摘要
本论文讨论粗糙集理论及其在信息系统中的应用。研究内容分为两大部分：第二、三两章讨论粗糙集数学理论的两个问题：第四、五两章讨论粗糙集理论在信息系统属性约简与决策规则优化中的应用。
第二章讨论了近似空间中的孤点在粗糙集代数结构中的作用，并由此刻划了粗相等类的代数结构。在近似空间中，如果某一个对象组成一个等价类，则称这样的对象为近似空间中的孤点。孤点不会位于任何粗糙集的边界上，它对粗糙集的代数结构产生特殊影响。本章的讨论同时说明了这样一个问题：在近似空间中，虽然任何一个集合都对应一个由上下近似组成的精确集集对，但另一方面，任给一个由两个具有包含关系的精确集构成的有序集对，却不一定有粗糙集对应它。
第三章讨论了近似空间中粗糙集之间的相似度量问题。在近似空间中，一个等价类是一个知识颗粒，是认识的最小单位：一个对象是否属于某个集合，或者说一个对象属于某个集合的程度，是由该对象所在的等价类与该集合的关系所确定的，换而言之，是由粗隶属函数所确定的。本章利用粗隶属函数，借鉴模糊集的相似度量方法，定义了粗糙集的几种相似度，讨论了它们的性质，并比较了它们的特点。
第四章讨论了一般(协调、不协调)完备决策信息系统的属性约简与决策规则优化。针对信息系统的确定性信息和不确定性信息，分别讨论了Pawlak约简和一般决策约简的性质与关系；给出了决策规则约简(值约简)与信息系统约简的区分函数求法；特别是给出了一种改进的区分矩阵，它既能用来求一般决策约简及其核，又能计算Pawlak约简及其核。本章的讨论，既考虑到了信息系统的协调与不协调，又区分了Pawlak约简与一般决策约简，改进、推广了前人的有关结论，从数学理论上澄清了对信息系统求核问题的一些错误认识。
第五章在相容粗糙集模型中，提出了定义上下近似算子的新方法，以此讨论不完备信息系统和集值信息系统的属性约简与优化决策规则获取问题。本章的具体工作如下：
第三节讨论了含有属性空值的不完备信息系统。采用最大相容分类方法，对不完备信息系统的论域进行分类。这种分类方法能够找出
This paper discusses rough set theory and its applications in information systems. In chapter 2 and 3, two mathematical problems of rough set theory are discussed. In chapter 4 and 5, applications of rough set theory in two aspects are studied which are attribute reduct and the acquisition of the optimal decision rules in information systems. The whole paper is structured as follows.
In chapter 2, the concept of "isolated point" is defined, whose influence on algebraic structure of rough set is demonstrated. Furthermore, rough equivalent classes are described by crisp sets and isolated points. In approximate space, the isolated point which consists one equivalent class itself is not contained in the boundary of any rough set. Hence, it plays an important and special role in the algebraic structure of rough sets. The discussion in this chapter illustrates such a problem that: each set generates an ordered pair of definable sets (the lower approximation and upper approximation) in approximate space, but for a certain ordered pair of definable sets, there may not exists any rough set corresponding to it.
In chapter 3, the similarity measure of rough sets in approximate space is discussed. In approximation space, one equivalent class which is a minimal unit of recognition can be viewed as a knowledge granularity. Therefore, whether an object belongs to one set, or namely the degree of an object belonging to one set, is determined completely by the relationship between this set and the equivalent class containing the object. In other words, it is determined by the rough membership function. Using rough membership function, various similarity degrees of rough sets are proposed referring to the concepts of similarity degrees of fuzzy sets. Their properties are analyzed and their characteristics are compared.
Chapter 4 discusses generalized decision reducts and the acquisition of optimal decision rules in general (consistent or inconsistent) decision
引文
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