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

Soft sets provide a robust mathematical framework for addressing uncertainty, offering innovative solutions for problems involving parametric data. Soft set operations are core concepts within soft set theory. In this paper, we introduce a novel soft product for soft sets, termed the soft star-product, along with its complete algebraic properties concerning various types of soft equalities and subsets. By analyzing the distributions of the soft star product over different soft set operations, we also explore the relationships between this product and other soft set operations. The paper concludes with an example that illustrates the method's effectiveness in various applications, utilizing the int-uni operator and the int-uni decision function within the soft star-product for the int-uni decision-making method, which identifies an optimal set of elements from available alternatives. This work is a valuable contribution to the soft set literature, as the theoretical foundation of soft computing methods is based on rigorous mathematical principles.