信息系统中的知识获取与不确定性度量的若干问题研究
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摘要
信息系统(信息表)是描述对象集具备某些属性特征的有利工具.信息系统中的知识发现是信息科学领域的研究热点.信息系统的不确定性度量也是数据挖掘和知识发现的重要议题.信息粒和信息熵理论是研究信息系统的不确定性问题的主要理论依据.本文以粒计算理论、粗糙集理论、模糊集理论和直觉模糊集理论为基础,研究信息系统中的不确定性度量和知识获取等方面的问题.主要内容包括粗糙集的不确定性度量、直觉模糊信息系统中的属性约简、直觉模糊集的熵、直觉模糊集间的包含度、相似度、相容度,以及形式背景中的多尺度概念格等问题.主要工作如下:
(1)作为粗糙集理论的重要研究内容之一,粗糙集的粗糙度和模糊度是很多学者广泛研究的问题.因为粗糙集的不确定性与其所在近似空间知识粒度的大小密切相关,本文提出了近似空间中集合的相对知识粒度的概念,结合模糊集理论和粒计算理论改进了粗糙集的不确定性度量方法.通过集合的相对知识粒度及边界熵给出了粗糙集的粗糙性度量函数与模糊性度量函数,这些度量在刻画了近似空间对粗糙集不确定性影响的同时,又去除了负域的干扰,并且满足随着近似空间知识粒的细分,粗糙集的粗糙度与模糊度均单调递减的性质.利用矩阵理论提出了易于实现的粗糙性度量与模糊性度量的矩阵算法.
(2)在直觉模糊信息系统中构造了一类广义的直觉模糊集的熵,重新修订了直觉模糊包含度的公理化定义.基于直觉模糊逻辑算子构造了多种直觉模糊包含度,并依此进一步构造出直觉模糊相似度,讨论了直觉模糊集的熵和相似度之间的关系.依据谓词逻辑的思想定义了直觉模糊相容度,并构造了基于直觉模糊三角模的直觉模糊相容度.
(3)在直觉模糊信息系统中,研究了对象集的分类问题和全序化问题.讨论了以绝对优势关系为代表的基于粗糙集方法的属性约简.依据对象集的属性值犹豫区间交叠的程度定义了α-不可辨识关系,给出了α-约简的方法.分析了直觉模糊信息系统的不确定性.针对直觉模糊序决策信息系统,利用依赖空间理论,分别讨论了协调的和不协调情况的属性约简.
(4)形式概念分析作为分析数据的一种有效方法已经被应用于许多领域.本文给出约简概念数量的有效方法,借助包含度的理论,通过事先给定的对象集U的一个划分和一个给定的尺度(或精度)α,得到一个新的Galois连接,进而生成α概念格.从理论上又证明由原始形式背景基于包含度导出的α形式背景得到的概念格与原形式背景生成的α概念格是相同的.然后利用已有概念格计算软件求出约简后的概念格.
Information systems (Information tables) provide a convenient and useful tool for rep-resenting a set of objects using a group of attributes. Knowledge acquisition in informationsystems is a key issue in the field of information science. Uncertainty measure in informationsystem has also attracted lots of attention in data mining and knowledge discovery. Informationgranulation and entropy theory are two main approaches to research uncertainty of an informa-tion system. Based on the theory of granular computing, rough sets, fuzzy sets and intuitionisticfuzzy sets, this dissertation study on the uncertainty measure and knowledge acquisition of in-formation systems, including uncertainty measure of rough sets, attribute reduction, entropy,inclusion measure, similarity measure, compatibility measure in intuitionistic fuzzy systemsand multiple scale concept lattice. The main contribution of this dissertation can be generalizedas follows:
(1) As one of the most important issues in rough set theory, roughness and fuzziness ofrough sets have been widely studied. Uncertainty of rough sets has close relativity with theknowledge granularities of the approximation space. We propose an improved method for mea-suring the uncertainty of rough sets based on fuzzy theory and granular computing theory. Adefinition of relative knowledge granulation and a concept of boundary entropy for an infor-mation system are given, under which the measure functions of roughness and fuzziness aremodified. The roughness of a rough set based on relative knowledge granularities not only re-?ects the action of the approximation space, but also gets rid of the effect of the negative regionof the rough set. Both of roughness and fuzziness are monotonously decreasing with the refin-ing of knowledge granularities in approximation spaces. Two matrix algorithms are presentedfor measuring the roughness and fuzziness of rough sets, which are easy to implement.
(2) In intuitionistc fuzzy system, a new kind of entropy for intuitionistic fuzzy sets is pro-posed, and some basic properties are examined. An axiomatic definition of inclusion measurebetween intuitionistic fuzzy (IF for short) sets is established. Some kinds of IF inclusion mea-sures are constructed by different IF operators, especially by IF implicator. Some new methodsfor measuring the degree of similarity between IF sets are proposed. Moreover, the similaritymeasure obtained from IF inclusion measure holds properties of normal similarity measure. Therelationships between similarity measure and entropy of intuitionistic fuzzy sets are analyzed.We then define the compatibility measure by the predicates logical idea and construct severalfunctions to measure compatibility for an intuitionistic t-norm.
(3) Intuitionistic fuzzy information systems are generalized models of single-valued fuzzyinformation systems. We propose some novel classification rules, totally ordered methods anduncertainty measures for intuitionistic fuzzy information systems. By introducing an absolutedominance relation in an intuitionistic fuzzy information system, a rough set approach is es-tablished, which can be extended to other forms of dominance relations in intuitionistic fuzzyinformation systems. For a given permissible discernibility degreeα, a novel rough set ap-proach based onα-indiscernibility relations is discussed and theα-determinant reductions areobtained. Furthermore, to evaluate uncertainty of an intuitionistic fuzzy information system,we design a roughness measure of a rough set depend on a relative knowledge granulation, bywhich the effect of the negative region of the rough set can be removed effectively. Then wedeal with attribute reductions of consistent and inconsistent intuitionistic fuzzy ordered decisioninformation systems based on the theory of dependence space.
(4) As an effective method for date analysis, formal concept analysis has been applied tomany fields. The method given in this discussion can reduce the number of concepts efficientlywith conserved main formal structure. Based on a kind of Galois connection via a conceptof inclusion degree, a complete lattice, calledα(αis a real number in [0,1]) concept lattice,is produced. A formal context can be converted into an inducedαcontext through a kind ofinclusion degree which is used to cope with a partition of the objects’set. Moreover, it isproved that theαconcept lattice produced by the original context is equal to the concept latticeproduced by the inducedαcontext. Finally, the concept lattices determined by an inclusiondegree is constructed from the induced context by using the well-known software of Galicia.
(1)作为粗糙集理论的重要研究内容之一,粗糙集的粗糙度和模糊度是很多学者广泛研究的问题.因为粗糙集的不确定性与其所在近似空间知识粒度的大小密切相关,本文提出了近似空间中集合的相对知识粒度的概念,结合模糊集理论和粒计算理论改进了粗糙集的不确定性度量方法.通过集合的相对知识粒度及边界熵给出了粗糙集的粗糙性度量函数与模糊性度量函数,这些度量在刻画了近似空间对粗糙集不确定性影响的同时,又去除了负域的干扰,并且满足随着近似空间知识粒的细分,粗糙集的粗糙度与模糊度均单调递减的性质.利用矩阵理论提出了易于实现的粗糙性度量与模糊性度量的矩阵算法.
(2)在直觉模糊信息系统中构造了一类广义的直觉模糊集的熵,重新修订了直觉模糊包含度的公理化定义.基于直觉模糊逻辑算子构造了多种直觉模糊包含度,并依此进一步构造出直觉模糊相似度,讨论了直觉模糊集的熵和相似度之间的关系.依据谓词逻辑的思想定义了直觉模糊相容度,并构造了基于直觉模糊三角模的直觉模糊相容度.
(3)在直觉模糊信息系统中,研究了对象集的分类问题和全序化问题.讨论了以绝对优势关系为代表的基于粗糙集方法的属性约简.依据对象集的属性值犹豫区间交叠的程度定义了α-不可辨识关系,给出了α-约简的方法.分析了直觉模糊信息系统的不确定性.针对直觉模糊序决策信息系统,利用依赖空间理论,分别讨论了协调的和不协调情况的属性约简.
(4)形式概念分析作为分析数据的一种有效方法已经被应用于许多领域.本文给出约简概念数量的有效方法,借助包含度的理论,通过事先给定的对象集U的一个划分和一个给定的尺度(或精度)α,得到一个新的Galois连接,进而生成α概念格.从理论上又证明由原始形式背景基于包含度导出的α形式背景得到的概念格与原形式背景生成的α概念格是相同的.然后利用已有概念格计算软件求出约简后的概念格.
Information systems (Information tables) provide a convenient and useful tool for rep-resenting a set of objects using a group of attributes. Knowledge acquisition in informationsystems is a key issue in the field of information science. Uncertainty measure in informationsystem has also attracted lots of attention in data mining and knowledge discovery. Informationgranulation and entropy theory are two main approaches to research uncertainty of an informa-tion system. Based on the theory of granular computing, rough sets, fuzzy sets and intuitionisticfuzzy sets, this dissertation study on the uncertainty measure and knowledge acquisition of in-formation systems, including uncertainty measure of rough sets, attribute reduction, entropy,inclusion measure, similarity measure, compatibility measure in intuitionistic fuzzy systemsand multiple scale concept lattice. The main contribution of this dissertation can be generalizedas follows:
(1) As one of the most important issues in rough set theory, roughness and fuzziness ofrough sets have been widely studied. Uncertainty of rough sets has close relativity with theknowledge granularities of the approximation space. We propose an improved method for mea-suring the uncertainty of rough sets based on fuzzy theory and granular computing theory. Adefinition of relative knowledge granulation and a concept of boundary entropy for an infor-mation system are given, under which the measure functions of roughness and fuzziness aremodified. The roughness of a rough set based on relative knowledge granularities not only re-?ects the action of the approximation space, but also gets rid of the effect of the negative regionof the rough set. Both of roughness and fuzziness are monotonously decreasing with the refin-ing of knowledge granularities in approximation spaces. Two matrix algorithms are presentedfor measuring the roughness and fuzziness of rough sets, which are easy to implement.
(2) In intuitionistc fuzzy system, a new kind of entropy for intuitionistic fuzzy sets is pro-posed, and some basic properties are examined. An axiomatic definition of inclusion measurebetween intuitionistic fuzzy (IF for short) sets is established. Some kinds of IF inclusion mea-sures are constructed by different IF operators, especially by IF implicator. Some new methodsfor measuring the degree of similarity between IF sets are proposed. Moreover, the similaritymeasure obtained from IF inclusion measure holds properties of normal similarity measure. Therelationships between similarity measure and entropy of intuitionistic fuzzy sets are analyzed.We then define the compatibility measure by the predicates logical idea and construct severalfunctions to measure compatibility for an intuitionistic t-norm.
(3) Intuitionistic fuzzy information systems are generalized models of single-valued fuzzyinformation systems. We propose some novel classification rules, totally ordered methods anduncertainty measures for intuitionistic fuzzy information systems. By introducing an absolutedominance relation in an intuitionistic fuzzy information system, a rough set approach is es-tablished, which can be extended to other forms of dominance relations in intuitionistic fuzzyinformation systems. For a given permissible discernibility degreeα, a novel rough set ap-proach based onα-indiscernibility relations is discussed and theα-determinant reductions areobtained. Furthermore, to evaluate uncertainty of an intuitionistic fuzzy information system,we design a roughness measure of a rough set depend on a relative knowledge granulation, bywhich the effect of the negative region of the rough set can be removed effectively. Then wedeal with attribute reductions of consistent and inconsistent intuitionistic fuzzy ordered decisioninformation systems based on the theory of dependence space.
(4) As an effective method for date analysis, formal concept analysis has been applied tomany fields. The method given in this discussion can reduce the number of concepts efficientlywith conserved main formal structure. Based on a kind of Galois connection via a conceptof inclusion degree, a complete lattice, calledα(αis a real number in [0,1]) concept lattice,is produced. A formal context can be converted into an inducedαcontext through a kind ofinclusion degree which is used to cope with a partition of the objects’set. Moreover, it isproved that theαconcept lattice produced by the original context is equal to the concept latticeproduced by the inducedαcontext. Finally, the concept lattices determined by an inclusiondegree is constructed from the induced context by using the well-known software of Galicia.
引文
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