Algebraic Applications on Multiset Filters of Residuated Lattices

A naive concept of a multiset is the repetition of its elements that obtained from a set and the number of occurences of a particular element in a multiset is a finite positive integer. In this paper, we introduced the concepts of congruence relation on a residuated lattice induced by a multiset filter and cosets of multiset filter are established and we present several important characterizations of them.