Anti fuzzy filters of $$CI$$ -algebras.

In this paper, we introduce the notion of anti fuzzy filter and study the $$\mathcal{N }$$ -subalgebra(filter) of $$CI$$ -algebra $$X$$ . We prove that every anti fuzzy filter of $$BE$$ -algebra is an anti fuzzy subalgebra, but it is not valid in $$CI$$ -algebra. Finally, the notion of fuzzy translations and fuzzy extension of anti fuzzy filter in $$CI$$ -algebras are introduced. We show that every anti fuzzy filter can be as an anti fuzzy extension, but converse may not be true in general. [ABSTRACT FROM AUTHOR]