Presents a fuzzy method for the recognition of strings of fuzzy symbols containing substitution, deletion, and insertion errors. As a preliminary step, we propose a fuzzy automaton to calculate a similarity value between strings. The adequate selection of fuzzy operations for computing the transitions of the fuzzy automaton allows us to obtain different string similarity definitions (including the Levenshtein distance). A deformed fuzzy automaton based on this fuzzy automaton is then introduced in order to handle strings of fuzzy symbols. The deformed fuzzy automaton enables the classification of such strings having an undetermined number of insertion, deletion and substitution errors. The selection of the parameters determining the deformed fuzzy automaton behavior would allow to implement recognizers adapted to different problems. The paper also presents algorithms that implement the deformed fuzzy automaton. Experimental results show good performance in correcting these kinds of errors.

Deformed fuzzy automata for correcting imperfect strings of fuzzy symbols

Using fuzzy context-free grammars one can easily describe a finite number of ways to derive incorrect strings together with their degree of correctness. However, in general there is an infinite number of ways to perform a certain task wrongly. In this paper we introduce a generalization of fuzzy context-free grammars, the so-called fuzzy context-free $K$-grammars, to model the situation of making a finite choice out of an infinity of possible grammatical errors during each context-free derivation step. Under minor assumptions on the parameter $K$ this model happens to be a very general framework to describe correctly as well as erroneously derived sentences by a single generating mechanism. 

Our first result characterizes the generating capacity of these fuzzy context-free $K$-grammars. As consequences we obtain: (i) bounds on modeling grammatical errors within the framework of fuzzy context-free grammars, and (ii) the fact that the family of languages generated by fuzzy context-free $K$-grammars shares closure properties very similar to those of the family of ordinary context-free languages.

The second part of the paper is devoted to a few algorithms to recognize fuzzy context-free languages: viz. a variant of a functional version of Cocke-Younger- Kasami's algorithm and some recursive descent algorithms. These algorithms turn out to be robust in some very elementary sense and they can easily be extended to corresponding parsing algorithms.

A Fuzzy Approach to Erroneous Inputs in Context-Free Language Recognition

Motivated by aspects of robustness in parsing a context-free language, we study generalized fuzzy context-free grammars. These so-called fuzzy context-free $K$-grammars provide a very 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 $\alpha$, the set containing all right-hand sides of rules with left-hand side equal to $\alpha$ 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.

Fuzzy Context-Free Languages. Part 1: Generalized Fuzzy Context-Free Grammars

We discuss the concept of robustness with respect to parsing or recognizing a context-free language. Our approach is based on the notions of fuzzy language, (generalized) fuzzy context-free grammar, and parser/recognizer for fuzzy languages. As concrete examples we consider a robust version of Cocke-Youger-Kasami's algorithm and a robust kind of recursive descent recognizer. Keywords and phrases: fuzzy language, fuzzy context-free grammar, fuzzy context-free $K$-grammar, grammatical error, parsing/recognition of fuzzy languages, Cocke-Youger-Kasami's algorithm, recursive descent.

/pdf/towards-robustness-in-parsing-fuzzifying-context-free-acxcwdb8re.pdf

M. Inui

Papers

The recognition of imperfect strings generated by fuzzy context sensitive grammars