ON THE CLASS OF SUBSETS OF RESIDUATED LATTICE WHICH INDUCES A CONGRUENCE RELATION

In this manuscript, we study the class of special sub sets connected with a subset in a residuated lattice and investigate some related properties. We describe the union of elements of this class. Using the intersection of all special subsets connected with a subset, we give a necessary and sufficient condition for a sub set to be a filter. Finally, by defining some operations, we endow this class with a residuated lattice structure and prove that it is isomorphic to the set of all congruence classes with respect to a filter.