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ARTICLE

(α, γ)-Anti-Multi-Fuzzy Subgroups and Some of Its Properties

Memet Şahin¹, Vakkas Uluçay², S. A. Edalatpanah^3,*, Fayza Abdel Aziz Elsebaee⁴, Hamiden Abd El-Wahed Khalifa⁵

1 Department of Mathematics, Gaziantep University, Gaziantep, Turkey
2 Department of Mathematics, Kilis 7 Aralık University, Kilis, Turkey
3 Department of Applied Mathematics, Ayandegan Institute of Higher Education, Tonekabon, Iran
4 Department of Mathematics, Helwan University, Cairo, Egypt
5 Department of Mathematics, Qassim University, Alasyah, Saudi Arabia

* Corresponding Author: S. A. Edalatpanah. Email:

Computers, Materials & Continua 2023, 74(2), 3221-3229. https://doi.org/10.32604/cmc.2023.033006

Received 04 June 2022; Accepted 09 August 2022; Issue published 31 October 2022

Abstract

Recently, fuzzy multi-sets have come to the forefront of scientists’ interest and have been used in algebraic structures such as multi-groups, multi-rings, anti-fuzzy multigroup and (α, γ)-anti-fuzzy subgroups. In this paper, we first summarize the knowledge about the algebraic structure of fuzzy multi-sets such as (α, γ)-anti-multi-fuzzy subgroups. In a way, the notion of anti-fuzzy multigroup is an application of anti-fuzzy multi sets to the theory of group. The concept of anti-fuzzy multigroup is a complement of an algebraic structure of a fuzzy multi set that generalizes both the theories of classical group and fuzzy group. The aim of this paper is to highlight the connection between fuzzy multi-sets and algebraic structures from an anti-fuzzification point of view. Therefore, in this paper, we define (α, γ)-anti-multi-fuzzy subgroups, (α, γ)-anti-multi-fuzzy normal subgroups, (α, γ)-anti-multi-fuzzy homomorphism on (α, γ)-anti-multi-fuzzy subgroups and these been explicated some algebraic structures. Then, we introduce the concept (α, γ)-anti-multi-fuzzy subgroups and (α, γ)-anti-multi-fuzzy normal subgroups and of their properties. This new concept of homomorphism as a bridge among set theory, fuzzy set theory, anti-fuzzy multi sets theory and group theory and also shows the effect of anti-fuzzy multi sets on a group structure. Certain results that discuss the (α, γ) cuts of anti-fuzzy multigroup are explored.

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Keywords

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