优势关系下的集值序值信息系统

集值序值信息系统分为合取/析取集值序值信息系统,分别深入分析了合取/析取集值序值信息系统已有优势关系的局限性,并对其不合理情形进行了讨论,进而提出了对对象进行更好划分的新优势关系。在此基础上,分别构建了优势关系下的合取/析取集值序值信息系统的粗集模型,并通过典型例子验证了该方法的有效性。     

集中有序集值信息系统

集值信息系统是完备信息系统的一种推广,按照语义可划分为合取集值信息系统和析取集值信息系统。属性偏好关系也有两种：属性递增偏好有序和属性递减偏好有序。提出一种新的属性偏好关系,建立了一种新的优势关系。这种优势关系能够表示一类属性偏好既不是递增有序也不是递减有序,而是趋近于某个标准值的情形,称这样的优势关系为属性集中有序,它可应用于某些集值信息系统。     

集值决策信息系统的知识约简与规则提取

本文用集值信息系统描述不完备信息系统。在集值信息系统中定义了两种不同的关系：相容关系和优势关系,给出了两种不同关系下集合的上下近似概念及其性质。研究了集值决策信息系统在两种不同关系下的广义决策约简,得到了广义决策约简的判定定理和辨识矩阵,从而得到了约简的具体操作方法。最后,基于两种关系从集值决策信息系统提取了最优广义决策规则,并进行了讨论。     

基于概率的有序信息系统

若信息系统中所有的条件属性都是偏好有序的,则称此信息系统为有序信息系统。首先,分析了区间值有序信息系统没有蕴含属性值区间上的概率分布信息的缺点,建立了一种基于概率的有序信息系统。然后,在这种信息系统上,研究了关于单调偏好有序属性和非单调偏好有序属性的二元偏好关系,建立了一种基于概率的优势关系,定义了基于这种优势关系的粗糙集模型。最后研究了基于概率的有序决策表及其决策规则。     

集值序信息系统的信息熵和知识粒度

针对已有文献中二元优势关系定义过于宽松的不足,在集值序信息系统中结合对象间的不同优势程度,提出δ-优势关系的概念;基于δ-优势关系,将信息熵和知识粒度引入集值序信息系统中进行不确定性的度量。结论表明提出的信息熵和知识粒度可以精确地度量集值序信息系统的不确定性。     

区间集值信息系统中的粗糙集理论

介绍集值信息系统和区间值信息系统,并提出了同时具有这两种系统特点的区间集值信息系统.依据属性值的语义关系,将区间集值信息系统分为两类：析取（I型）和合取（II型）系统,并对其分别提出了基于优势关系的粗糙集模型,讨论了相关性质.最后用实例分析验证了所提出系统的有效性.     

Dominance relation and rules in an incomplete ordered information system

Rough sets theory has proved to be a useful mathematical tool for classification and prediction. However, as many real‐world problems deal with ordering objects instead of classifying objects, one of the extensions of the classical rough sets approach is the dominance‐based rough sets approach, which is mainly based on substitution of the indiscernibility relation by a dominance relation. In this article, we present a dominance‐based rough sets approach to reasoning in incomplete ordered information systems. The approach shows how to find decision rules directly from an incomplete ordered decision table. We propose a reduction of knowledge that eliminates only that information that is not essential from the point of view of the ordering of objects or decision rules. © 2005 Wiley Periodicals, Inc. Int J Int Syst 20: 13–27, 2005.     

Set-valued information systems

Set-valued information systems are generalized models of single-valued information systems. Incomplete information systems can be viewed as disjunctively interpreted set-valued information systems. Since some objects in set-valued information systems may have more than one value for an attribute, so we define tolerance relation and use the maximal tolerance classes to classify the universe of discourse. In order to derive optimal decision rules from set-valued decision information systems, we propose the concept of relative reduct of maximal tolerance classes, and define a kind of discernibility function to compute the relative reduct by Boolean reasoning techniques. Finally, we define three kinds of relative reducts for set-valued information systems and used them to evaluate the significance of attributes.     

基于相似关系的集值决策信息系统的属性约简

属性约简是粗糙集理论中重要研究内容,由于现实应用领域中决策信息系统往往呈现出不完备性特点,为此,首先将不完备决策表转化为集值决策信息系统,并详细分析了集值决策信息系统下基于相似关系的分布约简和最大分布约简,在此基础上,构造了一种基于可区分对象集的属性约简算法,算法利用可区分对象集的集对,计算极小析取范式求解出所有的分布约简和最大分布约简。最后,利用实例分析验证了算法的有效性。     

集值信息系统基于优势关系下的知识约简

在集值信息系统中,把所有属性看成是一种准则,然后利用属性集值的取值分布定义了两种不同的优势关系,它们都是经典信息系统上优势关系的推广.针对这两种优势关系,给出了集值信息系统的知识约简与对象的相对约简的判定,定义了基于区分矩阵的区分函数,并利用布尔推理方法得到了这两种优势关系下的知识约简与对象的相对约简的具体操作方法.     

优势关系下模糊目标信息系统的决策规则优化

利用基于优势关系的模糊粗糙集模型,讨论了模糊决策信息系统中优化序决策规则的获取问题。利用优势关系定义了模糊目标信息系统中对象的三种属性约简。给出了它们的判定定理,构造相应的区分函数,利用布尔推理技术计算对象的属性约简,得到三类新的优化序决策规则。     

基于不协调置信优势原理关系的知识约简

置信优势关系粗糙集用于处理不完备有序决策系统,知识约简是核心问题之一。在不完备有序决策系统下区分两个对象需考虑决策值之间的偏好关系,因此给出置信优势原理关系的定义,将满足此关系的对象视为是不可区分的。提出不协调优势原理关系下的约简定义,进一步给出约简的判定定理和辨识矩阵,从而提供了在不完备有序决策系统下新的知识约简方法。通过实例验证了新的知识约简方法的有效性。     

Graded dominance interval-based fuzzy objective information systems

Dominance interval-based fuzzy objective information systems are generalized models of single-valued fuzzy information systems. By introducing a graded dominance relation to dominance interval-valued fuzzy objective information systems, we establish a graded dominance interval-valued rough set model (RSM), which is mainly based on replacing the indiscernibility relation in classical rough set theory with the graded dominance interval-valued relation. Furthermore, in order to simplify knowledge representation and extract nontrivial simpler graded dominance interval fuzzy decision rules, we propose two attribute reduction approaches to eliminate the redundant condition attributes that are not essential from the viewpoint of graded dominance interval-valued fuzzy decision rules. These results are helpful for decision-making analysis in dominance interval-valued fuzzy objective information systems.     

Entropy measures and granularity measures for interval and set-valued information systems

In many practical situations, some of the attribute values for an object may be interval and set-valued. The interval and set-valued information systems have been introduced. According to the semantic relation of attribute values, interval and set-valued information systems can be classified into two categories, disjunctive (type 1) and conjunctive (type 2) systems. This paper mainly focuses on semantic interpretation of type 1. Then, a new fuzzy preference relation for interval and set-valued information systems is defined. Moreover, based on the new fuzzy preference relation, the concepts of fuzzy information entropy, fuzzy rough entropy, fuzzy knowledge granulation and fuzzy granularity measure are studied and relationships between entropy measures and granularity measures are investigated. Finally, an illustrative example to substantiate the theoretical arguments is given. These results may supply a further understanding of the essence of uncertainty in interval and set-valued information systems.     

集值决策信息系统的知识约简与属性特征

本文定义了集值决策信息系统中的一种新的关系,给出了在这种关系下协调集值决策信息系统属性约简的判定定理和辨识矩阵,从而得到了知识约简的具体操作方法,并讨论了在属性约简中起不同作用的属性分类及其特征。定义了不协调集值决策信息系统的分配协调集,给出了一种将不协调集值决策信息系统转化为广义协调近似空间的方法,并证明了不协调集值决策信息系统的分配协调集就是广义协调近似表示空间的协调集。     

集值信息系统基于邻域关系的属性约简

集值信息系统是完备信息系统的广义形式,其中的一些对象在某些属性下的取值可能不止一个,反映的是信息的不确定性。在集值信息系统上引入对象的邻域关系,并以每个对象的邻域作为基本集,建立了集值信息系统的粗糙集方法。为了简化知识的表示,进一步在集值信息系统上提出了邻域协调集与邻域约简的概念,并讨论了这种邻域协调集的性质与判定。最后通过区分函数得到了计算集值信息系统邻域约简的方法。     

基于辨识矩阵的不完备多粒度约简

面向具有缺失属性值的不完备数据,文中从辨识矩阵的角度构造不完备信息系统和不完备决策系统的多粒度约简结构.首先,讨论基于悲观和乐观多粒度近似的不完备信息系统的约简性质,构造不完备信息系统和不完备决策系统的3种多粒度辨识矩阵.然后,理论性证明通过对构造的辨识矩阵进行析取、合取逻辑运算,可精确得到不完备信息系统和不完备决策系统的所有多粒度近似约简.最后通过实例验证文中多粒度约简方法的有效性和实用性.     

相对知识粒度序决策表的属性约简方法

序决策表中的知识约简越来越受到关注,在优势类和知识粒度的基础上,引入了序决策表中的一种知识相对粒度,度量了属性集在序决策表中的相对不确定性,进而给出了属性相对重要度的定义。并设计了序决策表的一种启发式属性约简算法,通过实例分析和验证了算法的有效性。     

Dominance-based rough set approach and knowledge reductions in incomplete ordered information system

Many methods based on the rough set to deal with incomplete information systems have been proposed in recent years. However, they are only suitable for the incomplete systems with regular attributes whose domains are not preference-ordered. This paper thus attempts to present research focusing on a complex incomplete information system—the incomplete ordered information system. In such incomplete information systems, all attributes are considered as criterions. A criterion indicates an attribute with preference-ordered domain. To conduct classification analysis in the incomplete ordered information system, the concept of similarity dominance relation is first proposed. Two types of knowledge reductions are then formed for preserving two different notions of similarity dominance relations. With introduction of the approximate distribution reduct into the incomplete ordered decision system, the judgment theorems and discernibility matrixes associated with four novel approximate distribution reducts are obtained. A numerical example is employed to substantiate the conceptual arguments.     

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.