Nondeterministic fuzzy automata

  • Authors:

  • Yongzhi Cao;Yoshinori Ezawa

  • Affiliations:

  • Institute of Software, School of Electronics Engineering and Computer Science, Peking University, Beijing 100871, China and Key Laboratory of High Confidence Software Technologies (Peking Universi ...;Faculty of Informatics, Kansai University, Osaka 569-1095, Japan

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2012

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Abstract

To handle fuzzy uncertainty in system modeling, nondeterministic finite automata have been generalized into fuzzy automata. After a reexamination of the notions of fuzzy automata in the literature, we ascertain that the fundamental property-nondeterminism-in nondeterministic finite automata has not been well embodied in the generalization. In order to reflect nondeterminism in fuzzy automata, we introduce nondeterministic fuzzy automata with or without @e-moves and fuzzy languages recognized by them. Like nondeterministic finite automata, nondeterministic fuzzy automata provide a mathematical representation of nondeterministic dynamic fuzzy systems. Moreover, we show that (deterministic) fuzzy automata, nondeterministic fuzzy automata, and nondeterministic fuzzy automata with @e-moves are all equivalent in the sense that they recognize the same class of fuzzy languages, which is an extension of the well-known equivalence among finite automata, nondeterministic finite automata, and nondeterministic finite automata with @e-moves.