On fuzzy filters of CI-algebras

In this paper after first introducing the fuzzy filter of CI-algebras we get several properties, we find that the notions of N-structured subalgebras, N-structured filters of CI-algebra and some of their basic properties and results are direct results on fuzzy filter of CI-algebra. Next we recall the contents of the filters in pseudo BL algebra. By exploring the equivalent condition of fuzzy normal filter, an open problem between two kinds of filters was solved. Jun and Xu et al. proved that in lattice implication algebra a positive implicative filter is implicative, and set the converse of it as an open problem. For the third part of this paper, we define the corresponding fuzzy filters and inspired by the fuzzy results we solve the open problem.