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

An (α,β)-Pythagorean fuzzy environment is an efficient tool for handling vagueness. In this paper, the notion of relative subgroup of a group is introduced. Using this concept, the (α,β)-Pythagorean fuzzy order of elements of groups in (α,β)-Pythagorean fuzzy subgroups is defined and examined variou...

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Published inAIMS mathematics Vol. 6; no. 9; pp. 9290 - 9308
Main Authors Bhunia, Supriya, Ghorai, Ganesh, Xin, Qin
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2021
Subjects
(α，β)-pythagorean fuzzy order
(α，β)-pythagorean fuzzy quotient group
(α，β)-pythagorean fuzzy subgroup
lagrange's theorem
β)-pythagorean fuzzy set
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ISSN2473-6988
2473-6988
DOI10.3934/math.2021540

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Abstract An (α,β)-Pythagorean fuzzy environment is an efficient tool for handling vagueness. In this paper, the notion of relative subgroup of a group is introduced. Using this concept, the (α,β)-Pythagorean fuzzy order of elements of groups in (α,β)-Pythagorean fuzzy subgroups is defined and examined various algebraic properties of it. A relation between (α,β)-Pythagorean fuzzy order of an element of a group in (α,β)-Pythagorean fuzzy subgroups and order of the group is established. The extension principle for (α,β)-Pythagorean fuzzy sets is introduced. The concept of (α,β)-Pythagorean fuzzy normalizer and (α,β)-Pythagorean fuzzy centralizer of (α,β)-Pythagorean fuzzy subgroups are developed. Further, (α,β)-Pythagorean fuzzy quotient group of an (α,β)-Pythagorean fuzzy subgroup is defined. Finally, an (α,β)-Pythagorean fuzzy version of Lagrange's theorem is proved.
AbstractList An (α,β)-Pythagorean fuzzy environment is an efficient tool for handling vagueness. In this paper, the notion of relative subgroup of a group is introduced. Using this concept, the (α,β)-Pythagorean fuzzy order of elements of groups in (α,β)-Pythagorean fuzzy subgroups is defined and examined various algebraic properties of it. A relation between (α,β)-Pythagorean fuzzy order of an element of a group in (α,β)-Pythagorean fuzzy subgroups and order of the group is established. The extension principle for (α,β)-Pythagorean fuzzy sets is introduced. The concept of (α,β)-Pythagorean fuzzy normalizer and (α,β)-Pythagorean fuzzy centralizer of (α,β)-Pythagorean fuzzy subgroups are developed. Further, (α,β)-Pythagorean fuzzy quotient group of an (α,β)-Pythagorean fuzzy subgroup is defined. Finally, an (α,β)-Pythagorean fuzzy version of Lagrange's theorem is proved.
Author Ghorai, Ganesh
Bhunia, Supriya
Xin, Qin
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CorporateAuthor Faculty of Science and Technology, University of the Faroe Islands, Vestarabryggja 15, FO 100 Torshavn, Faroe Islands
Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore 721102, India
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SubjectTerms (α，β)-pythagorean fuzzy order
(α，β)-pythagorean fuzzy quotient group
(α，β)-pythagorean fuzzy subgroup
lagrange's theorem
β)-pythagorean fuzzy set
Title On the fuzzification of Lagrange's theorem in $ (\alpha, \beta) $-Pythagorean fuzzy environment
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