不完备信息系统知识约简方法及应用研究
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摘要
波兰数学家Pawlak于1982年提出了粗糙集的概念。粗糙集理论作为一种描述不精确、不确定知识的数学工具为不确定性数据分析和处理提供了一种新方法；概念格理论是由德国数学家Wille在1982年创立的。它是一种有效的知识表示工具。粗糙集理论与概念格理论相辅相成,具有紧密的联系。
属性约简是信息系统知识发现中的关键问题,也是粗糙集理论的核心内容之一。针对完备信息系统,研究者提出了多种属性约简理论与方法。对于不完备信息系统,相关研究还不完善。本文基于粗糙集理论及概念格理论讨论不完备信息系统的属性约简理论、方法及约简算法,并将其应用于无线电信号识别领域。本文的主要研究成果如下：
1.研究了基于自反和传递关系的广义粗糙集模型中近似算子的性质,提出了关于拓扑结构的紧致性条件(COMP),证明了所有自反、传递关系构成的集合与满足紧致性条件(COMP)的所有拓扑构成的集合之间存在——对应的关系；在完全分配格上,基于覆盖提出了邻域的概念,基于邻域提出了新的上近似算子及下近似算子,并讨论了它们的基本性质。
2.根据不完备信息系统中数据缺省的实际情况,提出了基于属性贡献度的不可区分关系,并讨论了它与其它不可区分关系之间的联系；在Stefanowski提出的相似关系的基础上,给出了基于属性重要度的属性约简方法,并分别针对不完备信息系统和不完备决策表给出了属性约简算法。
3.针对不完备决策表,本文基于广义相似关系,给出了分配协调集与正域协调集的等价刻画条件及约简判定定理,借助区分矩阵与区分函数给出了分配约简与正域约简的计算方法。
4.提出了概念格中属性的一种相似关系,讨论了概念格中形式概念的属性约简特征和约简方法,基于属性相似关系及属性集的拓扑结构提出了一种形式概念生成的方法。通过MATLAB实验,验证了该方法的有效性。
5.以C波段无线电信号智能监测为应用背景,利用本文讨论的粗糙集理论和形式概念分析方法,建立了无线电信号的信息系统和形式背景,对信号进行了特征提取和规则挖掘,说明了这两种知识发现方法的合理性和有效性。
In 1982, Poland mathematician Pawlak proposed the concept of rough sets. Rough set theory is a mathematical tool to deal with uncertainty and incomplete information, which provides a new approach for the analysis and process of uncertainty data. The theory of concept lattice was initiated by German mathematician Wille in 1982, which is an effective tool of knowledge representation. Rough set theory and the theory of concept lattice complement each other, they are closely related.
Attribute reduction is a key problem in the knowledge discovery in information systems. Also, it is one of the core problems of rough set theory. Different kinds of attribute reduction theories and approaches were proposed with respect to complete information systems. As for incomplete information systems, the related researches are still not perfect. In this paper, based on rough set theory and the theory of concept lattice, we study the attribute reduction theory, attribute reduction methods and attribute reduction algorithms of incomplete information systems. Furthermore, we apply our theoretical results to the field of radio signal recognition. The main results and innovations in this thesis are summarized as follows:
1. The approximation operators based on reflexive and transitive relation in generalized rough set model are studied, compactness condition (COMP) about topology structure is proposed. It is proved that there is a one to one correspondence between the set of all reflexive and transitive relations and the set of all topologies which satisfies (COMP). In complete completely distributive lattice, the concept of neighborhood is presented based on covers. Furthermore, new upper approximation operators and lower approximation operators are proposed based on the neighborhood, and some basic properties are derived.
2. According to actual situation of missing data in the incompletely information systems, a new kind of indiscernibility relation is proposed based on contribution degree of attributes; the relationships between it and the other indiscernibility relations are discussed. Based on the similarity relation proposed by Stefanowski, a new method of attribute reduction based on important degree of attributes is presented; attributes reduction algorithms with respect to incompletely information and incompletely decision table are proposed, respectively.
3. For incompletely decision table, based on the generalization similarity relation, equivalent characterization conditions and reduction judging theorems of distribution consistent set and positive region consistent set are given; methods of distribution reduction and positive region reduction are given by discernibility matrix and discernibility function.
4. Similarity relation of attributes in formal context is proposed, reduction characterization and reduction approach of attributes are discussed in concept lattice. Based on the similarity relation of attributes and topology structure of the set of attributes, a method of formal concept generation is given. MATLAB experiments show that the method is effective.
5. We apply our theoretical results to the field of radio signal recognition. The information system and formal context of radio signal are constructed, and the methods of features extraction and rules mining are proposed. Experiments show these methods are effective and reasonable.
属性约简是信息系统知识发现中的关键问题,也是粗糙集理论的核心内容之一。针对完备信息系统,研究者提出了多种属性约简理论与方法。对于不完备信息系统,相关研究还不完善。本文基于粗糙集理论及概念格理论讨论不完备信息系统的属性约简理论、方法及约简算法,并将其应用于无线电信号识别领域。本文的主要研究成果如下：
1.研究了基于自反和传递关系的广义粗糙集模型中近似算子的性质,提出了关于拓扑结构的紧致性条件(COMP),证明了所有自反、传递关系构成的集合与满足紧致性条件(COMP)的所有拓扑构成的集合之间存在——对应的关系；在完全分配格上,基于覆盖提出了邻域的概念,基于邻域提出了新的上近似算子及下近似算子,并讨论了它们的基本性质。
2.根据不完备信息系统中数据缺省的实际情况,提出了基于属性贡献度的不可区分关系,并讨论了它与其它不可区分关系之间的联系；在Stefanowski提出的相似关系的基础上,给出了基于属性重要度的属性约简方法,并分别针对不完备信息系统和不完备决策表给出了属性约简算法。
3.针对不完备决策表,本文基于广义相似关系,给出了分配协调集与正域协调集的等价刻画条件及约简判定定理,借助区分矩阵与区分函数给出了分配约简与正域约简的计算方法。
4.提出了概念格中属性的一种相似关系,讨论了概念格中形式概念的属性约简特征和约简方法,基于属性相似关系及属性集的拓扑结构提出了一种形式概念生成的方法。通过MATLAB实验,验证了该方法的有效性。
5.以C波段无线电信号智能监测为应用背景,利用本文讨论的粗糙集理论和形式概念分析方法,建立了无线电信号的信息系统和形式背景,对信号进行了特征提取和规则挖掘,说明了这两种知识发现方法的合理性和有效性。
In 1982, Poland mathematician Pawlak proposed the concept of rough sets. Rough set theory is a mathematical tool to deal with uncertainty and incomplete information, which provides a new approach for the analysis and process of uncertainty data. The theory of concept lattice was initiated by German mathematician Wille in 1982, which is an effective tool of knowledge representation. Rough set theory and the theory of concept lattice complement each other, they are closely related.
Attribute reduction is a key problem in the knowledge discovery in information systems. Also, it is one of the core problems of rough set theory. Different kinds of attribute reduction theories and approaches were proposed with respect to complete information systems. As for incomplete information systems, the related researches are still not perfect. In this paper, based on rough set theory and the theory of concept lattice, we study the attribute reduction theory, attribute reduction methods and attribute reduction algorithms of incomplete information systems. Furthermore, we apply our theoretical results to the field of radio signal recognition. The main results and innovations in this thesis are summarized as follows:
1. The approximation operators based on reflexive and transitive relation in generalized rough set model are studied, compactness condition (COMP) about topology structure is proposed. It is proved that there is a one to one correspondence between the set of all reflexive and transitive relations and the set of all topologies which satisfies (COMP). In complete completely distributive lattice, the concept of neighborhood is presented based on covers. Furthermore, new upper approximation operators and lower approximation operators are proposed based on the neighborhood, and some basic properties are derived.
2. According to actual situation of missing data in the incompletely information systems, a new kind of indiscernibility relation is proposed based on contribution degree of attributes; the relationships between it and the other indiscernibility relations are discussed. Based on the similarity relation proposed by Stefanowski, a new method of attribute reduction based on important degree of attributes is presented; attributes reduction algorithms with respect to incompletely information and incompletely decision table are proposed, respectively.
3. For incompletely decision table, based on the generalization similarity relation, equivalent characterization conditions and reduction judging theorems of distribution consistent set and positive region consistent set are given; methods of distribution reduction and positive region reduction are given by discernibility matrix and discernibility function.
4. Similarity relation of attributes in formal context is proposed, reduction characterization and reduction approach of attributes are discussed in concept lattice. Based on the similarity relation of attributes and topology structure of the set of attributes, a method of formal concept generation is given. MATLAB experiments show that the method is effective.
5. We apply our theoretical results to the field of radio signal recognition. The information system and formal context of radio signal are constructed, and the methods of features extraction and rules mining are proposed. Experiments show these methods are effective and reasonable.
引文
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