Approximate bisimulations and state reduction of fuzzy automata under fuzzy similarity measures

Yang, Chao; Li, Yongming

doi:10.1016/j.fss.2019.07.010

Cited by 25 publications

(8 citation statements)

References 46 publications

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“…Given two fuzzy systems of the same kind such as fuzzy automata, fuzzy LTSs, fuzzy/weighted social networks, fuzzy Kripke models or fuzzy interpretations in a description logic, one can define a simulation or bisimulation between them either as a crisp relation or as a fuzzy relation between the sets of states (respectively, actors or individuals) of the systems. Bisimulations as crisp relations have been studied for fuzzy LTSs [4,5,[29][30][31], many-valued/fuzzy modal logics [9][10][11], weighted/fuzzy automata [8,32] and fuzzy description logics [19]. Simulations as crisp relations have been studied for fuzzy LTSs [20,24,31], weighted/fuzzy automata [8,32] and fuzzy description logics [16].…”

Section: Related Workmentioning

confidence: 99%

“…Bisimulations as crisp relations have been studied for fuzzy LTSs [4,5,[29][30][31], many-valued/fuzzy modal logics [9][10][11], weighted/fuzzy automata [8,32] and fuzzy description logics [19]. Simulations as crisp relations have been studied for fuzzy LTSs [20,24,31], weighted/fuzzy automata [8,32] and fuzzy description logics [16]. Bisimulations as fuzzy relations have been studied for weighted/fuzzy automata [2,6,27], fuzzy modal logics [11,18], weighted/fuzzy social networks [12,15] and fuzzy description logics [19].…”

Section: Related Workmentioning

confidence: 99%

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Fuzzy Simulations and Bisimulations between Fuzzy Automata

Nguyen¹

2022

Preprint

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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.

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Fuzzy Simulations and Bisimulations between Fuzzy Automata

Nguyen¹

2022

Preprint

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“…Also, Du and Zhu's researches on the analysis of social networks by fuzzy automata led to defining fuzzy relational structure and deducing knowledge by computing lower and upper approximations based on bisimulation [8]. The bisimulation relation models equivalence between states of nondeterministic automata [45]. The equivalence relation between states of an automaton is done to minimize the automaton, and the equivalence relation between states of two automata is usually done for comparing their behaviors [13,14,32].…”

Section: Related Workmentioning

confidence: 99%

Synthesizing fuzzy tree automata

Moghari

2022

RAIRO-Theor. Inf. Appl.

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Fuzzy tree automata are mathematical devices for modeling and analyzing vaguely defined tree structures. The behavior of a fuzzy tree automaton generates a fuzzy tree language by mapping a set of regular trees on a ranked alphabet to fuzzy membership values. It calculates the membership grade of trees using a set of rules that process their structural characteristics. This paper deals with constructing fuzzy tree automata models that their behavior satisfies a set of given logical propositions (called properties) on the structure of trees. Our goal is uncertainty modeling by synthesizing fuzzy tree automata whose behavior is described by fuzzy linguistic variables. In this regard, we first provide several patterns and heuristic tricks and techniques for constructing fuzzy tree automata that satisfy simple properties. Then, we develop a method for modeling complex propositional formulas based on the conversion of a logical formula into a computation tree, as well as a step-by-step combination of models.

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“…There is a huge amount of work on similarity measures that goes beyond the scope of this survey (Li, Qin and He 2014;Yang and Li 2020). • A number of articles on mathematical fuzzy logic with equality have been published where, apart from the usual axioms of fuzzy logic, a binary relation ≈ satisfying the axioms of a fuzzy equivalence relation is assumed.…”

Section: Semipositive-definite Fuzzy Equivalence Relations and Kernelsmentioning

confidence: 99%