Near open generalizations of rough sets and their applications

Abstract

Abstract Background The concept of near open sets is a potent tool that empowers researchers to achieve a more encompassing approximation of rough sets, thereby enhancing the accuracy of measurements. The evolution of rough set theory into various generalized forms, based on topological structures, has emerged as a significant approach in the realm of knowledge discovery within databases. Results This paper’s primary contribution lies in the introduction of a novel category of generalized near open sets, termed “inverse simply open sets,” within the context of the $$\text{j}$$ j -neighborhood space. The paper proposes diverse methods for extending the Pawlak’s rough approximations leading to the definition of new approximations in the $$\text{j}$$ j -neighborhood space. By employing these newly introduced generalizations, we establish fresh connections between two pivotal theories, namely “general topology and rough set theory”. Through a comprehensive investigation, we conduct multiple comparisons between our methodology and classical approaches. Furthermore, we showcase practical applications of these techniques within real-life scenarios, demonstrating their utility in decision-making processes. Conclusions We reduced the data’s ambiguity while increasing its accuracy measure. As a result, we may conclude that the proposed approximations were more precise than earlier techniques and contributed to the elimination of data ambiguity in real-world scenarios requiring accurate decisions.

Keywords

• Rough sets
• Topological space
• $$\text{j}$$ j -Near open set
• $$\text{j}$$ j -Neighborhood spaces
• $${\text{b}}_{\mathrm{j}}*$$ b j ∗ -Open set
• j-Inverse simply open sets