On Complex Intuitionistic Fuzzy Lie Sub-superalgebras

TL;DR

This paper introduces complex intuitionistic fuzzy structures into Lie superalgebras, defining new concepts and exploring their properties and behavior under anti-homomorphisms.

Contribution

It extends intuitionistic fuzzy Lie superalgebras by incorporating complex-valued membership functions and studies their algebraic properties and transformations.

Findings

Defined complex intuitionistic fuzzy Lie sub-superalgebras and ideals.

Analyzed properties under anti-homomorphisms.

Explored behavior of anti-complex fuzzy structures.

Abstract

A complex intuitionistic fuzzy Lie superalgebra is a generalization of intuitionistic fuzzy Lie superalgebra whose membership function takes values in the unit disk in the complex plane. In this research, the concepts of complex intuitionistic fuzzy sets are introduced to Lie superalgebras. We define the complex intuitionistic fuzzy Lie sub superalgebras and complex intuitionistic fuzzy ideals of Lie superalgebras. Then, we study some related properties of complex intuitionistic fuzzy Lie sub-superalgebras and complex intuitionistic fuzzy ideals. Finally, we define the image and preimage of complex intuitionistic fuzzy Lie sub-superalgebra under Lie superalgebra anti-homomorphism. The properties of anti-complex intuitionistic fuzzy Lie sub-superalgebras and anti-complex intuitionistic fuzzy ideals under anti-homomorphisms of Lie superalgebras are investigated.