Multi-level discrimination index for intuitionistic fuzzy coverings and its applications in feature selection

Intuitionistic fuzzy (IF) covering is a generalization of covering through replacing crisp sets with IF sets. Recently, IF covering has been widely considered in multi-attribute decision-making. However, there is a paucity of research on the uncertainty measure of IF coverings. Meanwhile, the uncertainty measure has close relationship with feature selection. The main purpose of this article is to investigate the uncertainty measure of IF coverings and develop a corresponding feature selection method. To begin with, for multiple IF coverings, we introduce four novel types of IF neighborhood operators and corresponding discrimination indices to measure their discrimination ability. Then, to analyze data from a fine granularity, we introduce the multi-level discrimination index (MLDI) for IF coverings based on $(a,b)$-aggregation functions. After that, we design a novel feature selection framework, which includes a fuzzy $c$-means clustering based generation method of IF coverings and a heuristic algorithm with conditional MLDI to find a relative reduction. Finally, we conduct a series of numerical experiments. The experimental results show that the proposed method can select better features than some existing methods for classification tasks. The obtained results bridge the gap in uncertainty measure of IF coverings and offer an effective feature selection approach for high-dimensional data classification.