Fuzzy Automata Based on Lattice-ordered Monoid with Algebraic and Topological Aspects

Tiwari, S. P.; Sharan, Shambhu

doi:10.1007/s12543-012-0108-y

Cited by 24 publications

(7 citation statements)

References 17 publications

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“…In this section, we recall the concepts related to residuated lattices [5,39]; L-fuzzy relations [24,39]; L-fuzzy automata [7,23,36]; L-fuzzy languages [7,39], and Lfuzzy objects [23,24].…”

Section: Preliminariesmentioning

confidence: 99%

On L-fuzzy partitioned automata

Tiwari

Singh

2019

Proceedings of the 2019 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and

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This paper is towards the study of theory of fuzzy automata with fuzzy partitions. Specifically, we study the concept of the L-fuzzy partitioned automaton corresponding to a given L-fuzzy automaton. Further, we introduce the concept of a crisp-deterministic L-fuzzy automaton corresponding to the Lfuzzy partitioned automaton such that both accept the same L-fuzzy language. Finally, the notion of the fuzzified L-fuzzy partitioned automaton corresponding to a given L-fuzzy partitioned automaton is introduced and a characterization of its L-fuzzy language is given.

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“…In this section, we recall the concepts related to residuated lattices [5,39]; L-fuzzy relations [24,39]; L-fuzzy automata [7,23,36]; L-fuzzy languages [7,39], and Lfuzzy objects [23,24].…”

Section: Preliminariesmentioning

confidence: 99%

On L-fuzzy partitioned automata

Tiwari

Singh

2019

Proceedings of the 2019 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and

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“…Ignjatovic et al [11] explained determinization of fuzzy finite automata with membership degree using complete residuated lattice. Tiwari and Sharan [18] defined the concept of fuzzy finite automata with membership degree using latticeordered monoids. For fuzzy finite automata, they explained some topological and algebraic concepts.…”

Section: Algebraic Aspectsmentioning

confidence: 99%

A Novel Approach for the Determination of Membership Values of the Strings in Fuzzy Languages

Singh¹,

Kumar²

2014

IJCA

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Classical automata theory can not deal with uncertainty. To deal with uncertainty in system modeling, fuzzy automata come into the existence. Fuzzy automaton depends on membership value. For finding the membership degree of strings in fuzzy automata, the concept of maxmin automaton and minmax automaton can be used. Many researchers have used the concept of maxmin automaton for finding the fuzzy languages. In this paper, the concept of min max automaton for finding the membership degree of strings in fuzzy automata has been used.

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“…In Birkhoff [8], Erné [10] page 1-138, García et al, [13], the terms polarity and axiality have been used for a contravariant Galois connections and covariant Galois connections between power sets, respectively. Automata are well known mathematical models of computations studied by several authors [16,18]. The use of Zadeh [37] fuzzy sets generalize the notion of automata to fuzzy automata, Santos [30] and Wee and Fu [34] initiated such studies and attracted researchers to develop fuzzy automata theory in several directions (cf., [24,28,34,36]).…”

Section: Introductionmentioning

confidence: 99%

“…Further, Ito [17], deals with the algebraic view of fuzzy automata. Recently, following the work of Ito [18], Tiwari, Yadav and Singh [32], studied fuzzy automata to explore its several algebraic properties the uniqueness of the maximal layer of cyclic automata and minimal layers of directable fuzzy automata along with relationships between upper semilattices and fuzzy automata were established. The studies concerning algebraic automata has been carried out by several researchers in various forms (cf., eg., [4,5,16,17,18,31,33]).…”

Section: Introductionmentioning

confidence: 99%

“…Recently, following the work of Ito [18], Tiwari, Yadav and Singh [32], studied fuzzy automata to explore its several algebraic properties the uniqueness of the maximal layer of cyclic automata and minimal layers of directable fuzzy automata along with relationships between upper semilattices and fuzzy automata were established. The studies concerning algebraic automata has been carried out by several researchers in various forms (cf., eg., [4,5,16,17,18,31,33]). In [5], for instance, some specific notions such as separateness, connectedness and retrievability of automata have been established and investigated in detail.…”

Section: Introductionmentioning

confidence: 99%

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An algebraic study of LB-valued general fuzzy automata: On the concept of the layers

Abolpour,

Shamsizadeh

2023

JAHLA

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The present study aims at introducing a new concept of layer of LB-valued general fuzzy automata (LB-valued GFA) where B is regarded as a set of propositions about the GFA, in which its underlying structure has been a lattice-ordered monoid. In general, it demonstrates that the layer plays a key role in the algebraic study of LB-valued GFA by characterizing the concepts of subautomata and separated subautomata of an LB-valued GFA in terms of its layers. In other words, it highlights that every LB-valued general fuzzy automaton has at least one strongly connected subautomaton. In specific, the characterization of some algebraic concepts such as subautomaton, retrievability and connectivity of an LB-valued GFA in terms of its layers is provided. In addition, it is shown that the maximal layer of a cyclic LB-valued general fuzzy automaton and minimal layer of a directable LB-valued general fuzzy automaton are unique. Finally, we investigate the different poset structures associated with an LB-valued general fuzzy automaton, demonstrating some of these posets as finite upper semilattice, and introducing the isotone Galois connections between some of the pairs of the posets/finite upper semilattices introduced.

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Fuzzy Automata Based on Lattice-ordered Monoid with Algebraic and Topological Aspects

Cited by 24 publications

References 17 publications

On L-fuzzy partitioned automata

On L-fuzzy partitioned automata

A Novel Approach for the Determination of Membership Values of the Strings in Fuzzy Languages

An algebraic study of LB-valued general fuzzy automata: On the concept of the layers

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