Implicative and positive implicative filters of residuated lattices in multiset context

Abstract

In this paper, we introduce the concept of multiset implicative filter and multiset positive implicative filter of residuated lattice. Also, we discuss their characterizations and we show that M is a multiset implicative filter of X if and only if the quotient residuated lattice X/M is a Heyting algebra.

Subject Classification:

• 03G10

Keywords:

• Multiset filter
• Multiset implicative filter
• Multiset positive implicative filter