ON THE CLASSIFICATION OF PYTHAGOREAN FUZZY SUBGROUPS OF ABELIAN GROUPS

Pythagorean fuzzy set is one of the most used tool for depicting uncertainty. A divisible subgroup is among the most significant categories of subgroups of an abelian group. The number of Pythagorean fuzzy subgroups in any group is infinite without a suitable equivalence constraint on the Pythagorea...

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Bibliographic Details
Published inTWMS journal of applied and engineering mathematics Vol. 15; no. 7; p. 1715
Main Authors Bhunia, S, Ghorai, G
Format Journal Article
LanguageEnglish
Published Turkic World Mathematical Society 01.07.2025
Subjects
Abelian groups
Fuzzy algorithms
Fuzzy logic
Fuzzy sets
Fuzzy systems
Mathematical research
Set theory
India
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Summary:Pythagorean fuzzy set is one of the most used tool for depicting uncertainty. A divisible subgroup is among the most significant categories of subgroups of an abelian group. The number of Pythagorean fuzzy subgroups in any group is infinite without a suitable equivalence constraint on the Pythagorean fuzzy sets. To get a meaningful categorization, a sufficient equivalent condition on the collection of all Pythagorean fuzzy subgroups needs to be defined. In this paper, the concept of Pythagorean fuzzy divisible subgroups of a group is introduced. An equivalence relation on Pythagorean fuzzy sets is defined. Several properties of this equivalence relation on Pythagorean fuzzy subgroups are explained. Pythagorean fuzzy subgroups related to their maximal chains are introduced. All possible Pythagorean fuzzy subgroups of finite abelian groups are investigated. Keywords: Pythagorean fuzzy set, Pythagorean fuzzy divisible subgroup, equivalence relation on PFS, maximal chains of PFSG, counting of PFSG. AMS Subject Classification: 03E72, 08A72, 20N25
ISSN:2146-1147