Attribute reduction in ordered information systems based on evidence theory

Attribute reduction is one of the most important problems in rough set theory. However, in real-world lots of information systems are based on dominance relation in stead of the classical equivalence relation because of various factors. The ordering properties of attributes play a crucial role in those systems. To acquire brief decision rules from the systems, attribute reductions are needed. This paper deals with attribute reduction in ordered information systems based on evidence theory. The concepts of plausibility and belief consistent sets as well as plausibility and belief reducts in ordered information systems are introduced. It is proved that a plausibility consistent set must be a consistent set and an attribute set is a belief reduct if and only if it is a classical reduction in ordered information system.     

基于随机优势关系的区间值信息系统

在区间值信息系统中引入了分布函数,得到了基于随机优势关系的区间值信息系统,构造了区间值信息系统的α-随机优势关系。利用Levy距离,对α-随机优势关系进行了计算,实例说明了方法的有效性。     

Attribute reduction based on evidence theory in incomplete decision systems

Attribute reduction is a basic issue in knowledge representation and data mining. This paper deals with attribute reduction in incomplete information systems and incomplete decision systems based on Dempster-Shafer theory of evidence. The concepts of plausibility reduct and belief reduct in incomplete information systems as well as relative plausibility reduct and relative belief reduct in incomplete decision systems are introduced. It is shown that in an incomplete information system an attribute set is a belief reduct if and only if it is a classical reduct and a plausibility consistent set must be a classical consistent set. In a consistent incomplete decision system, the concepts of relative reduct, relative plausibility reduct, and relative belief reduct are all equivalent. In an inconsistent incomplete decision system, an attribute set is a relative plausibility reduct if and only if it is a relative reduct, a plausibility consistent set must be a belief consistent set, and a belief consistent set is not a plausibility consistent set in general.     

基于优势关系下模糊目标信息系统的属性约简

在现实生活中,许多信息系统不仅是模糊的还是基于优势关系的。在基于优势关系下模糊目标信息系统中引入了广义决策的概念,提出了分别保持下广义决策、上广义决策、广义决策不变的三种不同约简,进一步给出了各属性约简的判定定理和辨识矩阵,提供了在优势关系下模糊目标信息系统属性约简的具体方法。通过实例验证了该方法的有效性,进一步丰富了粗糙集理论。     

基于决策熵的不完备信息系统的知识约简方法

为有效地解决不完备信息系统的知识约简,得到更优的决策规则集,研究了基于容差关系的决策熵在不完备信息系统中能客观反映决策规则的决策能力,提出了一种基于决策熵的不完备知识约简方法.该方法基于决策熵的思想,考虑了决策规则可信度和对象覆盖度,同时引入了容差关系,以决策熵的属性重要性度量为启发信息进行知识约简,最终得到确定的规则集.仿真实验结果表明了该算法的可行性.     

基于粗糙集理论的属性约简算法

粗糙集理论是一种新的数据挖掘方法,其主要思想是保持分类能力不变的情况下,通过属性约简,达到发掘知识并简化知识的目的.从大量数据发现知识时,属性约简是一个关键问题.在理解和分析基于粗糙集理论的数据挖掘算法基础上,提出了一个基于属性依赖度的属性约简算法.实验结果表明,该算法能更有效地对决策系统进行约简.     

Rule extraction based on granulation order in interval-valued fuzzy information system

Methods of fuzzy rule extraction based on rough set theory are rarely reported in incomplete interval-valued fuzzy information systems. This paper deals with such systems. Instead of obtaining rules by attribute reduction, which may have a negative effect on inducting good rules, the objective of this paper is to extract rules without computing attribute reducts. The data completeness of missing attribute values is first presented. Two different approximation methods are then defined. Two algorithms based on the two approximation methods, called MRBFA and MRBBA are proposed for rule extraction. The two algorithms are evaluated by a housing database from UCI. The experimental results show that MRBFA and MRBBA achieve better classification performances than the method based on attribute reduction.     

Rough set theory for the interval-valued fuzzy information systems

The notion of a rough set was originally proposed by Pawlak [Z. Pawlak, Rough sets, International Journal of Computer and Information Sciences 11 (5) (1982) 341-356]. Later on, Dubois and Prade [D. Dubois, H. Prade, Rough fuzzy sets and fuzzy rough sets, International Journal of General System 17 (2-3) (1990) 191-209] introduced rough fuzzy sets and fuzzy rough sets as a generalization of rough sets. This paper deals with an interval-valued fuzzy information system by means of integrating the classical Pawlak rough set theory with the interval-valued fuzzy set theory and discusses the basic rough set theory for the interval-valued fuzzy information systems. In this paper we firstly define the rough approximation of an interval-valued fuzzy set on the universe U in the classical Pawlak approximation space and the generalized approximation space respectively, i.e., the space on which the interval-valued rough fuzzy set model is built. Secondly several interesting properties of the approximation operators are examined, and the interrelationships of the interval-valued rough fuzzy set models in the classical Pawlak approximation space and the generalized approximation space are investigated. Thirdly we discuss the attribute reduction of the interval-valued fuzzy information systems. Finally, the methods of the knowledge discovery for the interval-valued fuzzy information systems are presented with an example.     

基于对称交叉熵的属性约简算法

针对交叉熵用来度量两个随机变量的差异程度时不满足对称性的问题,提出对称交叉熵的概念．研究在决策表的属性约简过程中决策属性集相对条件属性集对称交叉熵的变化规律,提出基于对称交叉熵的属性约简算法,同时还对其复杂度进行简单分析．实验分析表明,在多数情况下该算法能够得到决策表的最小相对约简．     

基于直觉模糊粗糙集的属性约简

针对Jensen下近似定义的局限性,提出一种新的等价类形式的近似算子表示,并将其推广到直觉模糊环境.在此基础上,将相对正域、相对约简、相对核等粗糙集的知识约简概念推广到直觉模糊环境,提出一种直觉模糊信息系统的启发式属性约筒算法.实例计算表明.该方法比Jensen的属性约简方法更为合理有效.     

一种基于相对区分表的属性约简算法

属性约简是知识获取中的核心问题之一。为了能较高效率地获得属性约简,在Rough Set理论基础上构造出了相对区分表,将基于相对区分表的属性约简的判定算法(JRA)作为子算法并结合归纳属性约简算法的优点,设计出了基于相对区分表的归纳属性约筒算法(RA)。算例说明该算法具有较高的属性约简效率,并能取得较好的约简结果。     

Fuzzy rough set theory for the interval-valued fuzzy information systems

The concept of the rough set was originally proposed by Pawlak as a formal tool for modelling and processing incomplete information in information systems, then in 1990, Dubois and Prade first introduced the rough fuzzy sets and fuzzy rough sets as a fuzzy extension of the rough sets. The aim of this paper is to present a new extension of the rough set theory by means of integrating the classical Pawlak rough set theory with the interval-valued fuzzy set theory, i.e., the interval-valued fuzzy rough set model is presented based on the interval-valued fuzzy information systems which is defined in this paper by a binary interval-valued fuzzy relations RF⁽ⁱ⁾(U×U) on the universe U. Several properties of the rough set model are given, and the relationships of this model and the others rough set models are also examined. Furthermore, we also discuss the knowledge reduction of the classical Pawlak information systems and the interval-valued fuzzy information systems respectively. Finally, the knowledge reduction theorems of the interval-valued fuzzy information systems are built.     

灰色信息系统基于集中有序关系下的知识约简

属性约简是粗糙集理论进行知识获取的核心问题之一。针对现实信息系统中属性值取值不确定的情况,结合灰色系统理论对集中有序关系进行扩展,建立了灰色信息系统中趋于某个标准值的一种偏好关系,并以集中有序关系下的优势度为启发式信息,给出了属性的重要性度量,在此基础上提出了适合于属性值为连续灰数的信息系统的属性约简算法,给出了约简的实际操作方法,并通过实例验证了算法的可行性。     

一种基于逻辑关系方程解的属性约简算法

粗糙集理论中所有的概念与运算都是通过代数学的等价关系和集合运算来定义的.在这种定义下,粗糙集理论的很多概念与运算的直观性较差.从逻辑代数的角度出发,建立了属性集与布尔矩阵以及逻辑关系方程之间的关系,给出了逻辑关系方程有解、有惟一解、有多个解的充分必要条件,在逻辑关系方程解的基础上给出了一种新的高效的属性约简算法.     

基于最大模的概念格属性约简算法

为了更加有效地对概念格中的属性进行约简,提出了一种基于属性最大模的概念格属性约简算法.根据形式背景中存在相同的属性列,对形式背景中的属性集合进行划分分类,并给出了一种新的属性特征识别方法.在此基础上,根据属性最大模之间的支配序性质,给出了基于最大模的概念格属性约简定理,揭示了属性最大模与属性特征的关系,并提出了一个算法.最后,通过一个实例表明了该算法的可行性与有效性.     

Approaches to knowledge reduction of covering decision systems based on information theory

In this paper, we propose some new approaches for attribute reduction in covering decision systems from the viewpoint of information theory. Firstly, we introduce information entropy and conditional entropy of the covering and define attribute reduction by means of conditional entropy in consistent covering decision systems. Secondly, in inconsistent covering decision systems, the limitary conditional entropy of the covering is proposed and attribute reductions are defined. And finally, by the significance of the covering, some algorithms are designed to compute all the reducts of consistent and inconsistent covering decision systems. We prove that their computational complexity are polynomial. Numerical tests show that the proposed attribute reductions accomplish better classification performance than those of traditional rough sets. In addition, in traditional rough set theory, MIBARK-algorithm [G.Y. Wang, H. Hu, D. Yang, Decision table reduction based on conditional information entropy, Chinese J. Comput., 25 (2002) 1-8] cannot ensure the reduct is the minimal attribute subset which keeps the decision rule invariant in inconsistent decision systems. Here, we solve this problem in inconsistent covering decision systems.     

基于动态容差关系的不完备信息表约简研究

在扩充粗糙集理论中,容差关系是一种处理不完备信息系统的工具.但容差关系可能会导致知识粒度较大,分类精度较低等问题.针对文献[2]提出的改进的容差关系,提出了动态容差关系得扩充粗糙集模型,设置了动态概率阈值.根据实际数据的不完备情况动态确立概率阈值,调整容差关系程度,仿真实验结果证明了该动态容差关系模型的有效性.     

基于多决策值等价类的属性约简

针对决策信息系统属性约简问题,引入条件属性的多决策值等价类概念,给出实现属性约简的必要条件,提出一种基于多决策值等价类的属性约简算法.该算法以单个条件属性的等价类的基为升序,对条件属性进行排序,逐一选择排序后的条件属性合并,直至合并后的条件属性子集的正域为全域,进一步判断其是否独立且不可区分关系与原信息系统的不可区分关系是否相同.当条件满足时,该条件属性子集即为决策信息系统的属性约简.通过实例验证了该算法求解属性约简的有效性.