On the fuzzification of Lagrange's theorem in $ (\alpha, \beta) $-Pythagorean fuzzy environment

Bhunia, Supriya; Ghorai, Ganesh; Xin, Qin

doi:10.3934/math.2021540

Cited by 5 publications

(2 citation statements)

References 24 publications

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“…Addis [1] proposed fuzzy homomorphism theorems for groups in 2018. In 2021, Bhunia [5] and Ghorai [7] presented the concept of (α, β)-Pythagorean fuzzy sets and characterized (α, β)-Pythagorean fuzzy subgroups.…”

Section: Introductionmentioning

confidence: 99%

An Approach to Lagrange’s Theorem in Pythagorean Fuzzy Subgroups

BHUNIA,

GHORAI

2024

KgJMat

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The Pythagorean fuzzy environment is a modern way of depicting uncertainty. The concept of Pythagorean fuzzy semi-level subgroups of any group is described in this paper. The Pythagorean fuzzy order of an element in a Pythagorean fuzzy subgroup is introduced and established various algebraic attributes. The relation between the Pythagorean fuzzy order of an element of a group and the order of that group is established. The Pythagorean fuzzy normalizer and Pythagorean fuzzy centralizer of Pythagorean fuzzy subgroups are discussed. Further, the concept of Pythagorean fuzzy quotient group and the index of a Pythagorean fuzzy subgroup are deﬁned. Finally, a framework is developed for proving Lagrange’s theorem in Pythagorean fuzzy subgroups.

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Section: Introductionmentioning

confidence: 99%

An Approach to Lagrange’s Theorem in Pythagorean Fuzzy Subgroups

BHUNIA,

GHORAI

2024

KgJMat

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“…In 2019, Bhunia and Ghorai [21] studied ðα, βÞ-Pythagorean fuzzy subgroups. In 2021, Bhunia et al [22,23] developed Pythagorean fuzzy subgroups. Abuhijleh et al [24] worked on complex fuzzy subgroups in 2021.…”

Section: Introductionmentioning

confidence: 99%

On the Algebraic Characteristics of Fuzzy Sub e-Groups

Bhunia

Ghorai

Kutbi

et al. 2021

Journal of Function Spaces

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Fuzzy set is a modern tool for depicting uncertainty. This paper introduces the concept of fuzzy sub e-group as an extension of fuzzy subgroup. The concepts of identity and inverse are generalized in fuzzy sub e-groups. Every fuzzy subgroup is proven to be a fuzzy sub e-group, but the converse is not true. Various properties of fuzzy sub e-groups are established. Moreover, the concepts of proper fuzzy sub e-group and super fuzzy sub e-group are discussed. Further, the concepts of fuzzy e-coset and normal fuzzy sub e-group are presented. Finally, we describe the effect of e-group homomorphism on normal fuzzy sub e-groups.

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On the Algebraic Attributes of (α, β)-Pythagorean Fuzzy Subrings and (α, β)-Pythagorean Fuzzy Ideals of Rings

et al. 2022

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α, β)-Pythagorean fuzzy set is a very efficient way for dealing with uncertainty. In this article, we introduce the notions of (α, β)-Pythagorean fuzzy subring and (α, β)-Pythagorean fuzzy ideal of a ring. Further, we briefly describe various results related to it. Also, we discuss level subring of an (α, β)-Pythagorean fuzzy subring. Moreover, we study the direct product and ring homomorphism of (α, β)-Pythagorean fuzzy subring.INDEX TERMS (α, β)-PFS, (α, β)-PFSR, (α, β)-PFID, (α, β)-PFLSR

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On the fuzzification of Lagrange's theorem in $ (\alpha, \beta) $-Pythagorean fuzzy environment

Cited by 5 publications

References 24 publications

An Approach to Lagrange’s Theorem in Pythagorean Fuzzy Subgroups

An Approach to Lagrange’s Theorem in Pythagorean Fuzzy Subgroups

On the Algebraic Characteristics of Fuzzy Sub e-Groups

On the Algebraic Attributes of (α, β)-Pythagorean Fuzzy Subrings and (α, β)-Pythagorean Fuzzy Ideals of Rings

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