Tri-level attribute reduction based on neighborhood rough sets

Tri-level attribute reduction is an interesting topic that aims to reduce the data dimensionality from different levels and granularity perspectives. However, existing research exhibits limitations, mainly in handling symbolic data, lack of effective reduction algorithms, and scarcity of data experiments and performance evaluations, which would be an obstacle to the further development of tri-level attribute reduction in theory and application. Hence, we systematically investigate tri-level attribute reduction based on neighborhood rough sets (NRSs) for numerical data. We first give the class-specific and object-specific attribute reduction conditions based on NRS, respectively. Furthermore, we explore and analyze relationships of tri-level reducts. From the perspective of forward and backward reduction, we propose algorithms of class-specific attribute reduction based on dependency degree, and object-specific reduction algorithms based on inconsistency degree. Finally, we introduce a novel metric to validate the efficiency of specific class and specific object attribute reductions. The results of data experiments show the feasibility and effectiveness of tri-level attribute reduction based on NRS in data analysis.