On L-valued tree automata: The topological characterization

Abstract

The current study aims to investigate the L-valued tree automata theory based on t-norm/t-conorm and it further examines their algebraic and L-valued topological properties. Specifically, the concept of L-valued operators with t-norm/t-conorm is introduced and the existing relationships between them are also studied. Interestingly, we associate L-valued co-topologies/topologies for a given L-valued tree automaton, using them to characterize some algebraic concepts. Further, we introduce the concepts of Alexandroff L-graded co-topologies and Alexandroff L-graded topologies which correspond to the L-valued operators with t-norm and L-valued operators with t-conorm/implicator, respectively. In addition, we aim to specify the relationship between the L-graded co-topologies/topologies, showing that the introduced L-graded co-topologies/topologies have some interesting consequences under homomorphism.