New kinds of hybrid filters of EQ-algebras

Abstract

The main goal of this paper is to introduce hybrid positive implicative and hybrid implicative (pre)filters of EQ-algebras. In the following, some characterizations of this hybrid (pre)filters are investigated and it is proved that the quotient algebras induced by hybrid positive implicative filters in residuated EQ-algebras are idempotent and residuated EQ-algebra. Moreover, the relationship between hybrid implicative prefilters and hybrid positive implicative prefilters are discussed and it is shown that these concepts coincide in good involutive EQ-algebras. Finally, it is proved that the quotient EQ-algebra respect to a hybrid positive implicative filter is involutive if and only if the hybrid filter is hybrid implicative filter.

Keywords

• eq-algebra
• hybrid positive implicative (pre)filter
• hybrid implicative (pre)filter