Logical distance-based fuzzy rough set model and its application in feature selection

Fuzzy rough set models based on binary similarity relations and their applications in feature selection have been explored extensively. However, distance-based relations, a natural type of binary relations, are seldom directly applied in fuzzy rough set models, and let alone in feature selection algorithms. Additionally, the existing feature selection algorithms based on fuzzy rough set theory frequently encounter challenges such as the inflexibility of selection rate adjustment, the associated high computational costs, etc. To counter these issues, we introduce a concept of logical distance functions and use it to establish a kind of fuzzy rough set models. We analyze the uncertainty of decision tables using related fuzzy rough approximation operators. Then we propose a novel uncertainty index based on the difference between the distance of decision attributes and that of condition attributes. Building upon this foundation, we design a forward greedy feature selection algorithm based on this uncertainty index. Compared to existing state-of-the-art feature selection algorithms, experimental results validate the effectiveness and efficiency of our approach, particularly demonstrating superior efficiency.