  A complex intuitionistic fuzzy Lie superalgebra is a generalization of
intuitionistic fuzzy Lie super-algebra whose membership function takes values
in the unit disk in the complex plane. In [4], we introduced and studied the
concepts of complex intuitionistic fuzzy Lie sub-superalgebras and complex
intuitionistic fuzzy ideals of Lie superalgebras. Moreover, we also, in [4],
defined the image and preimage of complex intuitionistic fuzzy Lie
sub-superalgebra under Lie superalgebra anti-homomorphism, and he investigated
the properties of anti-complex intuitionistic fuzzy Lie sub-superalgebras and
anti-complex intuitionistic fuzzy ideals under anti-homomorphisms of Lie
superalgebras. In this research, we use the concepts of complex intuitionistic
fuzzy Lie superalgebras to introduce the complex intuitionistic fuzzy bracket
products. Finally, we use the definitions of the image and preimage of complex
intuitionistic fuzzy ideals under Lie superalgebra anti-homomorphisms, to study
the characterizations of the image and preimage of the complex intuitionistic
fuzzy bracket products under Lie superalgebra anti-homomorphisms.
