Rational series and their languages
Rational series and their languages
Equivalence, reduction and minimization of finite automata over semirings
Theoretical Computer Science
Products of fuzzy finite state machines
Fuzzy Sets and Systems
Products of T-generalized state machines and T-generalized transformation semigroups
Fuzzy Sets and Systems
Automata, Languages, and Machines
Automata, Languages, and Machines
Fuzzy Sets and Systems: Theory and Applications
Fuzzy Sets and Systems: Theory and Applications
Theory of Codes
Automata: Theoretic Aspects of Formal Power Series
Automata: Theoretic Aspects of Formal Power Series
On covering of products of fuzzy finite state machines
Fuzzy Sets and Systems
R-Fuzzy Automata with a Time-Variant Structure
Proceedings of the 3rd Symposium on Mathematical Foundations of Computer Science
Fuzzy recognizers and recognizable sets
Fuzzy Sets and Systems - Mathematics
Determinism and fuzzy automata
Information Sciences—Informatics and Computer Science: An International Journal
On generalizations of adaptive algorithms and application of the fuzzy sets concept to pattern classification
Ambiguity in Graphs and Expressions
IEEE Transactions on Computers
Some considerations on fuzzy automata
Journal of Computer and System Sciences
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In this paper we present a different framework for the study of fuzzy finite machines and their fuzzy languages. Unlike the previous work on fuzzy languages, characterized by fuzzification at the level of their acceptors/generators, here we follow a top-down approach by starting our fuzzification with more abstract entities: monoids and particular families in monoids. Moreover, we replace the unit interval (in fact, a finite subset of the unit interval) as support for fuzzy values with the more general structure of a lattice. We have found that completely distributive complete lattices allow the fuzzification at the highest level, that of recognizable and rational sets. Quite surprisingly, the fuzzification process has not followed thoroughly the classical (crisp) theory. Unlike the case of rational sets, the fuzzification of recognizable sets has revealed a few remarkable exceptions from the crisp theory: for example the difficulty of proving closure properties with respect to complement, meet and inverse morphisms. Nevertheless, we succeeded to prove the McKnight and Kleene theorems for fuzzy sets by making the link between fuzzy rational/recognizable sets on the one hand and fuzzy regular languages and FT-NFA languages (languages defined by NFA with fuzzy transitions) on the other. Finally, we have drawn the attention to fuzzy rational transductions, which have not been studied extensively and which bring in a strong note of applicability.