Deformed fuzzy automata for correcting imperfect strings of fuzzy symbols

Abstract

This paper 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 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. This paper also presents algorithms that implement the deformed fuzzy automaton. Experimental results show good performance in correcting these kinds of errors.

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“…In the literature up to now, various variants of fuzzy automata have been proposed in different modeling situations (see, for example, [2,6,7,8,9,10,16,17,22,23,26,27,28,33,38]) and the notions of fuzzy automata and fuzzy languages have proved useful in many areas [1,4,11,12,13,20,21,30,31,32,34,35,37,39]. In terms of fuzzy transition functions, fuzzy automata may be broadly classified into three types: The first type [1,3,6,7,9,11,12,13,16,21,22,23,27,28,32,33,35,37,39] uses fuzzy transition functions like δ : Q × Σ −→ F (Q), where Q represents the state set, Σ is the input alphabet, and F (Q) is the set...…”

“…In terms of fuzzy transition functions, fuzzy automata may be broadly classified into three types: The first type [1,3,6,7,9,11,12,13,16,21,22,23,27,28,32,33,35,37,39] uses fuzzy transition functions like δ : Q × Σ −→ F (Q), where Q represents the state set, Σ is the input alphabet, and F (Q) is the set of all fuzzy subsets of Q. Note that such a fuzzy transition function can be equivalently converted into δ : Q × Σ × Q −→ [0, 1] and can also be represented by fuzzy states and fuzzy transition matrices.…”