本文選題：概念格　切入點(diǎn)：概念　出處：《河北大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：概念格理論(Concept Lattice Theory),也稱形式概念分析(簡(jiǎn)稱FCA),是1982年由德國(guó)數(shù)學(xué)家R.Wille提出的,主要用于描述形式背景中對(duì)象和屬性之間的關(guān)系。對(duì)于一個(gè)給定的形式背景,其概念由內(nèi)涵和外延兩部分組成,而概念格是給定形式背景的所有概念的分層結(jié)構(gòu),因此,如何快速地構(gòu)造概念格是概念格理論研究的一個(gè)重要內(nèi)容。本文在研究了已有概念格構(gòu)造算法的基礎(chǔ)上,一方面結(jié)合圖論的思想提出了一種新的概念格構(gòu)造算法,另一方面依據(jù)用戶需求,原形式背景中某些屬性和對(duì)象將不再需要,這使得將形式背景中的一些屬性和對(duì)象進(jìn)行刪除成為必然。對(duì)于屬性和對(duì)象同時(shí)減少后的形式背景,提出一種通過(guò)原概念格得到新形式背景下的概念格的便捷有效的概念格構(gòu)造算法。主要研究?jī)?nèi)容如下:1.在已有的形式背景之屬性拓?fù)鋱D的基礎(chǔ)上,定義了一種弱化的屬性拓?fù)鋱D,從而得到一種概念格的構(gòu)造算法。算法過(guò)程如下:首先,構(gòu)造形式背景之弱化的屬性拓?fù)鋱D;其次,通過(guò)在弱化的屬性拓?fù)鋱D中,尋找每個(gè)權(quán)值最大圈用以生成概念,進(jìn)而生成形式背景的所有概念;之后,構(gòu)造出概念格。通過(guò)分析說(shuō)明此算法復(fù)雜度較以往的一些算法復(fù)雜度降低。此外,通過(guò)一個(gè)實(shí)例,驗(yàn)證了這一算法的有效性。2.對(duì)于依據(jù)用戶需求的形式背景,提出了一種概念格的構(gòu)造算法并給出理論證明。算法過(guò)程如下:首先,根據(jù)形式背景的概念格Hasse圖的構(gòu)造,按照內(nèi)涵個(gè)數(shù)將原形式背景的概念格進(jìn)行分層;其次,按照自底向上的規(guī)則,對(duì)層中的概念依次判斷其類型,以此得到該層中的概念;再者,得到新形式背景下的所有概念。最后,通過(guò)一個(gè)實(shí)例,說(shuō)明算法的有效性。
[Abstract]:Concept Lattice Theoryn, also known as formal conceptual analysis, was proposed by German mathematician R. Wille in 1982. It is mainly used to describe the relationship between objects and attributes in formal background. The concept consists of two parts: intension and extension, and the concept lattice is the hierarchical structure of all concepts with a given formal background. How to construct concept lattice quickly is an important part of concept lattice theory. Based on the research of existing concept lattice construction algorithm, a new concept lattice construction algorithm based on graph theory is proposed in this paper. On the other hand, some properties and objects in the original formal background will no longer be required according to the user's requirements, which makes it necessary to remove some attributes and objects from the formal background. This paper presents a convenient and effective algorithm for constructing concept lattices under new formal background by using original concept lattices. The main contents of this paper are as follows: 1. On the basis of attribute topology graph of existing formal background, In this paper, a weak attribute topology graph is defined and an algorithm for constructing concept lattices is obtained. The algorithm is as follows: firstly, we construct a weakened attribute topology graph of formal background; secondly, we construct a weak attribute topology graph in a weakened attribute topology graph. The concept lattice is constructed by searching for the maximum cycle of each weight value to generate the concept and then to generate the formal background. The complexity of this algorithm is lower than that of some previous algorithms through analysis. In addition, through an example, the complexity of the algorithm is reduced. The validity of the algorithm is verified. 2. According to the formal background of user requirements, a concept lattice construction algorithm is proposed and the theoretical proof is given. The algorithm process is as follows: firstly, according to the construction of the formal background concept lattice Hasse graph, The concept lattice of the original formal background is stratified according to the number of connotations; secondly, according to the bottom-up rule, the concept in the layer is judged in turn and the concept in that layer is obtained. Finally, an example is given to illustrate the effectiveness of the algorithm.
【學(xué)位授予單位】：河北大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O153.1;O157.5

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