基于边界域的知识粗糙熵与粗集粗糙熵  

Entropy of Knowledge and Rough Set Based on Boundary Region

作　　者：程玉胜[1] 张佑生[1] 胡学钢[1] 

机构地区：[1]合肥工业大学计算机与信息学院

出　　处：《系统仿真学报》2007年第9期2008-2011,共4页Journal of System Simulation

基　　金：安徽省自然科学基金(070412061);国家自然科学基金(60575023);博士学科点专项基金(20050359012)

摘　　要：传统的知识粗糙熵表征了知识整体的统计特征,是总体的平均不确定性的量度,知识和粗集的不确定性值被放大。从Pawlak拓扑的角度,给出了一种基于边界域的知识粗糙熵新定义,并修正了粗集粗糙熵的定义,集合的不确定性可以通过边界域来描述,能更精确的度量知识不确定性;证明了知识粗糙熵和修正后的粗集粗糙熵都随着信息粒度的变小而单调减少等重要结论。最后,通过弹簧振子系统定性仿真例子,结合定性推理技术,构造属性约简的启发式算法,消去定性描述中的冗余,获得了其系统的定性微分方程,说明了粗集理论在定性推理与定性仿真技术中的重要应用价值。Traditional rough entropy of knowledge demonstrates the whole statistical features of knowledge and is a measurement of the whole average uncertainty, and as a result, the uncertainty of knowledge and rough set are magnified. A new definition of knowledge rough entropy is discussed based on boundary region from the aspect of Pawlak topology and the definition of rough entropy of rough set is rectified. This definition accurately reflects an idea that the uncertainty of set can be described by boundary region, which will measure knowledge and rough set uncertainty more accurately. Meanwhile, it thus proves such important conclusions as both rough entropy of knowledge and rectified rough entropy of rough set both monotonously reduce with the diminishing of information granularity. Lastly, through an example about qualitative simulation of physical system of spring, combining qualitative reasoning technology with knowledge information entropy based on rough sets theory, a heuristic algorithm for knowledge reduction is proposed which could be used to eliminate the redundancy in the qualitative description and the qualitative differential equations of this system were obtained. Simulation result shows that the rough sets theory is of good reliability and prospect in qualitative reasoning and qualitative simulation.

关 键 词：粗集理论 粗糙熵 不确定性度量 边界域 定性推理 定性仿真 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]