决策粗糙集的一种新分类区域及相关比较分析

分类区域是粗糙集理论进行属性约简的重要基础, 量化扩张分类区域则是一个科研重点. 本文主要针对决策粗糙集, 在二分类层面提出一种新的分类区域, 并进行与两类常用分类区域的比较分析. 首先, 采用集合区域自然地提出了二分类决策粗糙集的新分类区域; 其次, 对两类常用决策粗糙集分类区域进行了退化研究; 进而, 对三种分类区域进行了比较分析, 得到了新分类区域的优势; 最后, 用具体实例进行了详细说明. 特别地, 对比于变精度粗糙集与贝叶斯粗糙集, 本文还分析了三种决策粗糙集分类区域扩大分类正域的机理. 本文构建的分类区域, 具有对于经典Pawlak分类区域的扩张性, 更加紧密地联系了集合区域的基础结构, 呈现出对于已有分类区域的改进性.

A new type of classification region and relevant comparison analyses of the decision-theoretic rough set

Classification regions underlie attribute reduction in rough set theory, and the quantitative and extended ones become a research emphasis. According to the decision-theoretic rough set, this paper mainly proposes a new type of classification region in the two-category level, and further conducts relevant comparison analyses with the two usual types. By set regions, a new type of classification region is naturally proposed in the two-category decision-theoretic rough set; then, degeneration studies are made for two existing types; furthermore, the relevant comparison analyses are conducted among the three types, and the advantage of the proposed type is exhibited; finally, a concrete example is provided for detailed illustration. In particular, the enlargement mechanism of classification-positive region is also analyzed for the three types by comparison with the variable precision rough set and bayesian rough set. The new type has the extended feature for the classical classification regions, becomes more closely related to the basic structure of set regions, and exhibits improvements for the previous two types.