Some Characterizations of Certain Complex Fuzzy Subgroups

Alharbi, Abeer Ali; Alghazzawi, Dilshad

doi:10.3390/sym14091812

Cited by 3 publications

(2 citation statements)

References 42 publications

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“…After that, in 2012, Tamir et al [30] changed the range of CFS from a unit disc to a unit square of a complex plane to interpret the CFS in the cartesian form. Al-Husbain [31] invented the notion of complex fuzzy (CF) subgroups and Alharbi and Alghazzawi [32] invented various features of the CF subgroups. The theory of CF rings was invented by Al-Husban and Salleh [33].…”

Section: Introductionmentioning

confidence: 99%

Bipolar complex fuzzy submodules

Alsuraiheed,

ur Rehman,

Khan

et al. 2024

Phys. Scr.

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In this manuscript, we interpret the theory of bipolar complex fuzzy submodule (BCFSM) of a provided classical module over a ring by utilizing the well-known notion of bipolar complex fuzzy set (BCFS). We also devise the sum of two BCFS and investigate its related proposition for studying a few fundamental properties of the initiated BCFSM. Moreover, we investigate the cartesian product of two BCFS for developing properties of BCFSM. We also investigate that if a BCFS Ӈ_1 is a BCFSM of Ӎ_1, then image Ӻ(Ӈ) is a BCFSM of Ӎ_2 and the preimage Ӻ^(-1) (Ӈ) is a BCFSM of Ӎ_1, where, Ӎ_1 and Ӎ_2 are two modules and Ӻ:Ӎ_1→Ӎ_2 is a module homomorphism.

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Section: Introductionmentioning

confidence: 99%

Bipolar complex fuzzy submodules

Alsuraiheed,

ur Rehman,

Khan

et al. 2024

Phys. Scr.

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“…In 2021, Alolaiyan et al [35] established the existence of (α, β)-complex fuzzy normal subgroups of a given group and show that any complex fuzzy subgroup is a (α, β)-complex fuzzy subgroup. In 2022, Alharbi and Alghazzawi [37] introduced (ρ, η)-CFS and demonstrated the basics examples of the group under (ρ, η)-CFS. Gulzar et al [29] introduced the innovative idea of complex intuitionistic fuzzy subgroups (CIFSGs) and established that each CIFSGs creates two intuitionistic fuzzy subgroups.…”

Section: Introductionmentioning

confidence: 99%

A New Algebraic Structure of Complex Pythagorean Fuzzy Subfield

Mateen,

Alsuraiheed,

Hmissi

2023

IEEE Access

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The concept of complex Pythagorean fuzzy set (CPFS) is recent development in the field of fuzzy set (FS) theory. The significance of this concept lies in the fact that this theory assigned membership grades ψ and non-membership grades ψ from unit circle in plane, i.e., in the form of a complex number with the condition (ψ) 2 + ( ψ) 2 ≤ 1 instead from [0, 1] interval. This is an expressive technique for dealing with uncertain circumstances. The aim of this study is to proceed the classification of the unique framework of CPFS in algebraic structure that is field theory and examine its numerous algebraic features. Also, we initiate the important examples and results of certain field. Furthermore, we illustrate that every complex Pythagorean fuzzy subfield (CPFSF) generates two Pythagorean fuzzy subfields (PFSFs). We also prove many useful algebraic aspects of this notion for a CPFSF. Moreover, we demonstrate that intersection of two complex Pythagorean fuzzy subfields (CPFSFs) is also CPFSF. Additionally, we discuss the novel idea of level subsets of CPFSFs and demonstrate that level subset of CPFSF form subfield. Additionally, we improve the application of this theory to show the concept of the direct product of two CPFSFs is also a CPFSF and produce several novel results on direct product of CPFSFs. Finally, we explore the homomorphic images and inverse images of CPFSFs.

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A Comprehensive Study on Pythagorean Fuzzy Normal Subgroups and Pythagorean Fuzzy Isomorphisms

et al. 2022

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The Pythagorean fuzzy set is an extension of the intuitionistic fuzzy set used to handle uncertain circumstances in various decisions making problems. Group theory is a mathematical technique for dealing with problems of symmetry. This study deals with Pythagorean fuzzy group theory. In this article, we characterize the notion of a Pythagorean fuzzy subgroup and examine various algebraic properties of this concept. An extensive study on Pythagorean fuzzy cosets of a Pythagorean fuzzy subgroup, Pythagorean fuzzy normal subgroups of a group and Pythagorean fuzzy normal subgroup of a Pythagorean fuzzy subgroup is performed. We define the notions of Pythagorean fuzzy homomorphism and isomorphism and generalize the notion of factor group of a classical group relative to its normal subgroup by defining a PFSG of . At the end, the Pythagorean fuzzy version of fundamental theorems of isomorphisms is proved.

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Some Characterizations of Certain Complex Fuzzy Subgroups

Cited by 3 publications

References 42 publications

Bipolar complex fuzzy submodules

Bipolar complex fuzzy submodules

A New Algebraic Structure of Complex Pythagorean Fuzzy Subfield

A Comprehensive Study on Pythagorean Fuzzy Normal Subgroups and Pythagorean Fuzzy Isomorphisms

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