On LB-valued GFA: An LB-valued operator oriented view with t-norm/t-conorm and implicators

Abstract

This study aims at investigating [Formula: see text]-valued general fuzzy automata, for simplicity, [Formula: see text]-valued GFA, with respect to their algebraic properties and based on t-norm/t-conorm and general implicators, where [Formula: see text] stands for residuated lattice and [Formula: see text] is a set of propositions about the GFA, in which its underlying structure is a complete infinitely distributive lattice. Specifically, we introduce the concepts of [Formula: see text]-valued operators with t-norm and [Formula: see text]-valued operators with t-conorm. We also examine the relationships between the [Formula: see text]-valued operators with t-norm and [Formula: see text]-valued operators with t-conorm. Finally, we introduce the concepts of [Formula: see text]-valued operators with implicator and study the relationships between the [Formula: see text]-valued operators with the implicator and the [Formula: see text]-valued operators with t-norm/t-conorm. To clarify the notions and the results obtained in this study, some examples are submitted as well.