$\alpha$-Q-fuzzy Subgroups

TL;DR

This paper introduces and explores properties of $eta$-Q-fuzzy subsets and subgroups, analyzing their behavior under group anti-homomorphisms, contributing to fuzzy subgroup theory.

Contribution

It defines $eta$-Q-fuzzy subgroups and studies their properties and effects under group anti-homomorphisms, advancing fuzzy subgroup theory.

Findings

Properties of $eta$-Q-fuzzy subgroups are established.

Effects on images and inverse-images under anti-homomorphisms are analyzed.

Theoretical foundations for $eta$-Q-fuzzy structures are developed.

Abstract

In this paper, the notations of $\alpha$-Q-fuzzy subset and $\alpha$-Q-fuzzy subgroup are introduced, and necessary properties related to these two concepts are proven. In the past part in this work, the effect of the $\alpha$-Q-fuzzy subgroup on the image and inverse-image under group anti-homomorphism are studied.