Determinism and fuzzy automata

  • Authors:
  • Radim Bělohlávek

  • Affiliations:
  • Department of Computer Science, Palacký University of Olomouc, Czech Republic, Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, 30, Dubna 7, Ostrava, Czech Re ...

  • Venue:
  • Information Sciences—Informatics and Computer Science: An International Journal
  • Year:
  • 2002

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Abstract

The concept of a fuzzy automaton, as studied in the literature, is a direct generalization of the classical concept of a non-deterministic automaton. In this paper, we consider the question of whether there is a deterministic counterpart to the notion of a fuzzy automaton. We propose a definition of deterministic fuzzy automata and show that they are equally powerful as fuzzy automata. Compared to the classical notion of a deterministic automaton, the deterministic fuzzy automaton defined in our paper differs essentially only in that the final states form a fuzzy set. Moreover, we show that deterministic fuzzy automata are equally powerful as nested systems of deterministic automata.