Soft sets provide a strong mathematical foundation for managing uncertainty and inventing solutions to parametric data problems. Soft set operations are fundamental elements within soft set theory. In this paper, we introduce a new product operation for soft sets, called the “soft lambda-product,” and thoroughly examine its algebraic properties in relation to various types of soft equalities and subsets. By studying the distribution of the soft lambda-product over different soft set operations, we further investigate its relationship with other soft set operations. We conclude with an example demonstrating the method’s effectiveness across various applications, employing the int-uni operator and int-uni decision function within the soft lambda-product for the int-uni decision-making method, which identifies an optimal set of elements from available options. This work significantly contributes to the soft set literature, as the theoretical foundations of soft computing methods rely on solid mathematical principles.

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