The idea of a soft set offers a comprehensive mathematical basis for managing uncertainty. Since they provide innovative methods for solving issues involving parametric data, soft set operations are important ideas in soft set theory. Here, we provide a novel product operation for soft sets, known as the "soft plus-product," together with all of its algebraic characteristics in relation to various kinds of soft equalities and subsets. Furthermore, by examining the distributions of soft plus-product over various soft set operations, we investigate the relationships between this product and other soft set operations. We end with an example that demonstrates how the method can be used successfully in different scenarios using the int-uni operator and the int-uni decision function for the soft plus-product for the int-uni decision-making method, which chooses a set of optimal elements from the alternatives. This paper is an essential contribution to the literature on soft sets, as the theoretical foundations of soft computing approaches are derived from purely mathematical principles.