Nondeterministic fuzzy automata

Cao, Yongzhi; Ezawa, Yoshinori

doi:10.1016/j.ins.2011.12.024

Cited by 34 publications

(16 citation statements)

References 49 publications

(63 reference statements)

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“…Following [8], [25], in this work we address a more general FTS by taking into account nondeterminism. As a result, for each state s and label a, more than one possibility distribution may be returned by δ.…”

Section: Fuzzy-transition Systemsmentioning

confidence: 99%

A Behavioral Distance for Fuzzy-Transition Systems

Cao

Sun

Wang

et al. 2013

IEEE Trans. Fuzzy Syst.

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Abstract-In contrast to the existing approaches to bisimulation for fuzzy systems, we introduce a behavioral distance to measure the behavioral similarity of states in a nondeterministic fuzzy-transition system. This behavioral distance is defined as the greatest fixed point of a suitable monotonic function and provides a quantitative analogue of bisimilarity. The behavioral distance has the important property that two states are at zero distance if and only if they are bisimilar. Moreover, for any given threshold, we find that states with behavioral distances bounded by the threshold are equivalent. In addition, we show that two system combinators-parallel composition and productare non-expansive with respect to our behavioral distance, which makes compositional verification possible.

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Section: Fuzzy-transition Systemsmentioning

confidence: 99%

A Behavioral Distance for Fuzzy-Transition Systems

Cao

Sun

Wang

et al. 2013

IEEE Trans. Fuzzy Syst.

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“…For example, Cao et al [2,4] considered bisimulations for fuzzy transition systems (FTS) where both fuzzy transitions and nonderministic transitions co-exist. This model is further studied under fuzzy automata by Cao et al [3] and Pan et al [15]. Ćirić et al [5] investigated bisimulations for fuzzy automata.…”

Section: Introductionmentioning

confidence: 99%

Bisimulations for fuzzy transition systems revisited

Chen

Han

et al. 2018

International Journal of Approximate Reasoning

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Bisimulation is a well-known behavioral equivalence for discrete event systems, and has recently been adopted and developed in fuzzy systems. In this paper, we propose a new bisimulation, i.e., the group-by-group fuzzy bisimulation, for fuzzy transition systems. It relaxes the fully matching requirement of the bisimulation definition proposed by Cao et al. [IEEE Transaction on Fuzzy Systems, 19:540-552], and can equate more pairs of states which are deemed to be equivalent intuitively, but which cannot be equated in previous definitions. We carry out a systematic investigation on this new notion of bisimulation. In particular, a fixed point characterization of the group-by-group fuzzy bisimilarity is given, based on which, we provide a polynomial-time algorithm to check whether two states in a fuzzy transition system are group-by-group fuzzy bisimilar. Moreover, a modal logic, which is an extension of the Hennessy-Milner logic, is presented to completely characterize the group-by-group fuzzy bisimilarity.

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“…To the extracted FA, its stability had been also described [1]. For better solving some complicated problems in fuzzy information processing, some information fusions were performed well by FA [3] [4] [5]. At the same time, some controls of fuzzy automata had been applied in mechanical engineering [6] [7].…”

Section: Introductionmentioning

confidence: 99%

“…The automata had a partition according to recognizing and accepting the language feature that was certain, uncertain and fuzzy. The automata were classified into the deterministic finite-state automaton (DFA), the non-deterministic finite-state automaton (NFA) and the fuzzy automaton (FA) [5]. Correspondingly, the fuzzy automata were also classified into the finite-state deterministic fuzzy automaton (FDFA), the finite non-deterministic fuzzy automaton (FNFA), the fuzzy finite-state automaton (FFA) and the fuzzy infinite-state automaton (FIA) [1].…”

Section: Introductionmentioning

confidence: 99%

Application of Union of Fuzzy Automata on Target Tracking

Wu¹,

Han²,

Wu³

2017

JILSA

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For better applications of fuzzy automata on target tracking, this paper presents an associated method of fuzzy automata by discussing the relation between fuzzy automata. The equivalence is mainly discussed regarding these fuzzy automata. The target tracking based on the associated method of fuzzy automata is given. Moreover, the simulation result shows that the associated method is better than single fuzzy automaton relatively. The development of these researches in this paper in turn can quicken the applications of the fuzzy automata in various fields.

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Nondeterministic fuzzy automata

Cited by 34 publications

References 49 publications

A Behavioral Distance for Fuzzy-Transition Systems

A Behavioral Distance for Fuzzy-Transition Systems

Bisimulations for fuzzy transition systems revisited

Application of Union of Fuzzy Automata on Target Tracking

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