Determinization of fuzzy automata with membership values in complete residuated lattices

  • Authors:

  • Jelena Ignjatović;Miroslav irić;Stojan Bogdanović

  • Affiliations:

  • Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, P.O. Box 224, 18000 Niš, Serbia;Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, P.O. Box 224, 18000 Niš, Serbia;Faculty of Economics, University of Niš, Trg Kralja Aleksandra 11, 18000 Niš, Serbia

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2008

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Abstract

In this paper we introduce a new method for determinization of fuzzy finite automata with membership values in complete residuated lattices. In comparison with the previous methods, developed by Belohlavek [R. Belohlavek, Determinism and fuzzy automata, Information Sciences 143 (2002), 205-209] and Li and Pedrycz [Y.M. Li, W. Pedrycz, Fuzzy finite automata and fuzzy regular expressions with membership values in lattice ordered monoids, Fuzzy Sets and Systems 156 (2005), 68-92], our method always gives a smaller automaton, and in some cases, when the previous methods result in infinite automata, our method can result in a finite one. We also show that determinization of fuzzy automata is closely related to fuzzy right congruences on a free monoid and fuzzy automata associated with them, and in particular, to the concept of the Nerode's fuzzy right congruence of a fuzzy automaton, which we introduce and study here.