On a factorized L-fuzzy automaton and its L -fuzzy topological characterization

摘要

This paper is towards the study of L-fuzzy automata via theory of factorizations, where L is a complete residuated lattice. We study the concept of factorization of L-fuzzy sets and factorization of collection of L-fuzzy sets. Such factorizations are used (i) to study the concept of minimal L-fuzzy automaton, and (ii) to introduce L-fuzzy topologies for the study of concepts associated with an L-fuzzy automaton. Specifically, we introduce the notion of factorized L-fuzzy automaton corresponding to a given L-fuzzy automaton and study the minimality of such automaton. Further, we associate L-fuzzy topologies for factorized L-fuzzy automaton and use these to characterize some algebraic concepts. (c) 2020 Elsevier B.V. All rights reserved.