An efficient approach to attribute reductions of quantitative dominance-based neighborhood rough sets based on graded information granules

Lower approximations of quantitative dominance-based neighborhood rough sets aim to enhance the consistency of dominance principles by filtering out pairs of objects that do not meet a predefined threshold. In this paper, we propose a novel approach to reflect dominance principles intuitively by defining generalized decisions based on certain decision rules in quantitative dominance-based neighborhood rough sets. Building upon this framework, we construct upward and downward graded information granules that enable the partitioning of the universe. We analyze the properties of the graded information granules and investigate their relationship with approximating qualities. Furthermore, we introduce the concept of importance degree to quantify the uncertainties of graded information granules under different attributes, which exhibits a monotonic behavior with respect to attributes. Subsequently, we design an attribute reduction method and explore an accelerated process by updating the generalized decisions. Finally, we conduct experiments on several public datasets to evaluate the efficiency of our methodology in terms of attribute reductions. The superiority of our proposed method on running time is illustrated by statistical hypothesis with paired t-test. Also the precision accuracy of reduct set is evaluated by rough sets and machine learning. Additionally, we demonstrate how the structures of graded information granules can be revealed by varying the parameters.