@Article{cmc.2023.033006, AUTHOR = {Memet Şahin, Vakkas Uluçay, S. A. Edalatpanah, Fayza Abdel Aziz Elsebaee, Hamiden Abd El-Wahed Khalifa}, TITLE = {(α, γ)-Anti-Multi-Fuzzy Subgroups and Some of Its Properties}, JOURNAL = {Computers, Materials \& Continua}, VOLUME = {74}, YEAR = {2023}, NUMBER = {2}, PAGES = {3221--3229}, URL = {http://www.techscience.com/cmc/v74n2/50271}, ISSN = {1546-2226}, 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.}, DOI = {10.32604/cmc.2023.033006} }