Abstract
As the abstraction and equivalent technologies, simulation and bisimulation have been applied to the simplifications of some classical and uncertain models structures. The studies of the more generalized simulation and bisimulation technologies have not proceeded yet. With this problem in mind, we introduce the concepts, lemmas, theorems of nondeterministic fuzzy simulation and bisimulation, as well as the relevant proofs. According to the definitions of nondeterministic fuzzy simulation and bisimulation, we propose nondeterministic fuzzy quotients and a series of quotienting algorithms to generate the minimization of nondeterministic fuzzy simulation and bisimulation. By comparison with previous quotienting algorithms, we show that our quotienting algorithms are more generalized. This kind of quotienting algorithms not only suit for Nondeterministic fuzzy Kripke structure(NFKS), but also Fuzzy Kripke structure(FKS) and classical Kripke structure.
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