基于代数观点的邻域区间集粗糙集模型研究

描述部分已知概念的区间集粗糙集是对经典粗糙集的拓展,其属性值概念由上下边界集来描述,具有较好的不确定性刻画能力,能够有效促进数据挖掘、信息度量和知识发现等实际应用。现有研究主要针对离散型数据对象,不能很好地处理现实世界中大量存在的连续型数据对象,因此区间集粗糙集具有改进的空间。该文引入邻域关系,通过Hausdorff距离函数定义区间集邻域粒子,由此构造邻域区间集粗糙集模型,并从代数观点研究其相关概念及性质,最后用实例分析验证其有效性。

乐观多粒度区间集粗糙集

Pawlak粗糙集基于单个粒空间(一个等价关系)建立了上、下近似来刻画目标概念,而乐观多粒度粗糙集则利用多个粒空间(一族等价关系)对目标概念进行近似描述,是Pawlak粗糙集的一种扩展.区间集通过上、下界给出了概念的外延范围.在区间集粗糙集的基础上,提出了乐观多粒度区间集粗糙集,研究了它们的性质,并进一步给出了单个和多个粒空间下几种区间集粗糙集和乐观多粒度区间集粗糙集之间的关系.

基于依赖度的区间集决策信息表属性约简

区间集决策信息表拓展了经典决策信息表,但其属性约简研究较少。针对区间集决策信息表存在的问题,采用模型正域及相关依赖度提出属性约简及其启发式约简算法。在区间集粗糙集模型中,定义关于决策分类的正域与依赖度,证明粒化单调性等性质。提出基于依赖度的属性约简,设计启发式约简算法。实例分析与数据实验表明,设计的基于依赖度的启发式约简算法是有效的,所得结果有利于依赖学习与特征优化。

区间集概率粗糙集的单调性

概率粗糙集利用条件概率和两个阈值给出被近似集合和等价类之间满足一定包含程度的近似刻画。区间集通过上、下界给出了一个概念的外延范围。本文将被近似集合推广到区间集,提出了刻画概念外延范围的区间集概率粗糙集,研究了它们的性质。讨论了当被近似的区间集发生变化时,区间集概率粗糙下、上近似的单调性;进一步研究了当两个阈值单调时,相应的区间集概率粗糙下、上近似的单调性。

A Decision Model Based on Grey Rough Sets Integration with Incomplete Information

In this paper, for multiple attribute decision-making problem in which attribute values are interval grey numbers and some of them are null values, a decision model based on grey rough sets integration with incomplete information is proposed. We put forward incidence degree coefficient formula for grey interval, by information entropy theory and analysis technique, the method and principle is presented to fill up null values. We also establish the method of grey interval incidence cluster. Because grey system theory and Rough set theory are complementary each other, decision table with preference information is obtained by the result of grey incidence cluster. An algorithm for inducing decision rules based on rough set theory and the dominance relationship is presented. In some extent, this algorithm can deal with decision-making problem in which the attribute values are interval grey numbers and some of them are null values. Contrasted with classical model of cluster decision-making, the algorithm has an advantage of flexibility and compatibility to new information.