本文選題：概念格 + 三支概念格�。� 參考：《西北大學》2016年博士論文

【摘要】：形式概念分析是1982年德國數(shù)學家Wille提出的一種將哲學概念及其層次結構進行數(shù)學化描述,進而進行知識表示的理論.如今這一理論與多種學科交叉融合,已在計算機網(wǎng)絡、機器學習、中醫(yī)藥分析及專家系統(tǒng)等領域有廣泛的應用.在形式概念分析中,概念格構造始終是一個重要而有意義的研究方向.本文主要研究基于不同伽略瓦連接的概念格構造,即經(jīng)典概念格的構造,三支概念格的構造,以及三支面向對象(屬性)概念格的構造,并探討經(jīng)典概念格與三支概念格間的關系,面向對象(屬性)概念格與三支面向對象(屬性)概念格間關系以及三支概念格與三支面向對象(屬性)概念格間的關系.具體內容如下：(1)從微觀與宏觀兩個角度研究了經(jīng)典概念格的構造問題.微觀上,利用粒的觀點,把對象子集按照其基數(shù)分成層,求解每層對象子集所對應的內涵,探究內涵所在的層與層之間的關系,給出了判斷獲取所有內涵的截止條件,進而得到概念格.宏觀上,采用化整為零的思想,把原形式背景分解為多個子背景,首先提出了基于對象集次極小覆蓋的背景分解,基于屬性集次極小覆蓋的背景分解以及基于兩域次極小覆蓋的背景分解,并證明了此三種背景分解存在且唯一；其次,證明了每種分解中相應子背景的概念構成的集合是原形式背景的概念構成的集合,最后實現(xiàn)了利用并行算法求解概念格.(2)利用經(jīng)典概念格的構造方法構造三支概念格.通過升維分類的思想,區(qū)分形式背景與其補背景的對象集和屬性集,定義了I-型混合形式背景和Ⅱ-型混合形式背景,證明了I-型(Ⅱ-型)混合形式背景所對應的概念格同構于對象(屬性)誘導的三支概念格.(3)研究了三支面向對象(屬性)概念格的形成與構造問題.通過在對象集和屬性間引入局部完全擁有及局部完全不擁有的定義,首先定義了三支面向對象(屬性)算子,三支面向對象(屬性)概念,三支面向對象(屬性)概念外延以及三支面向對象(屬性)概念內涵.其次證明了所有三支面向對象(屬性)概念構成的集合在三支面向對象(屬性)概念外延(內涵)的包含關系下構成完備格,即三支面向對象(屬性)概念格.最后利用面向對象(屬性)概念格的構造方法構造三支面向對象(屬性)概念格,證明了Ⅰ-型(Ⅱ[-型)混合形式背景所對應的面向對象(屬性)概念格同構于三支面向對象(屬性)概念格.(4)討論了經(jīng)典概念格、三支概念格以及三支面向對象(屬性)概念格之間的關系.基于三支概念格及三支面向對象(屬性)概念格的構造方法,首先證明了經(jīng)典概念格到對象(屬性)誘導的三支概念格存在保Λ(V)序嵌入.其次證明了面向對象(屬性)概念格到三支面向對象(屬性)概念格存在保V(V)序嵌入.最后證明了對象(屬性)誘導的三支概念格反同構(同構)于三支面向對象(屬性)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，

本文編號：2036867