Fuzzy automata with ε-moves compute fuzzy measures between strings

Authors:
J. J. Astrain;J. R. González de Mendívil;J. R. Garitagoitia
Affiliations:
Departamento de Matemática e Informática, Universidad Pública de Navarra, 31006 Pamplona, Spain;Departamento de Matemática e Informática, Universidad Pública de Navarra, 31006 Pamplona, Spain;Departamento de Matemática e Informática, Universidad Pública de Navarra, 31006 Pamplona, Spain
Venue:
Fuzzy Sets and Systems
Year:
2006

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Abstract

This paper introduces fuzzy automata with transitions by empty string (@?-moves), and shows their relationship with other classes of classical fuzzy automata. The @?-move represents a state change of the automaton without consuming any symbol of the input string. In approximate string matching, @?-moves allow to model the effect of the insertion of a symbol (one of the possible edit operations). We provide a fuzzy measure between strings based on the concepts of string alignments and fuzzy edit operations. The main contribution of this paper is to prove that a particular class of fuzzy automata with @?-moves computes those fuzzy measures without restricting the number of errors between the strings. Given a fuzzy measure, a building method for constructing the fuzzy automaton with @?-moves that computes it, is also proposed.