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The paper presents a novel method for generating increasing and decreasing soft rough set approximations that addresses limitations of a previous approach by Shawkat et al. [3], which su ered from issues such as the modi ed soft lower approximation not being equal to the universe set and the modi ed soft upper approximation being empty. The proposed method is described through propositions and examples and can be applied to both qualitative and quantitative real-world problems. It is compared to the classical soft rough set model and aims to improve accuracy by converting partial ordered relations to linear ordered relations, such as directed or total directed relations, where every subset becomes crisp. The concepts and results are illustrated through examples. Overall, the new method o ers a generic solution that addresses the shortcomings of the previous approach and can improve the accuracy of soft rough set approximations in various domains. Mathematics Subject Classi cation (2020): 03C55, 03E04, 54G20 and 92C50.

This study expands the idea of a K−proximity relation and its characteristics to a soft K−proximity by creating various forms of it from a soft K−proximity. Additionally, it investigates the properties of a soft K−proximity neighborhood, soft K−proximity mappings, and the product of soft K−proximity spaces.