New Properties of Anti Fuzzy Ideals of Regular Semigroups

Asaad, Samah H.; Mohammed, Akram S.

doi:10.30526/32.3.2287

Cited by 1 publication

(1 citation statement)

References 2 publications

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“…Recently, the above theories have developed in many directions and found its applications in a wide variety of fields including algebraic structures. For example, on fuzzy sets [6][7][8], on fuzzy multi sets [9][10][11] on anti-fuzzy group theory [12][13][14][15][16][17] are some of the selected works. Rosenfeld [18] defined the notion of fuzzy subgroup.…”

Section: Introductionmentioning

confidence: 99%

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

Şahin¹,

Uluçay²,

Edalatpanah³

et al. 2023

Computers, Materials &Amp; Continua

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Recently, fuzzy multi-sets have come to the forefront of scientists' interest and have been used in algebraic structures such as multi-groups, multirings, 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 )-antimulti-fuzzy subgroups, (α, γ )-anti-multi-fuzzy normal subgroups, (α, γ )-antimulti-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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