Soft difference-product: A new product for soft sets with its decision-making

A thorough mathematical foundation for handling uncertainty is provided by the concept of soft sets. Soft set operations are key concepts in soft set theory since they offer novel approaches to problems requiring parametric data. The “soft difference-product” a new product operation for soft sets, is proposed in this study along with all of its algebraic properties concerning different types of soft equalities and subsets. Additionally, we explore the connections between this product and other soft set operations by investigating the distributions of soft difference-product over other soft set operations. Using the uni-int operator and the uni-int decision function for the soft-difference product, we apply the uni-int decision-making method, which selects a set of optimal elements from the alternatives by giving an example that shows how the approach may be conducted effectively in various areas. Since the theoretical underpinnings of soft computing techniques are drawn from purely mathematical concepts, this study is crucial to the literature on soft sets.