General relations between partially ordered multisets and their chains and antichains

In this paper we begin with the basics of multisets and their operations introduced in [5, 22] and define a multiset relation, an equivalence multiset relation and explore some of their basic properties. We also define a partially ordered multiset as a multiset relation being reflexive, antisymmetric and transitive, chains and antichains of a partially ordered multiset, and extend Dilworth's Theorems for partially ordered sets in the context of partially ordered multisets.