  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.
