Estimating the entropy of covering-based rough setapproximation operators

Rough set theory provides a robust framework for dealing with inconsistent data by utilizing equivalence relations to group indiscernible instances.A significant extension of this framework is the concept of covering-based rough sets, where equivalence relations are replaced with coverings.The effectiveness of covering-based rough sets in practical applications largely depends on the choice of an appropriate covering.To guide this selection, various metrics have been proposed to evaluate the quality of coverings, including entropy.While entropy serves as a valuable measure, its exact computation is often prohibitively expensive.In this paper, we propose an efficient method for estimating the entropy of covering-based rough set approximation operators, making the metric more feasible for practical use.We assess the accuracy of these estimates through experiments on both synthetic coverings and coverings for real-world datasets, the latter constructed using the Mapper algorithm, from the field of topological data analysis.