A study of the properties of soft sets on the M-semilattice

Abstract Integrates the concept of an m-semilattice with the theory of soft sets, and introduces definitions for soft m-semilattices, soft sub-m-semilattices, soft ideals, and ideal soft m-semilattices. Several algebraic properties of soft m-semilattice are proved, especially those after combining the concepts of intersection, union, and direct product of soft sets. After establishing the definition of soft m-semilattice homomorphism, the relationship between m-semilattice homomorphism, m-semilattice isomorphism, soft m-semilattice homomorphism and soft m-semilattice, soft sub m-semilattice, soft ideal, ideal soft m-semilattice is studied.