article

Construction of fuzzy automata from fuzzy regular expressions

Authors:

Aleksandar Stamenkovi,

Miroslav ĆiriAuthors Info & Claims

Fuzzy Sets and Systems, Volume 199

Pages 1 - 27

https://doi.org/10.1016/j.fss.2012.01.007

Published: 01 July 2012 Publication History

Abstract

Li and Pedrycz have proved fundamental results that provide different equivalent ways to represent fuzzy languages with membership values in a lattice-ordered monoid, and generalize the well-known results of the classical theory of formal languages. In particular, they have shown that a fuzzy language over an integral lattice-ordered monoid can be represented by a fuzzy regular expression if and only if it can be recognized by a fuzzy finite automaton. However, they did not give any efficient method for constructing an equivalent fuzzy finite automaton from a given fuzzy regular expression. In this paper we provide such an efficient method. Transforming scalars appearing in a fuzzy regular expression @ainto letters of the new extended alphabet, we convert the fuzzy regular expression @ato an ordinary regular expression @a"R. Then, starting from an arbitrary nondeterministic finite automaton A that recognizes the language @?@a"R@? represented by the regular expression @a"R, we construct fuzzy finite automata A"@a and A"@a^r with the same or even less number of states than the automaton A, which recognize the fuzzy language @?@a@?represented by the fuzzy regular expression @a. The starting nondeterministic finite automaton A can be obtained from @a"R using any of the well-known constructions for converting regular expressions to nondeterministic finite automata, such as Glushkov-McNaughton-Yamada's position automaton, Brzozowski's derivative automaton, Antimirov's partial derivative automaton, or Ilie-Yu's follow automaton.

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Cited By

Martinek P(2022)Fuzzy multiset finite automata with outputSoft Computing - A Fusion of Foundations, Methodologies and Applications10.1007/s00500-022-07274-726:24(13205-13217)Online publication date: 1-Dec-2022
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Stamenkovi Airi MBai M(2018)Ranks of fuzzy matrices. Applications in state reduction of fuzzy automataFuzzy Sets and Systems10.1016/j.fss.2017.05.028333:C(124-139)Online publication date: 15-Feb-2018
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Garhwal SJiwari R(2016)Conversion of fuzzy automata into fuzzy regular expressions using transitive closureJournal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology10.3233/IFS-15203830:6(3123-3129)Online publication date: 1-Jan-2016
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Index Terms

Construction of fuzzy automata from fuzzy regular expressions
1. Computing methodologies
  1. Artificial intelligence
    1. Knowledge representation and reasoning
      1. Probabilistic reasoning
2. Theory of computation
  1. Formal languages and automata theory
  2. Logic

Index terms have been assigned to the content through auto-classification.

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cover image Fuzzy Sets and Systems

Fuzzy Sets and Systems Volume 199, Issue

July, 2012

136 pages

ISSN:0165-0114

Issue’s Table of Contents

Copyright © Elsevier B.V. © 2012.

Publisher

Elsevier North-Holland, Inc.

United States

Publication History

Published: 01 July 2012

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Cited By

Martinek P(2022)Fuzzy multiset finite automata with outputSoft Computing - A Fusion of Foundations, Methodologies and Applications10.1007/s00500-022-07274-726:24(13205-13217)Online publication date: 1-Dec-2022
https://dl.acm.org/doi/10.1007/s00500-022-07274-7
Stamenkovi Airi MBai M(2018)Ranks of fuzzy matrices. Applications in state reduction of fuzzy automataFuzzy Sets and Systems10.1016/j.fss.2017.05.028333:C(124-139)Online publication date: 15-Feb-2018
https://dl.acm.org/doi/10.1016/j.fss.2017.05.028
Garhwal SJiwari R(2016)Conversion of fuzzy automata into fuzzy regular expressions using transitive closureJournal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology10.3233/IFS-15203830:6(3123-3129)Online publication date: 1-Jan-2016
https://dl.acm.org/doi/10.3233/IFS-152038
Vychodil V(2015)Pseudovarieties of algebras with fuzzy equalitiesFuzzy Sets and Systems10.1016/j.fss.2014.07.014260:C(110-120)Online publication date: 1-Feb-2015
https://dl.acm.org/doi/10.1016/j.fss.2014.07.014
González de Mendívil JGaritagoitia J(2015)A comment on "Construction of fuzzy automata from fuzzy regular expressions"Fuzzy Sets and Systems10.1016/j.fss.2014.06.001262:C(102-110)Online publication date: 1-Mar-2015
https://dl.acm.org/doi/10.1016/j.fss.2014.06.001
ĆIri MIgnjatovi JJančI IDamljanovi N(2012)Computation of the greatest simulations and bisimulations between fuzzy automataFuzzy Sets and Systems10.1016/j.fss.2012.05.006208(22-42)Online publication date: 1-Dec-2012
https://dl.acm.org/doi/10.1016/j.fss.2012.05.006

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