TY  - EJOU
AU  - Şahin, Memet 
AU  - Uluçay, Vakkas 
AU  - Edalatpanah, S. A. 
AU  - Elsebaee, Fayza Abdel Aziz 
AU  - Khalifa, Hamiden Abd El-Wahed 

TI  - (<b>α</b>, <b>γ</b>)-Anti-Multi-Fuzzy Subgroups and Some of Its Properties
T2  - Computers, Materials \& Continua

PY  - 2023
VL  - 74
IS  - 2
SN  - 1546-2226

AB  - 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.
KW  - Fuzzy set; anti-fuzzy multi set; anti-fuzzy multi subgroup; anti-fuzzy multi normal subgroup

DO  - 10.32604/cmc.2023.033006