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Fundamental Group of $L^{B}$ $L^{B}$ -Valued General Fuzzy Automata

Kh. Abolpour

Department of Mathematics, Shiraz Branch, Islamic Azad University, Shiraz, Iran

Corresponding author.

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and

A. Borumand Saeid

Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran

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https://doi.org/10.1142/S1793005722500272Cited by:0 (Source: Crossref)

Abstract

This study aims to investigate $L^{B}$ $L^{B}$ -valued GFA from algebraic and topological perspectives, where $L$ $L$ 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 $L^{B}$ $L^{B}$ -valued general fuzzy automata (or simply $L^{B}$ $L^{B}$ -valued GFA) contractible spaces, $L^{B}$ $L^{B}$ -valued GFA path homotopy, $L^{B}$ $L^{B}$ -valued GFA retraction, $L^{B}$ $L^{B}$ -valued GFA deformation retraction, $L^{B}$ $L^{B}$ -valued GFA path connected space and $L^{B}$ $L^{B}$ -valued GFA homotopy equivalent space are introduced and explicated. In addition, $L^{B}$ $L^{B}$ -valued GFA fundamental groups are proposed and studied. Regarding these issues, some properties are also established and explained.

Keywords:

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