基于逻辑或的双量化粗糙集模型的计算分析与属性约简

摘要

Double quantification has a fundamental function for completely describing approximate space in rough set, and the rough set model based on logical OR of precision and grade is a basic extended model with double quantification. Aiming at this model, calculation analysis is mainly conducted, and attribute reduction in approximate space is further explored. Based on both basic structures and calculation formulas of model regions, macroscopic algorithm and structural algorithm are constructed. The analysis and comparison results show that the structural algorithm has more advantages in calculation complexity. Based on approximate space, basic properties on four-region preservation are discussed, and attribute reduction with the region preservation criterion is proposed and investigated. In particular, a type of extended quantitative reduction is obtained for the classical qualitative reduction. Some generalized thoughts are provided for optimal calculations and reduction applications of double-quantitative rough set models.%双量化具有完备刻画粗糙集近似空间的重要功能，而精度与程度的逻辑或粗糙集模型则是一类基本的双量化扩张模型。针对该模型进行深入的计算分析，进而探讨其在近似空间中的属性约简。利用区域结构，分析计算公式，在此基础上构建宏观算法和结构算法，算法的分析和比较结果说明结构算法具有较好的计算复杂性。基于近似空间讨论关于4区保持的基本性质，提出区域保持的属性约简，得到经典定性约简的一类扩张量化约简。该研究为双量化粗糙集模型的优化计算与约简应用提供泛化思路。