Products of fuzzy finite state machines

Malik, Davender S.; Mordeson, John N.; Sen, M. K.

doi:10.1016/s0165-0114(96)00166-2

Cited by 53 publications

(31 citation statements)

References 2 publications

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“…Definition 2.1 [5] A fuzzy finite state machine (ffsm) is a triple 1)(1)(1)(1)(1) 100122212012222222 {(,(,)(,)(,),)(,,)(,,) …”

Section: Preliminariesmentioning

confidence: 99%

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Products of cyclic fuzzy finite state machines

Huang¹,

Deng²

2015

Proceedings of the 2015 International Conference on Advanced Engineering Materials and Technology

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Abstract. A cyclic fuzzy finite state machine is a fuzzy finite state machine which is generated by a state. In this paper, we study products of cyclic fuzzy finite state machine. We prove that two cyclic finite state machines are cyclic when the full direct product(or restricted direct product, or cascade product, or wreath product) of them is cyclic. However, products of two cyclic fuzzy finite state machines are not necessarily cyclic. We introduce the concept of strong cyclic fuzzy finite state machine, and prove that products(including full direct product, restricted direct product, cascade product and wreath product ) of two strong cyclic fuzzy finite state machines are strong cyclic.

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“…Definition 2.1 [5] A fuzzy finite state machine (ffsm) is a triple 1)(1)(1)(1)(1) 100122212012222222 {(,(,)(,)(,),)(,,)(,,) …”

Section: Preliminariesmentioning

confidence: 99%

“…Malik et al [3][4][5][6] introduced the concepts of fuzzy finite state automata, fuzzy transformation semigroup, covering, direct product, cascade product, wreath product and Cartesian composition. Almost achievements of fuzzy automata which are obtained by Malik et al were written in [7].…”

Section: Introductionmentioning

confidence: 99%

Products of cyclic fuzzy finite state machines

Huang¹,

Deng²

2015

Proceedings of the 2015 International Conference on Advanced Engineering Materials and Technology

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“…The above definition of fuzzy automaton is different from the definition of ( [9], [11], [12], [16]), in the sense of defining µ only. The above definition 2.1 is, in fact, a generalization of the crisp deterministic finite state automaton, whereas definitions in ( [9], [11], [12], [16]) are generalizations of the crisp nondeterministic finite state automaton.…”

Section: Homomorphisms and Strongly Connected Fuzzy Automatonmentioning

confidence: 99%

“…The above definition 2.1 is, in fact, a generalization of the crisp deterministic finite state automaton, whereas definitions in ( [9], [11], [12], [16]) are generalizations of the crisp nondeterministic finite state automaton. If A = (Q, Σ, µ) is a fuzzy automaton then the fuzzy function µ is extended to a fuzzy function µ…”

Section: Homomorphisms and Strongly Connected Fuzzy Automatonmentioning

confidence: 99%

“…fuzzy transition function) ( [5], [11], [12], [16], [18], [20]). Structure preserving fuzzy transition functionsisomorphisms in general and homomorphisms in particular -plays crucial role for equivalent and reduction of a fuzzy automaton( [10], [11], [12], [14], [15], [16], [17]). The aim of this paper is to construct all elements of the group of (weak) fuzzy automaton automorphisms.…”

Section: Introductionmentioning

confidence: 99%

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On Cardinality of the Group of Weak Fuzzy Automaton Isomorphisms

Dhure¹,

Chaudhari²

2013

IJCA

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Recent studies on fuzzy automata are influenced by algebraic techniques to tackle issues like reduction, minimization and their languages. Fuzzy automaton homomorphism is one such majorally discussed technique. This paper is concerned with the group of (weak) fuzzy automaton automorphisms and constructions of all (weak) fuzzy automaton automorphisms over arbitrary fuzzy automaton. It is shown that (1) every arbitrary fuzzy automaton is decomposed into distinct primaries, (2) primaries are maximal singly generated fuzzy automata and (3) every weak fuzzy automaton homomorphism on an arbitrary fuzzy automaton is uniquely determined into weak fuzzy automaton homomorphisms on all its primaries. Therefore, the discussion begun over strongly connected fuzzy automaton and continue constructions as well as characterizations of (weak) fuzzy automaton homomorphisms, isomorphisms, endomorphisms and automorphisms sequentially over perfect fuzzy automaton, singly generated fuzzy automaton and primaries of fuzzy automaton. Finally, it is obtained that the group of weak fuzzy automaton automorphisms and its cardinality over arbitrary fuzzy automaton. Keywords:Fuzzy function, fuzzy automaton (strongly connected, perfect and singly generated),(Weak) fuzzy automaton automorphism (homomorphism, isomorphism), primaries and basis of a fuzzy automaton.

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