Essential Corrigenda to "Generalized approximation spaces generation from $\mathbb{I}_{j}$-neighborhoods and ideals with application to Chikungunya disease"

TL;DR

This paper corrects errors and inaccuracies in a previous work on generalized approximation spaces using $ ext{I}_j$-neighborhoods and ideals, providing revised results, counterexamples, and clarifications.

Contribution

It identifies and corrects errors in the prior research, offering accurate formulations, counterexamples, and improved understanding of generalized approximation spaces.

Findings

Corrected flawed proofs and results.

Provided counterexamples demonstrating inaccuracies.

Enhanced clarity and properties of the concepts.

Abstract

In the work "Generalized approximation spaces generation from $\mathbb{I}_{j}$-neighborhoods and ideals with application to Chikungunya disease, published in \emph{AIMS Mathematics}, \textbf{9}(4) (2024), 10050$-$10077," Al-Shami and Hosny introduced a novel approach for generating generalized neighborhoods through $\mathbb{I}_{j}$-neighborhoods with ideals, subsequently deriving new methods for generalized approximations based on these neighborhoods. However, several errors have been identified in their results, concepts, and methods, along with significant inaccuracies in the provided examples and comparison tables. This paper aims to address and correct these errors, providing counterexamples to illustrate the inaccuracies in the proposed results. Furthermore, we correct several flawed proofs and present the revised formulations of these results and concepts. Additionally, we offer properties and clarifications to enhance the understanding of these concepts.