基于描述子的信息系统属性约简及决策规则优化

在不完备信息系统中,利用描述子来表达决策规则．引入描述子简化和约简的概念,给出描述子的区分函数,利用布尔推理理论求取描述子的约简,并由此获取信忠系统的优化决策规则．从保持原系统决策信息的角度出发,定义信息系统的Gs-约简和Ds-约简,G-约简和D-约简．通过对这几种约简及其关系的讨论,从不同角度考察了信息系统中属性的重要性．以上结果对于完备信息系统同样有效．     

不完备信息系统中基于相似关系的知识约简

以具有丢失型未知属性值的不完备信息系统为研究对象,根据非对称相似关系,讨论了知识约简问题.在不完备决策系统中,引入了近似、粗糙分布约简以及广义决策约简,讨论了它们之间的相互关系,给出了近似分布约简的判定定理、可辨识矩阵以及约简公式,并进行了实例分析,为从不完备信息系统中获取知识提供了新的理论基础与操作手段.     

不完备系统中基于优势关系的最优可信规则获取

以具有遗漏型未知属性值的不完备目标信息系统为研究对象,根据优势关系,提出升序和降序最优可信规则.给出基于优势关系的描述子的概念,由此获得不完备目标信息系统中的升序和降序可信规则.定义了基于区分矩阵的区分函数用以计算对象的升序和降序约简,从而获得升序和降序最优可信规则,为从不完备目标信息系统中获取规则提供了新的理论基础与技术手段.     

不完备模糊决策信息系统的粗集模型与精度约简

在不完备信息系统和模糊决策信息系统概念及其粗集模型的基础上,本文提出了不完备模糊决策信息系统的概念,给出了不完备模糊决策信息系统的粗糙集模型,它既不同于不完备近似空间上的信息系统又不同于完备空间上的模糊决策信息系统。该模型是完备模糊决策信息系统和经典决策信息系统粗糙集模型的推广。文中还给出了系统的精度约简概念及其约简算法。     

不完备模糊决策系统的启发式约简算法

在不完备信息系统和模糊决策信息系统的基础上,提出一种基于相容关系的不完备模糊决策信息系统的粗糙集模型,并重新定义了不完备模糊决策信息系统上任意子集的上下近似,给出了基于属性依赖度的启发式知识约简算法,通过实例验证了算法的可行性.     

基于扩展粗糙集模型的集值不完备信息系统决策研究

在客观世界中信息系统往往是不完备的。该文将粗糙集模型经过扩展后应用于属性值为集合值的不完备信息系统,给出了几种不同的上下近似集定义,着重建立和分析了一种不完备决策表,研究了对应的粗糙集模型扩展后的属性约简的方法,并根据约简生成了决策规则。     

不完备信息系统中的否定决策规则和知识约简

为了从不完备信息系统中获得否定决策规则,提出了描述子否定支撑集的概念,基于此定义了下、上近似集合,讨论其性质,并给出了如何通过该模型获取确定性和可信性否定决策规则的方法．为了便于应用,给出基于分辨矩阵的否定决策规则约简的方法,实例分析的结果表明了该方法的有效性．     

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.     

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。     

不完备区间值信息系统中的粗集理论

针对不完备区间值信息系统,提出了一种用于分类的偏序关系,并给出了计算这种偏序关系约简的实际操作方法．在不完备区间值决策系统中,根据基于偏序关系的粗糙集模型,引入了上、下近似约简的概念．上、下近似约简是保持所有决策类的下、上近似都不发生变化的最小属性子集,借此获取简化的决策规则．     

Decision-relative discernibility matrices in the sense of entropies

Abstract

In rough set theory, attribute reduction is a basic issue, which aims to hold the discernibility of the attribute set. To obtain all of the reducts of an information system or a decision table, researchers have introduced many discernibility matrices based reduction methods. However, the reducts in the sense of positive region can only be obtained by using the existing discernibility matrices. In this paper, we introduce two discernibility matrices in the sense of entropies (Shannon’s entropy and complement entropy). By means of the two discernibility matrices, we can achieve all of the reducts in the sense of Shannon’s entropy and all of the reducts in the sense of complement entropy, respectively. Furthermore, we discover the relationships among the reducts in the sense of preserving positive region, Shannon’s entropy and complement entorpy. The experimental studies show that by the proposed decision-relative discernibility matrices based reduction methods, all the reducts of a decision table in sense of entropies can be obtained.     

Dominance-based rough set approach to incomplete interval-valued information system

Since preference order is a crucial feature of data concerning decision situations, the classical rough set model has been generalized by replacing the indiscernibility relation with a dominance relation. The purpose of this paper is to further investigate the dominance-based rough set in incomplete interval-valued information system, which contains both incomplete and imprecise evaluations of objects. By considering three types of unknown values in the incomplete interval-valued information system, a data complement method is used to transform the incomplete interval-valued information system into a traditional one. To generate the optimal decision rules from the incomplete interval-valued decision system, six types of relative reducts are proposed. Not only the relationships between these reducts but also the practical approaches to compute these reducts are then investigated. Some numerical examples are employed to substantiate the conceptual arguments.     

Induction of multiple fuzzy decision trees based on rough set technique

The integration of fuzzy sets and rough sets can lead to a hybrid soft-computing technique which has been applied successfully to many fields such as machine learning, pattern recognition and image processing. The key to this soft-computing technique is how to set up and make use of the fuzzy attribute reduct in fuzzy rough set theory. Given a fuzzy information system, we may find many fuzzy attribute reducts and each of them can have different contributions to decision-making. If only one of the fuzzy attribute reducts, which may be the most important one, is selected to induce decision rules, some useful information hidden in the other reducts for the decision-making will be losing unavoidably. To sufficiently make use of the information provided by every individual fuzzy attribute reduct in a fuzzy information system, this paper presents a novel induction of multiple fuzzy decision trees based on rough set technique. The induction consists of three stages. First several fuzzy attribute reducts are found by a similarity based approach, and then a fuzzy decision tree for each fuzzy attribute reduct is generated according to the fuzzy ID3 algorithm. The fuzzy integral is finally considered as a fusion tool to integrate the generated decision trees, which combines together all outputs of the multiple fuzzy decision trees and forms the final decision result. An illustration is given to show the proposed fusion scheme. A numerical experiment on real data indicates that the proposed multiple tree induction is superior to the single tree induction based on the individual reduct or on the entire feature set for learning problems with many attributes.     

基于描述符的输出调度IP核的设计与实现

输出调度是实现QoS支持的重要技术。基于报文的输出调度技术由于实现简单等优点，广泛应用于各种QoS部件的设计与实现中。然而，基于报文的输出调度由于需要缓存大量待调度报文，因此增加了设备的芯片面积和实现成本。针对上述问题，提出了一种基于描述符的输出调度技术，通过对携带报文长度信息的描述符进行调度，在保证系统性能的前提下，可有效降低输出调度的存储空间需求。还介绍了基于此种输出调度算法的IP核设计与实现，介绍了模块的外部接口、参数配置以及内部处理流程。最后，通过实验验证了此IP核的可行性。     

基于不协调决策信息系统的有效教学影响因素分析

有效教学理念的推广与实施是新课程改革的重点项目之一,然而在深入贯彻有效教学方针的过程中,教学效果不明显等问题不断凸显.首先根据粗糙集约简理论给出约简算法.其次在对有效教学影响因素进行实地调查研究的基础上,通过随机抽样得到有关有效教学影响因素分析表,并将其转化为决策信息系统.然后利用约简算法对有效教学影响因素实例进行分析,得到分布约简、最大分布约简、分配约简、下近似约简和上近似约简.最后对有效教学影响因素决策信息系统的约简结果进行解释,从而指导有效教学方案的制定,提高有效教学的效果.     

A Mathematical Foundation for Improved Reduct Generation in Information Systems

When data sets are analyzed, statistical pattern recognition is often used to find the information hidden in the data. Another approach to information discovery is data mining. Data mining is concerned with finding previously undiscovered relationships in data sets. Rough set theory provides a theoretical basis from which to find these undiscovered relationships. We define a new theoretical concept, strong compressibility, and present the mathematical foundation for an efficient algorithm, the Expansion Algorithm, for generation of all reducts of an information system. The process of finding reducts has been proven to be NP-hard. Using the elimination method, problems of size 13 could be solved in reasonable times. Using our Expansion Algorithm, the size of problems that can be solved has grown to 40. Further, by using the strong compressibility property in the Expansion Algorithm, additional savings of up to 50% can be achieved. This paper presents this algorithm and the simulation results obtained from randomly generated information systems. Received 6 May 1999 / Revised 3 December 1999 / Accepted in revised form 17 January 2000     

Propositional Satisfiability Algorithm to Find Minimal Reducts for Data Mining

A fundamental problem in data mining is whether the whole information available is always necessary to represent the information system (IS). Reduct is a rough set approach in data mining that determines the set of important attributes to represent the IS. The search for minimal reduct is based on the assumption that within the dataset in an IS, there are attributes that are more important than the rest. An algorithm in finding minimal reducts based on Propositional Satisfiability (SAT) algorithm is proposed. A branch and bound algorithm is presented to solve the proposed SAT problem. The experimental result shows that the proposed algorithm has significantly reduced the number of rules generated from the obtained reducts with high percentage of classification accuracy.     

不完备模糊系统的优势关系粗糙集与知识约简

以不完备模糊决策系统为研究对象,根据拓展的优势关系,构建了粗糙模糊集模型,以获取不完备模糊决策系统中的"at least"和"atmost"决策规则.为了获取简化的"at least"和"at most"规则,在不完备模糊决策系统中,提出了两种相对约简(相对下近似约简与相对上近似约简)的概念,给出了求得这两种约简的判定定理及区分函数,并进行了实例分析.