An approach to Set-Valued Anti-Homomorphism of T-Rough Ideals on $\Gamma$-Semigroups

TL;DR

This paper introduces set-valued anti-homomorphisms for $ ext{Gamma}$-semigroups, explores their properties, and generalizes approximation operators, providing examples and extending the theoretical framework of $ ext{Gamma}$-semigroup mappings.

Contribution

It presents the novel concepts of set-valued anti-homomorphism and strong set-valued anti-homomorphism for $ ext{Gamma}$-semigroups, along with generalized approximation operators.

Findings

Properties of lower and upper approximations under anti-homomorphisms are established.

Examples illustrate the behavior of approximations under these mappings.

The framework extends the understanding of $ ext{Gamma}$-semigroup structure and mappings.

Abstract

In this paper, the concepts of set-valued anti-homomorphism and strong set-valued anti-homomorphism of $\Gamma$-semigroup are introduced. The notions of generalized lower and upper approximation operators, constructed by means of set-valued mapping, which is a generalization of the notion of lower and upper approximation of $\Gamma$-semigroup, are provided. Some significant properties of lower and upper approximations of $\Gamma$-semigroup under (strong)set-valued anti-homomorphisms are discussed. We provide examples for the properties of lower and upper approximations of $\Gamma$-semigroup under (strong)set-valued anti-homomorphisms. This article explores the notion of a set-valued anti-homomorphism for $\Gamma$-semigroups, which is a generalization of anti-homomorphism in general