基于双论域笛卡尔积的粗糙熵与知识粒度

基于笛卡尔积,确立双直积论域覆盖空间,并研究其中的粗糙熵与知识粒度.首先,将双论域近似空间诱导出两个单论域覆盖空间,构建双直积论域覆盖空间.将双论域粗糙熵与知识粒度定位于一个单论域覆盖空间.通过结构模拟与粒替换,确定对称单论域覆盖空间与双直积论域覆盖空间的粗糙熵与知识粒度.对于三套双度量,得到相关的双量和、上下确界、粒化单调性及三支线性组合性.最后,通过数据模拟与仿真实验验证度量构建与理论性质的有效性.

Rough Entropy and Knowledge Granularity Based on Cartesian Product of Double Universes

According to the Cartesian product,the covering space on two-dimensional direct product universe is constructed, and the corresponding rough entropy and knowledge granularity are investigated. Firstly, two single-universe covering spaces are induced by double-universes approximate space, and two-dimensional covering space is constructed.Then, the rough entropy and knowledge granularity based on double-universes are positioned at a single-universe covering space, and the two measures are determined in covering spaces on symmetrical single-universe and compositive two-dimensional universe by structural simulation and granular replacement. For the three sets of double metrics, the double-metrics sum, supremum and infimum, granulation monotonicity and three-way linear combination are achieved. Finally, data simulation and simulation experiment verify the effectiveness of the measure construction and the theoretical properties.