On quotient machines of a fuzzy automaton and the minimal machine

Basak, N.; Gupta, Aarti

doi:10.1016/s0165-0114(01)00064-1

Cited by 34 publications

(26 citation statements)

References 3 publications

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“…Reduction of number of states of fuzzy automata was studied in [1,14,41,44,50,53], and the algorithms given there were also based on the idea of computing and merging indistinguishable states. They were called minimization algorithms, but the term minimization is not adequate because it does not mean the usual construction of the minimal one in the set of all fuzzy automata recognizing a given fuzzy language, but just the procedure of computing and merging indistinguishable states.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy relation equations and reduction of fuzzy automata

Ćirić

Stamenković

Ignjatović

et al. 2010

Journal of Computer and System Sciences

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We show that the state reduction problem for fuzzy automata is related to the problem of finding a solution to a particular system of fuzzy relation equations in the set of all fuzzy equivalences on its set of states. This system may consist of infinitely many equations, and finding its non-trivial solutions may be a very difficult task. For that reason we aim our attention to some instances of this system which consist of finitely many equations and are easier to solve. First, we study right invariant fuzzy equivalences, and their duals, the left invariant ones. We prove that each fuzzy automaton possesses the greatest right (resp. left) invariant fuzzy equivalence, which provides the best reduction by means of fuzzy equivalences of this type, and we give an effective procedure for computing this fuzzy equivalence, which works if the underlying structure of truth values is a locally finite residuated lattice. Moreover, we show that even better reductions can be achieved alternating reductions by means of right and left invariant fuzzy equivalences. We also study strongly right and left invariant fuzzy equivalences, which give worse reductions than right and left invariant ones, but whose computing is much easier. We give an effective procedure for computing the greatest strongly right (resp. left) invariant fuzzy equivalence, which is applicable to fuzzy automata over an arbitrary complete residuated lattice.

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Section: Introductionmentioning

confidence: 99%

Fuzzy relation equations and reduction of fuzzy automata

Ćirić

Stamenković

Ignjatović

et al. 2010

Journal of Computer and System Sciences

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show abstract

“…For example, minimization of fuzzy Mealy machine with output is discussed in [5], while the minimization of fuzzy finite automata with two-valued state transition functions is presented in [12]. Likewise the minimization of fuzzy finite automata with crisp final states without output is studied in [3]. The minimization of fuzzy machines is covered in the literature, cf.…”

Section: Introductionmentioning

confidence: 99%

Minimization of lattice finite automata and its application to the decomposition of lattice languages

Pedrycz

2007

Fuzzy Sets and Systems

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“…There are many papers on the minimization problem of fuzzy finite automata. For example, minimization of Mealy type of fuzzy finite automata is discussed in [2], minimization of fuzzy finite automata with crisp final states without outputs is studied in [1], and minimization of fuzzy machines becomes the subject of [16,17,23,24].…”

Section: Introductionmentioning

confidence: 99%

Minimization of states in automata theory based on finite lattice-ordered monoids

Hong-xuan

2007

Information Sciences

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On quotient machines of a fuzzy automaton and the minimal machine

Cited by 34 publications

References 3 publications

Fuzzy relation equations and reduction of fuzzy automata

Fuzzy relation equations and reduction of fuzzy automata

Minimization of lattice finite automata and its application to the decomposition of lattice languages

Minimization of states in automata theory based on finite lattice-ordered monoids

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