## Fuzzy Context-Free Languages — Part 1: Generalized Fuzzy Context-Free Grammars Abstract

Citations: | 1 - 1 self |

### BibTeX

@MISC{Asveld_fuzzycontext-free,

author = {Peter R. J. Asveld},

title = {Fuzzy Context-Free Languages — Part 1: Generalized Fuzzy Context-Free Grammars Abstract},

year = {}

}

### OpenURL

### Abstract

Motivated by aspects of robustness in parsing a context-free language, we study generalized fuzzy context-free grammars. These fuzzy context-free K-grammars provide a general framework to describe correctly as well as erroneously derived sentences by a single generating mechanism. They model the situation of making a finite choice out of an infinity of possible grammatical errors during each context-free derivation step. Formally, a fuzzy context-free K-grammar is a fuzzy context-free grammar with a countable rather than a finite number of rules satisfying the following condition: for each symbol α, the set containing all right-hand sides of rules with left-hand side equal to α forms a fuzzy language that belongs to a given family K of fuzzy languages. We investigate the generating power of fuzzy context-free K-grammars, and we show that under minor assumptions on the parameter K, the family of languages generated by fuzzy context-free K-grammars possesses closure properties very similar to those of the family of ordinary context-free languages. Key words: formal language, fuzzy context-free grammar, grammatical error, algebraic closure property 1