Fuzzy automata with fuzzy relief

Virant, Jernej; Zimic, Nikolaj

doi:10.1109/91.366572

Cited by 28 publications

(22 citation statements)

References 4 publications

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“…2 and the FTS S given here. In the literature, there are a large number of formal description tools for dynamic fuzzy systems such as various fuzzy automata [1], [8], [12], [28], [34], [41], fuzzy Petri nets [6], [9], [31], fuzzy control systems [10], [15], [30], fuzzy discrete event systems [7], [13], [25], [33], neuro-fuzzy systems [17], and so on. In general, they are not FTSs, but it is possible to translate a system's description in one of these formalisms into the FTS representing its behavior.…”

Section: Fuzzy Transition Systemsmentioning

confidence: 99%

“…The basic idea in the formulation is that, unlike the classical case, a fuzzy automaton can switch from one state to another one to a certain (truth) degree, and thus it is capable of capturing the uncertainty appearing in states or state transitions of a system. In the literature up to now (see, for example, [1], [8], [12], [14], [19], [23], [28], [34], [39], [41]), a great variety of types of fuzzy automata has been proposed in different modeling situations and the notion of fuzzy automata has proved useful in many areas such as learning control and pattern recognition. In parallel, various fuzzy Petri nets have been formulated and extensively investigated (see [4]- [6], [9], [18], [31] and the references therein).…”

Section: Introductionmentioning

confidence: 99%

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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: Fuzzy Transition Systemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Bisimulations for Fuzzy-Transition Systems

Cao

Chen

Kerre

2011

IEEE Trans. Fuzzy Syst.

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“…An other paper shows a definition of a fuzzy automaton, which has the state, input, and output sets as fuzzy sets. The state transition function is defined as moving on a fuzzy relief with fuzzy peak-states and boundaries between different membership functions [17] .…”

Section: Related Workmentioning

confidence: 99%

A Fuzzy Rough Rule Based System Enhanced By Fuzzy Cellular Automata

Gamal¹,

El-Fetouh²,

Barakat³

2013

IJACSA

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Abstract-Handling uncertain knowledge is a very tricky problem in the current world as the data, we deal with, is uncertain, incomplete and even inconsistent. Finding an efficient intelligent framework for this kind of knowledge is a challenging task. The knowledge based framework can be represented by a rule based system that depends on a set of rules which deal with uncertainness in the data. Fuzzy rough rules are a good competitive in dealing with the uncertain cases. They are consisted of fuzzy rough variables in both the propositions and consequences. The fuzzy rough variables represent the lower and upper approximations of the subsets of a fuzzy variable. These fuzzy variables use labels (fuzzy subsets) instead of values. An efficient fuzzy rough rule based system must depend on good and accurate rules. This system needs to be enhanced to view the future recommendations or in other words the system in time sequence. This paper tries to make a rule based system for uncertain knowledge using fuzzy rough theory to generate the desired accurate rules and then use fuzzy cellular automata parallel system to enhance the rule based system developed and find out what the system would look like in time sequence so as to give good recommendations about the system in the future. The proposed model along with experimental results and simulations of the rule based systems of different data sets in time sequence is illustrated.

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“…In the literature up to now, various variants of fuzzy automata have been proposed in different modeling situations (see, for example, [2,6,7,8,9,10,16,17,22,23,26,27,28,33,38]) and the notions of fuzzy automata and fuzzy languages have proved useful in many areas [1,4,11,12,13,20,21,30,31,32,34,35,37,39]. In terms of fuzzy transition functions, fuzzy automata may be broadly classified into three types: The first type [1,3,6,7,9,11,12,13,16,21,22,23,27,28,32,33,35,37,39] uses fuzzy transition functions like δ : Q × Σ −→ F (Q), where Q represents the state set, Σ is the input alphabet, and F (Q) is the set...…”

Section: Introductionmentioning

confidence: 99%

“…In terms of fuzzy transition functions, fuzzy automata may be broadly classified into three types: The first type [1,3,6,7,9,11,12,13,16,21,22,23,27,28,32,33,35,37,39] uses fuzzy transition functions like δ : Q × Σ −→ F (Q), where Q represents the state set, Σ is the input alphabet, and F (Q) is the set of all fuzzy subsets of Q. Note that such a fuzzy transition function can be equivalently converted into δ : Q × Σ × Q −→ [0, 1] and can also be represented by fuzzy states and fuzzy transition matrices.…”

Section: Introductionmentioning

confidence: 99%

Nondeterministic fuzzy automata

Cao

Ezawa

2012

Information Sciences

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Fuzzy automata have long been accepted as a generalization of nondeterministic finite automata. A closer examination, however, shows that the fundamental property-nondeterminism-in nondeterministic finite automata has not been well embodied in the generalization. In this paper, we introduce nondeterministic fuzzy automata with or without -moves and fuzzy languages recognized by them. Furthermore, we prove that (deterministic) fuzzy automata, nondeterministic fuzzy automata, and nondeterministic fuzzy automata with -moves are all equivalent in the sense that they recognize the same class of fuzzy languages.

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Fuzzy automata with fuzzy relief

Cited by 28 publications

References 4 publications

Bisimulations for Fuzzy-Transition Systems

Bisimulations for Fuzzy-Transition Systems

A Fuzzy Rough Rule Based System Enhanced By Fuzzy Cellular Automata

Nondeterministic fuzzy automata

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