【作者】 马丽；

【导师】 米据生；

【作者基本信息】 河北师范大学 ， 应用数学， 2016， 博士

【摘要】 概念格也被称为Galois格,其基本思想是根据二元关系提出的一种概念层次结构.作为形式概念分析理论中的一种核心的数据结构,已成为目前数据分析与知识发现的有效工具,在众多领域取得了较广泛而成功的应用,并逐渐显现多学科交叉与融合的趋势.概念格理论里有关概念格的生成是重要的问题之一.当数据量增多时生成的概念格的层次结构会变得复杂而难处理.为了适当简化格的结构,有效缩减形式概念的生成,本文以形式背景为研究对象,基于不确定性理论来考虑概念格的生成与知识发现.主要内容包括格观念下的知识约简,基于相似度的Galois格,基于邻域系统包含度的多尺度概念格,决策形式背景的命题推演及不完备决策形式背景的知识获取.主要成果和创新点如下:1.从格的角度出发,通过定义格上的分划,借助粗糙集的思想引入一对近似算子,并讨论了它们的性质,给出协调集和约简的定义,进而给出约简的判定条件,进一步给出相对协调集和相对约简的定义和判定定理.为知识约简提供一种新的思路.2.利用一种相似度,引入两种新的Galois连接并讨论了它们的性质,在此基础上研究了由特定Galois连接诱导产生的概念格及有关基本性质,给出了特定约简的定义和协调集的两个判定定理,将概念格的已有相关结果做了进一步推广.3.基于一种包含度建立新的Galois连接,在由属性形成的强弱邻域的基础上,给出特定邻域系统下生成多尺度概念格,并验证基于邻域系统的多尺度概念格可有其对应的诱导背景生成.实例验证通过选择调试合适的参数来控制概念格的结构,在实际应用中达到缩减概念数量的目的.4.通过弱化形式背景中形式概念构成的条件,定义了比形式概念更为广泛的认知基础单位,即命题.通过定义必然命题和充分命题,在确定了一个命题的程度即确定度的基础上讨论了命题的一些相关性质及获得一些新命题的有效方法.为命题之间的不确定推理提供了一种新的框架.5.给出不完备决策形式背景中的近似概念的生成,规则的提取和属性约简的相关研究结果.为不完备决策形式背景的知识获取提供一种新的思路.更多还原

【Abstract】 The concept lattice is also called the Galois lattice, and its basic idea is based on a binary relation of concept hierarchy. As a core data structure of formal concept analysis theory, concept lattice becomes the currently effective tool for data analysis and knowledge discovery, in many areas it made more extensive and successful applications, and gradually the tendency of many subjects crossing and integration.The formation of concept lattice is one of the most important problems in the concept lattice theory. When the amount of data is increasing, the concept lattice hierarchy will become more complicated and difficult to deal with. In order to simplify lattice structure and effectively reduce the generation of formal concept, many studies on formation of concept lattice and knowledge discovery based on uncertainty theory were to be considered.Knowledge reduction under the view of lattice, Galois lattice based on the similarity,multi-scaled concept lattice based on neighborhood system, the propositional reasoning in formal decision context and knowledge acquisition of incomplete formal decision context are respectively proposed in this dissertation. The original work obtained includes the following aspects:1. We propose some new concepts such as knowledge reduction and consistent set based on rough set theory under the view of lattice. By means of defining lower approximate and upper approximate operators, we give two specific reductions. Then, we present the judgment theorems for consistent sets and proved. These representations are the deeper reveals the essence of knowledge, and some relevant results of knowledge reduction are obtained.2. By using similarity degree, we introduced two new Galois connections and discussed their properties, on the basis we studied the basic properties of concept lattice induced by the specific Galois connection. Moreover, we gave the definition of a specific reduction, and proposed two judgment theorems for consistent sets and proved. Some relevant results of concept lattice have been done to promote.3. Based on a kind of Galois connection via a concept of inclusion degree using a special neighborhood system, we propose a multi-scaled concept lattice. We show that theconcept lattice produced by the original context is equal to the concept lattice produced by the induced context. An example shows that the structure of concept lattice is controlled by choosing appropriate parameters, and the purpose of reducing the number of concepts is achieved in practical application.4. On the basis of a formal context, by weakening the composition condition of concept form, we give the basic unit of cognition, i.e. proposition. Based on some basic concepts such as necessarily proposition and sufficient proposition, some related properties of the proposition and the relationship between various propositions are given, and the effective ways to obtain a new proposition is proposed. Using the determine degree of proposition, we discuss the propositional reasoning in formal decision context, and provide a new framework in a formal context for uncertain reasoning.5. The results of the research on the generation of approximate concepts, rules extraction and attribute reduction in incomplete formal decision context are presented. It provides a new way of thinking for knowledge acquisition in incomplete formal decision context.更多还原