On the fuzzification of Lagrange's theorem in (α,β)-Pythagorean fuzzy environment

Supriya Bhunia, Ganesh Ghorai, Qin Xin

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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.
Original languageEnglish
Pages (from-to)9290-9308
Number of pages19
JournalAIMS Mathematics
Volume6
Issue number9
Publication statusPublished - 22 Jun 2021

Keywords

  • (α, β)-Pythagorean fuzzy set
  • (α, β)-Pythagorean fuzzy subgroup
  • (α, β)-Pythagorean fuzzy quotient group
  • Lagrange’s theorem

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