Approximation of fuzzy context-free grammars

  • Authors:

  • Yongbing Wang;Yongming Li

  • Affiliations:

  • College of Mathematic and Information Science, Shaanxi Normal University, Xi'an 710062, China and School of Mathematics and Computation, Anqing Teachers College, Anqing 246133, China;College of Mathematic and Information Science, Shaanxi Normal University, Xi'an 710062, China and College of Computer Science, Shaanxi Normal University, Xi'an 710062, China

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2009

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Abstract

Fuzzy context-free max-* grammar (or FCFG"*, for short), as a straightforward extension of context-free grammar, has been introduced to express uncertainty, imprecision, and vagueness in natural language fragments. Li recently proposed the approximation of fuzzy finite automata, which may effectively deal with the practical problems of fuzziness, impreciseness and vagueness. In this paper, we further develop the approximation of fuzzy context-free grammars. In particular, we show that a fuzzy context-free grammar under max-* compositional inference can be approximated by some fuzzy context-free grammar under max-min compositional inference with any given accuracy. In addition, some related properties of fuzzy context-free grammars and fuzzy languages generated by them are studied. Finally, the sensitivity of fuzzy context-free grammars is also discussed.