In recent years, there has been considerable scholarly interest in the exploration of fuzzy \(\beta\) covering, which synergizes fuzzy set theory with rough set theory to formulate the concept of a fuzzy \(\beta\) neighborhood. This paper introduces an innovative discernibility measure pertaining to fuzzy \(\beta\) coverings, aimed at characterizing the distinguishing capability of a fuzzy \(\beta\) covering family. To this end, the parameterized fuzzy \(\beta\) neighborhood is introduced as a methodological tool to delineate the similarity between samples and evaluate the distinguishing capacity of a particular fuzzy \(\beta\) covering family. Subsequently, we propose a novel uncertainty measure, termed relative decision self-information with respect to fuzzy \(\beta\) covering, by employing fuzzy rough approximations and the concept of self-information. This measure is designed to assess the classification efficacy of attribute subsets. A comprehensive analysis of the measure is conducted, highlighting its enhanced effectiveness in attribute reduction due to its integration of both lower and upper approximations of a fuzzy decision. Finally, an attribute reduction algorithm is utilized to address the issue of redundant fuzzy coverings. Comprehensive experimental results indicate that the proposed method effectively assesses uncertainty across diverse datasets and demonstrates enhanced efficiency in attribute reduction relative to several existing algorithms.
