A limit theorem in some dynamic fuzzy systems

Kurano, Masami; Yasuda, Masami; Nakagami, Jun-ichi; Yoshida, Yūji

doi:10.1016/0165-0114(92)90078-i

Cited by 71 publications

(30 citation statements)

References 4 publications

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“…It is clearly a limitation, because many fuzzy systems are (or should be seen as) infinite-state or infinite-event. For example, the dynamic fuzzy systems studied in [21], fuzzy discrete event systems modeled by max-product automata [25], and fuzzy stochastic automata [34] involve an infinite number of states and fuzzy automata for computing with all words in [8] require an infinite number of events. This observation motivates us to introduce and explore the concept of bisimulation for general fuzzy systems which may be infinitestate or infinite-event.…”

Section: Introductionmentioning

confidence: 99%

Bisimulations for Fuzzy-Transition Systems

Cao

Chen

Kerre

2011

IEEE Trans. Fuzzy Syst.

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Abstract-There has been a long history of using fuzzy language equivalence to compare the behavior of fuzzy systems, but the comparison at this level is too coarse. Recently, a finer behavioral measure, bisimulation, has been introduced to fuzzy finite automata. However, the results obtained are applicable only to finite-state systems. In this paper, we consider bisimulation for general fuzzy systems which may be infinite-state or infiniteevent, by modeling them as fuzzy transition systems. To help understand and check bisimulation, we characterize it in three ways by enumerating whole transitions, comparing individual transitions, and using a monotonic function. In addition, we address composition operations, subsystems, quotients, and homomorphisms of fuzzy transition systems and discuss their properties connected with bisimulation. The results presented here are useful for comparing the behavior of general fuzzy systems. In particular, this makes it possible to relate an infinite fuzzy system to a finite one, which is easier to analyze, with the same behavior.

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Section: Introductionmentioning

confidence: 99%

Bisimulations for Fuzzy-Transition Systems

Cao

Chen

Kerre

2011

IEEE Trans. Fuzzy Syst.

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“…More precisely, e P c ðV; tÞ is a fuzzy number in view of the following Lemma which is proved in Kurano et al (1992): …”

Section: Bond Valuation Under Imprecise Informationmentioning

confidence: 99%

Bond pricing under imprecise information

Agliardi

2010

Oper Res Int J

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“…Also, credibilistic risk models for reward processes is being considered, whose risk is computed by the corresponding recursive equations. For the approach by possibility theory, for example, Avrachenkov [1], Thomason [13] and Kurano et al [6]. For recent developments for fuzzy theory and fuzzy logic, refer to [16,17].…”

Section: Introductionmentioning

confidence: 99%