Attribute selection for incomplete decision systems by maximizing correlation and independence with mutual granularity

Rough set theory has been widely used in attribute selection. However, there are few researchers who have explored the relationship between attributes from the perspective of knowledge granularity. Additionally, existing attribute selection methods are mostly tailored for complete decision systems and are not applicable to incomplete ones. In light of the aforementioned challenge, this paper primarily focuses on addressing the issue of attribute selection for incomplete decision systems by utilizing the correlation among attributes formed through knowledge granularity. Firstly, the concept of mutual granularity is defined by introducing discernment granularity and conditional discernment granularity into incomplete decision systems. Secondly, an attribute selection algorithm based on mutual granularity is presented for incomplete decision systems. Thirdly, a novel method for enhancing mutual granularity is proposed, which takes into account both the independence and correlation among candidate and selected attributes, with the aim of quantifying the uncertainty inherent in incomplete decision systems. Fourthly, an attribute selection algorithm based on enhanced mutual granularity is proposed. Finally, experimental results show that the proposed attribute selection method can effectively select the more relevant attributes with lower redundancy, thereby demonstrating strong classification capabilities when applied to incomplete decision systems.