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.

本文旨在通过分解理论研究L-模糊自动机，其中L是一个完全剩余格。我们研究的因式分解的概念大号-模糊集与集的分解大号-模糊集。这种分解用于 (i) 研究最小L -模糊自动机的概念，以及 (ii) 引入L -模糊拓扑以研究与L -模糊自动机相关的概念。具体来说，我们引入了对应于给定L模糊自动机的分解L模糊自动机的概念，并研究了这种自动机的极小性。此外，我们将L- 因式分解L -模糊自动机的模糊拓扑，并使用这些拓扑来表征一些代数概念。