Canonization of max-min fuzzy automata
| Autor: | José Ramón González de Mendívil, Federico Fariña Figueredo |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Fuzzy automata
Discrete mathematics 0209 industrial biotechnology TheoryofComputation_COMPUTATIONBYABSTRACTDEVICES Reduction (recursion theory) Mathematics::General Mathematics Logic Powerset construction Structure (category theory) 02 engineering and technology Nonlinear Sciences::Cellular Automata and Lattice Gases Fuzzy logic ComputingMethodologies_PATTERNRECOGNITION TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES 020901 industrial engineering & automation Factorization Artificial Intelligence Deterministic automaton Simple (abstract algebra) 0202 electrical engineering electronic engineering information engineering 020201 artificial intelligence & image processing ComputingMethodologies_GENERAL Computer Science::Formal Languages and Automata Theory Mathematics |
| Zdroj: | Fuzzy Sets and Systems. 376:152-168 |
| ISSN: | 0165-0114 |
| DOI: | 10.1016/j.fss.2019.03.009 |
| Popis: | 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 M ˆ ( 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 M ˆ ( . ) 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 Godel structure (also called max-min fuzzy automata). These fuzzy automata are always determinizable and have been proved useful in practical applications. |
| Databáze: | OpenAIRE |
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