经典概念格与三支概念格的构造及知识获取理论

发布时间：2018-06-18 21:05

  本文选题：概念格 + 三支概念格　； 参考：《西北大学》2016年博士论文

【摘要】：形式概念分析是1982年德国数学家Wille提出的一种将哲学概念及其层次结构进行数学化描述,进而进行知识表示的理论.如今这一理论与多种学科交叉融合,已在计算机网络、机器学习、中医药分析及专家系统等领域有广泛的应用.在形式概念分析中,概念格构造始终是一个重要而有意义的研究方向.本文主要研究基于不同伽略瓦连接的概念格构造,即经典概念格的构造,三支概念格的构造,以及三支面向对象(属性)概念格的构造,并探讨经典概念格与三支概念格间的关系,面向对象(属性)概念格与三支面向对象(属性)概念格间关系以及三支概念格与三支面向对象(属性)概念格间的关系.具体内容如下：(1)从微观与宏观两个角度研究了经典概念格的构造问题.微观上,利用粒的观点,把对象子集按照其基数分成层,求解每层对象子集所对应的内涵,探究内涵所在的层与层之间的关系,给出了判断获取所有内涵的截止条件,进而得到概念格.宏观上,采用化整为零的思想,把原形式背景分解为多个子背景,首先提出了基于对象集次极小覆盖的背景分解,基于属性集次极小覆盖的背景分解以及基于两域次极小覆盖的背景分解,并证明了此三种背景分解存在且唯一；其次,证明了每种分解中相应子背景的概念构成的集合是原形式背景的概念构成的集合,最后实现了利用并行算法求解概念格.(2)利用经典概念格的构造方法构造三支概念格.通过升维分类的思想,区分形式背景与其补背景的对象集和属性集,定义了I-型混合形式背景和Ⅱ-型混合形式背景,证明了I-型(Ⅱ-型)混合形式背景所对应的概念格同构于对象(属性)诱导的三支概念格.(3)研究了三支面向对象(属性)概念格的形成与构造问题.通过在对象集和属性间引入局部完全拥有及局部完全不拥有的定义,首先定义了三支面向对象(属性)算子,三支面向对象(属性)概念,三支面向对象(属性)概念外延以及三支面向对象(属性)概念内涵.其次证明了所有三支面向对象(属性)概念构成的集合在三支面向对象(属性)概念外延(内涵)的包含关系下构成完备格,即三支面向对象(属性)概念格.最后利用面向对象(属性)概念格的构造方法构造三支面向对象(属性)概念格,证明了Ⅰ-型(Ⅱ[-型)混合形式背景所对应的面向对象(属性)概念格同构于三支面向对象(属性)概念格.(4)讨论了经典概念格、三支概念格以及三支面向对象(属性)概念格之间的关系.基于三支概念格及三支面向对象(属性)概念格的构造方法,首先证明了经典概念格到对象(属性)诱导的三支概念格存在保Λ(V)序嵌入.其次证明了面向对象(属性)概念格到三支面向对象(属性)概念格存在保V(V)序嵌入.最后证明了对象(属性)诱导的三支概念格反同构(同构)于三支面向对象(属性)概念格.
[Abstract]:Formal conceptual analysis is a theory put forward by German mathematician Wille in 1982 to mathematically describe philosophical concepts and their hierarchical structure and then to express knowledge. The theory has been widely used in computer network, machine learning, traditional Chinese medicine analysis and expert system. In formal conceptual analysis, concept lattice construction is always an important and meaningful research direction. This paper mainly studies the construction of concept lattices based on different Galois connections, that is, the construction of classical concept lattices, the construction of three branches of concept lattices, and the construction of three branches of object oriented (attribute) concept lattices. The relations between classical concept lattices and three concept lattices, between object oriented concept lattices and three object oriented concept lattices, and between three concept lattices and three object oriented concept lattices are discussed. The main contents are as follows: (1) the construction of classical concept lattices is studied from micro and macro perspectives. Microscopically, the object subset is divided into layers according to its cardinal number, and the corresponding connotation of each object subset is solved, and the relationship between the layers in which the connotation is located is explored, and the cutoff conditions for judging and obtaining all the connotations are given. Then the concept lattice is obtained. Macroscopically, the original formal background is decomposed into several subbackgrounds by using the idea of fragmentation. Firstly, the background decomposition based on the subminimal covering of object sets is proposed. The background decomposition based on the subminimal cover of the attribute set and the background decomposition based on the two-domain subminimal cover are proved to exist and unique. It is proved that the set of concepts formed by the corresponding subbackground in each decomposition is the set of the concept composition of the original formal background. Finally, three concept lattices are constructed using the method of constructing classical concept lattices by using the parallel algorithm to solve the concept lattice. Based on the idea of ascending dimension classification, the object set and attribute set of formal background and its complement background are distinguished, and I- type mixed form background and 鈪，

本文编号：2036867