Finite determinization of fuzzy automata using a parametric product-based t-norm

This paper presents a novel approach for the approximate determinization of fuzzy automata over the product structure. We introduce the parametric modification of the product t-norm in the pre-determinization setting. On the one hand, the behavior of a fuzzy automaton over the parametric t-norm diff...

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Veröffentlicht in:Fuzzy sets and systems Jg. 488; S. 108990
Hauptverfasser: Micić, Ivana, Stanimirović, Stefan, González de Mendívil, José Ramón, Ćirić, Miroslav, Jančić, Zorana
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 15.07.2024
Schlagworte:
Brzozowski's procedure
Finite determinization
Fuzzy automata
Minimal deterministic fuzzy automaton
Parametric t-norm
Product t-norm
Finite determinization
Fuzzy automata
Brzozowski's procedure
Product t-norm
Parametric t-norm
Minimal deterministic fuzzy automaton
ISSN:0165-0114, 1872-6801
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Zusammenfassung:This paper presents a novel approach for the approximate determinization of fuzzy automata over the product structure. We introduce the parametric modification of the product t-norm in the pre-determinization setting. On the one hand, the behavior of a fuzzy automaton over the parametric t-norm differs from the behavior of the fuzzy automaton over the product t-norm only in words with a degree of acceptance below the given parameter. However, using the parametric t-norm, we obtain an algorithm that outputs a finite minimal deterministic fuzzy automaton whose behavior differs from the starting fuzzy automaton described above. By setting the parameter to a sufficiently small value, the proposed algorithm provides a deterministic fuzzy automaton with behavior that differs insignificantly from the starting fuzzy automaton, as the difference is achieved only for words accepted by the starting fuzzy automaton with an insignificant value. As a tradeoff, the proposed approach provides finite determinization, even when all other determinization methods would result in an infinite deterministic automaton. We support this fact with an illustrative example.
ISSN:0165-0114
1872-6801
DOI:10.1016/j.fss.2024.108990