Innovative methods for generalized rough approximation spaces, inspired by grills and maximal neighborhoods

Alreshidi, B.; Aldawood, M.; Azzam, A. A.

doi:10.47974/JIM-2421

Open Access Research Article

Innovative methods for generalized rough approximation spaces, inspired by grills and maximal neighborhoods

B. Alreshidib.alreshidi@psau.edu.saDepartment of MathematicsFaculty of Science and HumanitiesPrince Sattam Bin Abdulaziz UniversityAlkharj, 11942, Saudi ArabiView full profile → , M. Aldawoodm.aldawood@psau.edu.saDepartment of MathematicsFaculty of Science and HumanitiesPrince Sattam Bin Abdulaziz UniversityAlkharj, 11942, Saudi ArabiView full profile → , ^*A. A. AzzamCorresponding authorazzam0911@yahoo.comAffiliation 1Department of MathematicsFaculty of Science and HumanitiesPrince Sattam Bin Abdulaziz UniversityAlkharj, 11942, Saudi ArabiAffiliation 2Department of MathematicsFaculty of scienceNew Valley UniversityElkharga, 72511, EgyptView full profile →

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pp. 477–490Vol. 29Issue 2February 2026DOI: 10.47974/JIM-2421XML

Received:: 10 Jun 2025
Published Online:: 14 Feb 2026
Article type:: Research Article
Language:: EN
Article no.:: JIM-2421
Pages:: 477–490

Abstract

Rough set theory is a well-known mathematical framework for dealing with data that is unclear or ambiguous, especially through the use of approximation spaces. These approximation spaces are important for sorting data into sets by telling the difference between elements that can be defined and those that can’t. However, traditional techniques often face challenges in boundary areas where classification remains ambiguous. To alleviate these limitations, the current work sought to explore innovative approaches that incorporate four distinct types of maximal neighborhoods with grill structures to enhance the accuracy of rough approximation spaces. This research seeks to devise novel methodologies to improve approximation precision and reduce boundary areas, hence optimizing data classification. This paper examines the characteristics of these innovative tactics through theoretical analysis and numerical examples. The results show that using maximal neighborhoods with grill structures greatly improves classification accuracy compared to standard rough set methods, with Neighborhood Type 4 being the most effective. The study shows that the number of boundary regions has gone down a lot, which means that the classification process is more accurate and careful. A comparative analysis with existing methods illustrates the benefits of the proposed methodology in terms of approximation precision and classification efficacy. This study progresses rough set theory by introducing innovative approaches to improve accuracy and reliability in data classification inside uncertain environments.

Keywords

Rough set theory Maximal neighborhoods Grill structures Approximation accuracy Data classification Boundary region

Subject Classifications

03E7203E9991B0654A05

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