<p>The goal of this research is to introduce and investigate a new class of weighted multiset machines that consume input as multisets and produce output as multisets. The first step is to propose the notion of a Mealy-type weighted multiset machine, and characterize them with their input–output multisets. In particular, we introduce the notions of totally consumed input multiset (tc-mset), consumed input multiset (c-mset) and partially consumed input multiset (pc-mset) for Mealy-type weighted multiset machine and illustrate these concepts with concrete examples. In the next step, we present and examine the concepts of (complete) input–output weighted multiset behavior, observability, equivalence, and reduction of initialized Mealy type weighted multiset machine. After that to enrich the algebraic study, we introduce the concepts of congruences and homomorphisms within the context of Mealy-type weighted multiset machine and demonstrate the homomorphism theorem, which formalizes the connection between them, e.g., the quotient map of a Mealy-type weighted multiset machine is a strong epimorphism, and each strong homomorphic image of a Mealy-type weighted multiset machine is equivalent to itself. In the last, to connect two Mealy-type weighted multiset machines in parallel and series connections, we define the concepts of direct products or restricted direct products and cascade products of Mealy-type weighted multiset machines and characterize them with their input–output multiset behavior.</p>