Associative filters and associative pseudofilters of residuated lattices in multiset context

Abstract There is an open problem in [5] stated as follows: “Is there a suitable and useful definition of associative filter in residuated lattice?” Yes, here the concept is defined as follows: filter F is associative of L if α → (β → ω) ∈ F ⇔ (α → β) → ω ∈ F for any α,β,ω ∈ L. Also this concept is developed in the context of multisets and thus the notions of multiset associative filter, multiset pre-associative filter, multiset associative pseudofilter have been introduced followed by the relationship between multiset associative filter and other multiset filters have been found.