On the characterization of Pythagorean fuzzy subgroups

Bhunia, Supriya; Ghorai, Ganesh; Xin, Qin

doi:10.3934/math.2021058

Cited by 13 publications

(6 citation statements)

References 20 publications

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“…In the future, the notion foundations laid in this article can be used to find the Abelian subgroups of finite p -groups [ 34 ], verify Lagrange's theorem [ 35 , 36 ], compute annihilator [ 37 ], aggregation [ 38 ], and fundamental isomorphism theorems [ 39 ] for lattice-valued intuitionistic fuzzy subgroups type-3. There are several generalizations of fuzzy sets [ 40 – 42 ] where lattice-valued algebraic structures can be defined by replacing [0,1] with a suitable lattice L . The research findings can be utilized for application in algebra [ 43 , 44 ] and real-life problems [ 45 ] to handle uncertainty and ambiguity more accurately.…”

Section: Discussionmentioning

confidence: 99%

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Homomorphisms of Lattice-Valued Intuitionistic Fuzzy Subgroup Type-3

Kousar

Saleem

Kausar

et al. 2022

Computational Intelligence and Neuroscience

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The lattice-valued intuitionistic fuzzy set was introduced by Gerstenkorn and Tepavcevi as a generalization of both the fuzzy set and the L -fuzzy set by incorporating membership functions, nonmembership functions from a nonempty set X to any lattice L , and lattice homomorphism from L to the interval 0,1 . In this article, lattice-valued intuitionistic fuzzy subgroup type-3 (LIFSG-3) is introduced. Lattice-valued intuitionistic fuzzy type-3 normal subgroups, cosets, and quotient groups are defined, and their group theocratic properties are compared with the concepts in classical group theory. LIFSG-3 homomorphism is established and examined in relation to group homomorphism. The research findings are supported by provided examples in each section.

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Section: Discussionmentioning

confidence: 99%

“…ere are several generalizations of fuzzy sets [40][41][42] where lattice-valued algebraic structures can be defined by replacing [0, 1] with a suitable lattice L. e research findings can be utilized for application in algebra [43,44] and real-life problems [45] to handle uncertainty and ambiguity more accurately.…”

Section: Discussionmentioning

confidence: 99%

Homomorphisms of Lattice-Valued Intuitionistic Fuzzy Subgroup Type-3

Kousar

Saleem

Kausar

et al. 2022

Computational Intelligence and Neuroscience

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“…The collection of Pythagorean membership grades is bigger than intuitionistic membership grades, which is very important in decision making problems. Bhunia et al [5] proposed Pythagorean fuzzy subgroups in 2021. several results related to Pythagorean fuzzy sets and Pythagorean fuzzy subgroups were provided by [7], [14].…”

Section: Introductionmentioning

confidence: 99%

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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“…To find more about intuitionistic fuzzy subgroups, we recommend reading [34][35][36][37][38]. Recently, Bhunia et al [39] defined Pythagorean fuzzy subgroups and explored different attributes of this concept.…”

Section: Introductionmentioning

confidence: 99%

On $q$ -Rung Orthopair Fuzzy Subgroups

Razzaque

Razaq

2022

Journal of Function Spaces

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The q -rung orthopair fuzzy environment is an innovative tool to handle uncertain situations in various decision-making problems. In this work, we characterize the idea of a q -rung orthopair fuzzy subgroup and examine various algebraic attributes of this newly defined notion. We also present q -rung orthopair fuzzy coset and q -rung orthopair fuzzy normal subgroup along with relevant fundamental theorems. Moreover, we introduce the concept of q -rung orthopair fuzzy level subgroup and proved related results. At the end, we explore the consequence of group homomorphism on the q -rung orthopair fuzzy subgroup.

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On the characterization of Pythagorean fuzzy subgroups

Cited by 13 publications

References 20 publications

Homomorphisms of Lattice-Valued Intuitionistic Fuzzy Subgroup Type-3

Homomorphisms of Lattice-Valued Intuitionistic Fuzzy Subgroup Type-3

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

On $q$ -Rung Orthopair Fuzzy Subgroups

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On the characterization of Pythagorean fuzzy subgroups

Cited by 13 publications

References 20 publications

Homomorphisms of Lattice-Valued Intuitionistic Fuzzy Subgroup Type-3

Homomorphisms of Lattice-Valued Intuitionistic Fuzzy Subgroup Type-3

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

On q -Rung Orthopair Fuzzy Subgroups

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On $q$ -Rung Orthopair Fuzzy Subgroups