. Moreover, a fuzzy modal logic interpreted on distributions is adopted to characterize the limited bisimulation.