Fundamental group of LB-valued general fuzzy automata

Abstract

This study aims to investigate [Formula: see text]-valued GFA from algebraic and topological perspectives, where [Formula: see text] stands for residuated lattice and B is a set of propositions about the general fuzzy automata, in which its underlying structure is a complete infinitely distributive lattice. Further, the concepts of [Formula: see text]-valued general fuzzy automata (or simply [Formula: see text]-valued GFA) contractible spaces, [Formula: see text]-valued GFA path homotopy, [Formula: see text]-valued GFA retraction, [Formula: see text]-valued GFA deformation retraction, [Formula: see text]-valued GFA path connected space and [Formula: see text]-valued GFA homotopy equivalent space are introduced and explicated. In addition, [Formula: see text]-valued GFA fundamental groups are proposed and studied. Regarding these issues, some properties are also established and explained.