Tripolar Complex Fuzzy Lie Subalgebras of Lie Algebras

The tripolar complex fuzzy set ($\mathcal{TCFS}$) is an extension of the bipolar complex fuzzy set ($\mathcal{BCFS}$), which itself generalizes traditional fuzzy sets and bipolar fuzzy sets. In this paper, we further develop this framework by introducing the concept of tripolar complex fuzzy Lie bra...

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Bibliographic Details
Published inEuropean journal of pure and applied mathematics Vol. 18; no. 3; p. 6489
Main Authors Balamurugan, M., Ellammal, G., Iampan, Aiyared
Format Journal Article
LanguageEnglish
Published 01.08.2025
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ISSN1307-5543
1307-5543
DOI10.29020/nybg.ejpam.v18i3.6489

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Summary:The tripolar complex fuzzy set ($\mathcal{TCFS}$) is an extension of the bipolar complex fuzzy set ($\mathcal{BCFS}$), which itself generalizes traditional fuzzy sets and bipolar fuzzy sets. In this paper, we further develop this framework by introducing the concept of tripolar complex fuzzy Lie brackets and investigating their algebraic properties. Additionally, we demonstrate that the scalar multiplication and addition of tripolar complex fuzzy Lie subalgebras yield another tripolar complex fuzzy Lie subalgebra. Moreover, we establish that the homomorphic image of a nilpotent (or solvable) tripolar complex fuzzy Lie ideal remains a nilpotent (or solvable) tripolar complex fuzzy Lie ideal. Finally, we establish that every nilpotent tripolar complex fuzzy Lie ideal is solvable.
ISSN:1307-5543
1307-5543
DOI:10.29020/nybg.ejpam.v18i3.6489