Approximation of fuzzy context-free grammars |
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Authors: | Yongbing Wang Yongming Li |
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Affiliation: | a College of Mathematic and Information Science, Shaanxi Normal University, Xi’an 710062, China b School of Mathematics and Computation, Anqing Teachers College, Anqing 246133, China c College of Computer Science, Shaanxi Normal University, Xi’an 710062, China |
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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. |
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Keywords: | Fuzzy context-free grammars Fuzzy context-free languages Approximation Equivalence Sensitivity |
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