Neutrosophic Regular Filters and Fuzzy Regular Filters in Pseudo-BCI Algebras

Abstract

Neutrosophic set is a new mathematical tool
for handling problems involving imprecise, indeterminacy and inconsistent data. Pseudo-BCI algebra is a
kind of non-classical logic algebra in close connection
with various non-commutative fuzzy logics. Recently,
we applied neutrosophic set theory to pseudo-BCI algebras. In this paper, we study neutrosophic filters
in pseudo-BCI algebras. The concepts of neutrosophic
regular filter, neutrosophic closed filter and fuzzy regular
filter in pseudo-BCI algebras are introduced, and
some basic properties are discussed. Moreover, the
relationships among neutrosophic regular filter, fuzzy
filters and anti-grouped neutrosophic filters are presented, and the results are proved: a neutrosophic filter
(fuzzy filter) is a neutrosophic regular filter (fuzzy
regular filter), if and only if it is both a neutrosophic
closed filter (fuzzy closed filter) and an anti-grouped
neutrosophic filter (fuzzy anti-grouped filter).