Redefined neutrosophic filters in BE-algebras

Abstract

Neutrosophic set theory is a mathematical tool for handling problems involving imprecise, indeterminacy and inconsistent data.  In 2015, neutrosophic set theory is applied to BE-algebra, and the notion of neutrosophic filter is introduced.  In this paper, some mistakes and deficiencies of original definition of neutrosophic filter are pointed out by some examples.  Moreover, a new definition of neutrosophic filter is established, some basic properties are presented, and the relationships between fuzzy filters and neutrosophic filters are discussed.  Finally, the concept of implicative neutrosophic filter in BE-algebra is introduced, and some necessary and sufficient conditions for a neutrosophic filter to be implicative are presented.