Double-quantitative distance measurement and classification learning based on the tri-level granular structure of neighborhood system

In terms of neighborhood rough sets, the tri-level granular structure of neighborhood system (carrying the neighborhood granule, swarm, and library) establishes a granular computing mechanism for knowledge-based learning. However, its hierarchical exploration is inadequate, while its measurement can be extended for robust applications. Regarding this tri-level granular structure, the double-quantification technology is novelly introduced to make a thorough investigation, especially on the double-quantitative distance measurement and classification learning. Firstly, the size valuation and logical operation are hierarchically supplemented at higher levels. Secondly, the relative and absolute distances of bottom neighborhood granules are linearly combined to a double-quantitative distance, and all the three types of distances are promoted to both the middle swarm level and the top library level. Finally, the double-quantitative distance powerfully characterizing the difference of neighborhood granules is utilized to generate a double-quantitative classifier KNGD, and relevant data experiments show that this new classifier outperforms or balances two existing classifiers, i.e., the relative classifier KNGR and absolute classifier KNGA. By theory, example, and experiment, this study hierarchically perfects the tri-level granular structure of neighborhood system, and the corresponding double-quantification integration and extension offer the robust knowledge measurement and effective classification learning.