Roughness of Bipolar Soft Sets via Ideals and its Applications

Abstract

The essential objectives of this study are to propose enhancements and modifications to the bipolar soft rough sets methodology by incorporating ideals. The paper introduces two distinct types of ideal bipolar soft approximation operators, which serve as extensions to the existing bipolar soft rough approximation operator. Furthermore, two approaches are employed to establish and investigate a novel type of bipolar approximation space, referred to as the bi-ideal bipolar soft approximation space. This work also explores the relationships between these proposed techniques and previous methods, detailing their respective characteristics and advantages. By enlarging the ideal bipolar lower approximations and reducing the ideal bipolar upper approximations, these strategies significantly reduce the ambiguity and uncertainty within the decision-making process. The paper additionally outlines several key metrics related to ideal bipolar soft spaces, enriching the theoretical understanding of these structures. A practical application of the proposed spaces is presented in the context of multi-attribute group decision-making (MAGDM) problems. To support this, an algorithm is developed to facilitate the selection of the most optimal alternative from a range of options, accompanied by a practical example to demonstrate its effectiveness. The analysis highlights the reliability, adaptability, and superiority of the proposed MAGDM framework. Furthermore, a concise comparison with existing methodologies is provided, showcasing the advantages and robustness of the proposed approach in addressing complex decision-making challenges.