Attribute reduction based on weighted neighborhood constrained fuzzy rough sets induced by grouping functions

Abstract

Attribute reduction can extract the most critical attributes from multi-dimensional datasets, this reduces data dimensionality, simplifies data processing and analysis, and the fuzzy rough set (FRS) model-based attribute reduction method is one of the most commonly used attribute reduction methods. In this paper, we construct a new FRS model named G-WNC-FRS for attribute reduction by introducing a new inter-sample distance and two aggregation functions. Specifically, we first introduce the weighted neighborhood constrained distance between samples to make the difference in attributes between different class samples obvious. Then we introduce two not necessarily associative aggregation functions, overlap and grouping functions, to replace the commonly used triangular norms and triangular conorms in FRS model. Finally, we design G-WNC-FRS-based attribute reduction algorithm to select important attributes for classification tasks. Numerical experiments on 11 datasets demonstrate that the attribute reduction algorithm based on G-WNC-FRS has a strong ability to eliminate redundant attributes. Additionally, noise experiments and sensitivity experiments on 4 datasets show that the algorithm has high noise immunity and is able to adapt to different types of datasets.