1. Canonization of max-min fuzzy automata
- Author
-
José Ramón González de Mendívil and Federico Fariña Figueredo
- Subjects
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 - Abstract
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.
- Published
- 2019