Extending Approximations Spaces Using Nearly Open Sets, Subset Neighborhoods, and Ideals: A Medical Application

Abstract

The close resemblance between rough sets and topology arises from the analogy between topological operators and rough approximations. This connection fosters combined studies between them. Therefore, this paper is created new approximations by leveraging topological concepts. Additionally, it is depicted that how a specific combination of ideals is utilized to approach rough from a topological perspective. As, ideals are valuable topological tools for reducing uncertainty. So, ideal structures are used to create new generalized approximation spaces that minimize vagueness. Initially, new topologies concepts are proposed relying on various types of the subset neighborhoods via ideals, and their relationships are analyzed. Thereafter, new approximations are derived from the proposed topological concepts. Moreover, all the present results are compared with earlier models to highlight the advantages and merits of the current technique. The present manners are more precise than previous approaches as they are particularly valuable for reducing vagueness. More importantly, three distinct perspectives are presented to elicit membership functions. To emphasize the importance of this paper, a numerical example related to Chikungunya disease is provided. This enables specialists to accurately assess the factors influencing Chikungunya disease. So, specialists and consultants can handle insufficient data regarding disease symptoms, resulting in easier and more accurate patient diagnoses. The study wraps up with a summary and proposals for future research.