Bipolar Complex Fuzzy Lie Subalgebras: Structural Properties and Application in Decision-Making

Manivannan Balamurugan, Ganesan Ellammal, Ghulam Muhiuddin and Nabilah Abughazalah

Journal of Mathematics, 2026, vol. 2026, 1-21

Abstract: A bipolar complex fuzzy set (BCFS integrates the characteristics of both bipolar and complex fuzzy sets, enabling a nuanced representation of uncertainty and ambiguity. This approach is particularly valuable in systems where positive and negative information coexist. In this paper, we extend the concept of BCFSs to Lie algebras. Specifically, we introduce the notion of a bipolar complex fuzzy Lie subalgebra (BCFLSA and explore its fundamental properties. We show that the direct product of BCFLSAs also forms a BCFLSA. Furthermore, we defined the c,d,e,f-cut and c,d,e,f-strong cut of a BCFLSA and its properties. We examined the properties of BCFLSAs under Lie algebra morphisms, providing deeper insights into their structural and functional aspects. An application for the proposed bipolar complex fuzzy TOPSIS method is also illustrated with suitable example.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:6470174

DOI: 10.1155/jom/6470174

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