Relations and Functions on Union-Soft Sets

In this article, the theoretical aspects of union-soft sets by extending the notions of equivalence relations, partition, composition of relations, and function to the framework of union-soft sets are introduced. Further the Cartesian product, the relation between union-soft sets, induced relations from the universal set and the attribute set with examples are discussed. Moreover, the composition of union-soft set relationships with examples and some related theorems are demonstrated. Finally, the concepts of a union-soft set function and their respective composition function are examined.