Soft Theta-product: A New Product for Soft Sets with Its Decision-Making

Abstract

For handling uncertainty, the theory of soft sets provides a thorough mathematical foundation. Soft set operations are significant concepts in soft set theory, as they offer new approaches to problems involving parametric data. In this context, we introduce a new product operation for soft sets, called “soft theta-product” and investigate its whole algebraic properties in terms of different types of soft subsets and soft equalities. Additionally, we explore the relations of this soft product with other soft set operations by investigating the distributions of the soft theta-product over them. In conclusion, using the uni-int decision function for the soft-theta product together with the uni-int operator for the uni-int decision-making method, which chooses a collection of optimal elements from the alternatives, we provide an example demonstrating how the technique may be effectively applied in a range of areas. As the theoretical underpinnings of soft computing techniques are drawn from purely mathematical concepts, this study is an essential contribution to the literature on soft sets.