Abstract
This paper aims to study the L-fuzzy automata theory based on t-norm, t-conorm and general implicator, alongwith to investigate the algebraic and L-fuzzy topological properties of L-fuzzy automata. Specifically, we introduce L-fuzzy operators based on t-norm, t-conorm and implicator, and establish their relationships. Interestingly, we associate L-fuzzy co-topologies and L-fuzzy topologies for a given L-fuzzy automaton and use these to characterize some algebraic concepts. Further, we introduce the concepts of L-graded co-topologies, L-graded topologies and establish their relationships. We also demonstrate that the introduced L-graded co-topologies and L-graded topologies have some exciting consequences under a homomorphism.
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