Certain Structure of Lagrange’s Theorem with the Application of Interval-Valued Intuitionistic Fuzzy Subgroups

Kattan, Doha A.; Amin, M.R.; Bariq, Abdul

doi:10.1155/2022/3580711

Cited by 7 publications

(6 citation statements)

References 27 publications

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“…Structure preserving LIFSG-3 maps are also discussed, and it is observed that they can be derived by extending group homomorphism. 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 .…”

Section: Discussionmentioning

confidence: 99%

“…Lattice-valued intuitionistic fuzzy normal subgroups type-3 and latticevalued intuitionistic fuzzy factor subgroups type-3 of G are governed by normal subgroups and factor groups of G. Structure preserving LIFSG-3 maps are also discussed, and it is observed that they can be derived by extending group homomorphism. 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.…”

Section: Discussionmentioning

confidence: 99%

“…From ( 35) and ( 38), we get ζ I L (xyx −1 ) � ζ I L (y). Similarly, from (36) and (39), we get ξ I L (xyx −1 ) � ξ I L (y). us, I L is LIFNSG-3 of G. Hence proved.…”

Section: Lattice-valued Intuitionistic Fuzzy Normal Subgroups Type-3mentioning

confidence: 95%

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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%

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Homomorphisms of Lattice-Valued Intuitionistic Fuzzy Subgroup Type-3

Kousar

Saleem

Kausar

et al. 2022

Computational Intelligence and Neuroscience

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“…This section is devoted to present three definitions and lemmas that will be used in the paper [5]. Definition 1 (subgroup).…”

Section: Definitions and Lemmasmentioning

confidence: 99%

Lagrange’s Theorem in Group Theory: Proof and Applications

Zhu¹

2023

HSET

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There are many propositions in group theory, among which Lagrange’s theorem is a representative example and its own meaning can be taken as a generalization of the Euler's theorem resulting from the number theory. Lagrange's theorem can be understood as follows. Suppose that is a group and denotes a subgroup of . This theorem clarify that the order of a subgroup divides that of a group .The conjecture and discovery of Lagrange's theorem has led to the establishment of a unique framework in places such as calculus and statistics, allowing a certain interpretation for some problems. This paper presents the corollaries and applications of Lagrange's theorem, which can help to understand the properties of Lagrange's theorem easily, and can help to familiarize with how to apply Lagrange's theorem on various propositions. The basic concepts and fundamental theories of groups, rings and domains are the main contents of modern algebra, and the companion set and exponent are the most fundamental concepts in group theory.

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“…In Ref. [ 43 ], Kattan et al proved the interval-valued intuitionistic fuzzy version of Lagrange's theorem.…”

Section: Introductionmentioning

confidence: 99%