Intuitionistic Fuzzy Lie Sub-superalgebras and Ideals of Lie Superalgebras

In order to show the applications of intuitionistic fuzzy sets and generalize the concepts of fuzzy Lie sub-super algebras and fuzzy ideals of Lie superalgebras, the theory of intuitionistic fuzzy Lie superalgebras is introduced in this paper. By defining Z₂-graded intuitionistic fuzzy vector subspaces, intuitionistic fuzzy Lie sub-superalgebras and intuitionistic fuzzy ideals of a Lie superalgebra are given. Some examples are utilized to show the definitions of intuitionistic fuzzy Lie sub-superalgebras and intuitionistic fuzzy ideals. The relations between intuitionistic fuzzy Lie sub-superalgebras (intuitionistic fuzzy ideals) and Lie sub-superalgebras (ideals) are also investigated.