Feature selection based on information entropy with variable precision fuzzy mixed granularity

Fuzzy rough set theory allows defining different fuzzy relationships for different attribute types to quantify the similarity between objects. Meanwhile, information entropy, a powerful tool for quantifying uncertainty, is further extended within this framework to fuzzy rough set-based information entropy. The granularity division of traditional fuzzy entropy usually relies on fuzzy similarity relationships. In this paper, we first define variable precision mixed fuzzy granularity, combine it with fuzzy entropy to construct the information entropy based on variable precision mixed fuzzy granularity, and define fuzzy granularity entropy (FGe), fuzzy granularity joint entropy (FGJe), fuzzy granularity conditional entropy (FGCe), and fuzzy granularity mutual information (FGMI), and study the relationship and related properties among them. Then the importance function for evaluating the importance of features is constructed using FGMI, which lays the foundation for the feature selection (FS) algorithm. To evaluate the performance of the algorithm, numerical experiments are conducted on 15 public datasets and compared with other algorithms. The experimental results show that the method shows good adaptability and FS ability for handling different types of data.