×

On quotient machines of a fuzzy automaton and the minimal machine. (English) Zbl 1015.68130

Summary: The concept of Substitution-Property (SP) partition for a finite fuzzy automaton is formulated, and the quotient automaton with respect to an SP partition is defined. The state minimization problem for such automata by using the method of quotient machines is solved.

MSC:

68Q70 Algebraic theory of languages and automata
Full Text: DOI

References:

[1] Bacon, G. C., Decomposition of stochastic automata, Inform. and Control, 7, 320-329 (1964) · Zbl 0134.24702
[2] Dubois, D.; Prade, H., Fuzzy Sets and Systems: Theory and Applications (1980), Academic Press: Academic Press New York · Zbl 0444.94049
[3] Harrison, M. A., Introduction to Switching and Automata Theory (1965), McGraw-Hill: McGraw-Hill New York · Zbl 0196.51702
[4] A. Kandel, S.C. Lee, Fuzzy Switching and Automata: Theory and Applications, Crane, Russak, 1980.; A. Kandel, S.C. Lee, Fuzzy Switching and Automata: Theory and Applications, Crane, Russak, 1980.
[5] Mizumoto, M.; Toyoda, J.; Tonaka, K., Some considerations on fuzzy automata, J. Comput. System Sci., 3, 409-422 (1969) · Zbl 0183.29501
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.