论文标题
模糊自动机之间的模糊模拟和双向词
Fuzzy Simulations and Bisimulations between Fuzzy Automata
论文作者
论文摘要
在完整的残留晶格上，两个模糊自动机之间的模拟和双向词由®等定义。 （2012年）作为自动机状态集合之间的模糊关系。但是，它们充当自动机之间的清晰关系。特别是，如果两个模糊自动机之间存在一个（正向）的一分化，那么它们所识别的模糊语言是清晰相等的。 Stanimirović等人介绍的近似模拟和双拟合。 （2020）旨在使这种现象模糊化。但是，它们仅针对模糊的自动机定义，在一个完整的heyting代数上定义，并且不给出自动机状态之间的确切关系。在本文中，我们在完整的残留晶格上介绍和研究模糊自动机之间的模糊模拟和双相似。这些概念是新颖的，具有良好的特性。它们在任何完整的残留晶格上定义为模糊自动机。我们证明，模糊自动机识别的模糊语言被模糊的模拟和模糊的双相模中模糊不变。我们还证明，模糊模拟和分成型的概念具有轩尼诗 - 米勒纳特性，这是对两个模糊自动机之间最大模糊模拟或分配的逻辑表征。此外，我们提供的结果表明，与模拟和三拟合的概念相比，与模拟和分配的概念更笼统，更精致。以及Stanimirović等人引入的近似模拟和三拟合的概念。
Simulations and bisimulations between two fuzzy automata over a complete residuated lattice were defined by Ćirić et al. (2012) as fuzzy relations between the sets of states of the automata. However, they act as a crisp relationship between the automata. In particular, if there exists a (forward) bisimulation between two fuzzy automata, then the fuzzy languages recognized by them are crisply equal. Approximate simulations and bisimulations introduced by Stanimirović et al. (2020) aim at fuzzifying this phenomenon. However, they are defined only for fuzzy automata over a complete Heyting algebra and do not give the exact relationship between states of the automata. In this article, we introduce and study fuzzy simulations and bisimulations between fuzzy automata over a complete residuated lattice. These notions are novel and have good properties. They are defined for fuzzy automata over any complete residuated lattice. We prove that the fuzzy language recognized by a fuzzy automaton is fuzzily preserved by fuzzy simulations and fuzzily invariant under fuzzy bisimulations. We also prove that the notions of fuzzy simulation and bisimulation have the Hennessy-Milner properties, which are a logical characterization of the greatest fuzzy simulation or bisimulation between two fuzzy automata. In addition, we provide results showing that our notions of fuzzy simulation and bisimulation are more general and refined than the notions of simulation and bisimulation introduced by Ćirić et al. and the notions of approximate simulation and bisimulation introduced by Stanimirović et al.
