Bipolar Complex Fuzzy Lie Subalgebras: Structural Properties and Application in Decision‐Making
Manivannan Balamurugan, Ganesan Ellammal, Ghulam Muhiuddin, Nabilah Abughazalah
Source abstract
A bipolar complex fuzzy set ( 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 s to Lie algebras. Specifically, we introduce the notion of a bipolar complex fuzzy Lie subalgebra ( and explore its fundamental properties. We show that the direct product of s also forms a . Furthermore, we defined the (( c , d ), ( e , f ))‐cut and (( c , d ), ( e , f ))‐strong cut of a and its properties. We examined the properties of s 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.
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