Canonization of max-min fuzzy automata

In this paper, we propose a canonization method for fuzzy automata, i.e., a determinization method that is able to return a minimal fuzzy deterministic automaton equivalent to the original fuzzy automaton. The canonization method is derived from the well-known Brzozowski's algorithm for ordinar...

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Bibliographic Details
Published in:Fuzzy sets and systems Vol. 376; pp. 152 - 168
Main Authors: González de Mendívil, José R., Fariña Figueredo, Federico
Format: Journal Article
Language:English
Published: Elsevier B.V 01.12.2019
Subjects:
Canonization
Determinization
Fuzzy automata
Fuzzy deterministic automata
Gödel structure
Minimization
Fuzzy deterministic automata
Minimization
Canonization
Determinization
Gödel structure
Fuzzy automata
ISSN:0165-0114, 1872-6801
Online Access:Get full text
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Summary:In this paper, we propose a canonization method for fuzzy automata, i.e., a determinization method that is able to return a minimal fuzzy deterministic automaton equivalent to the original fuzzy automaton. The canonization method is derived from the well-known Brzozowski's algorithm for ordinary nondeterministic automata. For a given fuzzy automaton A, we prove that the construction Mˆ(r(N(r(A))) returns a minimal fuzzy deterministic automaton equivalent to A. In that construction, r(.) represents the reversal of a fuzzy automaton, N(.) is the determinization of a fuzzy automaton based on fuzzy accessible subset construction, and Mˆ(.) is the determinization of a fuzzy automaton via factorization of fuzzy states which also includes a simple reduction of a particular case of proportional fuzzy states. The method is accomplished for fuzzy automata with membership values over the Gödel structure (also called max-min fuzzy automata). These fuzzy automata are always determinizable and have been proved useful in practical applications.
ISSN:0165-0114
1872-6801
DOI:10.1016/j.fss.2019.03.009