On Fuzzy Positive Implicative Filters inBE-Algebras

We study several degrees in defining a fuzzy positive implicative filter, which is a generalization of a fuzzy filter inBE-algebras.

Fantastic filters of lattice implication algebras

The notion of a fantastic filter in a lattice implication algebra is introduced, and the relations among filter, positive implicative filter, and fantastic filter are given. We investigate an equivalent condition for a filter to be fantastic, and state an extension property for fantastic filter.