【作者】 高乐；

【导师】 魏玲；

【作者基本信息】 西北大学 ， 应用数学， 2022， 硕士

【摘要】 形式概念分析是由德国数学家Wille于1982年所提出的一种用于数据分析和知识发现的数学工具,其优点在于明确的语义内涵和对信息的充分表达.形式背景和概念格作为形式概念分析中两个基本的概念,前者表达了完整的原始数据,而后者基于形式概念利用格结构层次化的展现了形式背景所蕴含的知识.然而,概念格较为复杂的结构也为相关研究带来不便,因此概念格结构的简化成为这一领域非常重要的研究方向之一.部分研究者将机器学习中的聚类方法引入形式概念分析,通过将对象、属性或概念聚类对原始概念格结构进行总结或抽象,进而实现知识的简化.然而这样的研究大多是围绕聚类方法的提出或改进,并未对后续新的知识结构和相关性质进行研究.因此,本文从实际生活中对属性的自然分类出发,考虑多种不同的分类逻辑,将研究重心放在对象和属性类之间二元关系的确定以及不同分类逻辑所形成的分类形式背景和概念格的研究上,并通过实例进行相应分析.具体内容如下:1.对具有属性分类的形式背景进行形式化描述,提出悲观分类形式背景和悲观分类概念格,研究其与原形式背景和概念间关系,建立原概念格与悲观分类概念格间的映射,并给出悲观分类概念格的构造定理.2.定义语义明晰的乐观分类形式背景及概念格,研究其与原形式背景和概念间关系,引入概念包含映射,研究原概念格与乐观分类概念格之间的关系,并给出对应的概念格生成方法.3.结合模糊形式概念分析理论,定义模糊分类形式背景及其概念格,研究其与原背景和原概念格间的关系以及不同阈值下模糊分类概念格间关系.更多还原

【Abstract】 Formal concept analysis,proposed by Wille in 1982,is a mathematical tool for data analysis and knowledge discovery.Because of the concise of knowledge expression and the visibility of knowledge presentation in formal concept analysis,extensive researches about this theory were proposed by many scholars.Formal context and concept lattice are two basic notions in formal concept analysis where the former one gives the data foundation,and the latter one presents a hierarchical structure of the knowledge in formal contexts.However,the complex structure of concept lattice may also occur some inconvenience in its practical applications,thus the simplification of concept lattice has become one of the most important research topics in formal concept analysis.For example,some researchers introduced the clustering methods from machine learning into formal concept analysis,achieve the simplification of knowledge by summarizing and abstracting the original concept lattice through the clusters of objects,attributes or concepts.However,most researches only focus on the selection of clustering methods,but ignore the subsequent new knowledge structures.Therefore,this paper presents three kinds of models based on different situations of attributes classification in real life,and focuses on the binary relation between objects and attribute classes,also the corresponding classified formal contexts and their concept lattices.After then,the analysis is carried out through examples.The details are as follows:1.The formal context with attribute classification is formally described,and the pessimistic classified context and corresponding pessimistic classified concept lattice are proposed.The relationships between operators and concepts in pessimistic classified context and those in the original context are studied,the mapping between the original concept lattice and the pessimistic classified concept lattice is established,and the generation method of the pessimistic classified concept lattice is presented.2.The optimistic classified context and its concept lattice are defined,the relationships between operators and concepts in optimistic classified context and those in the original context are studied,and the connection of the original concept lattice and the optimistic classified concept lattice is explored by using concept inclusion mapping,then the generation method of optimistic classified concept lattice is presented.3.Combined with the theory of fuzzy formal concept analysis,the fuzzy classified context and fuzzy classified concept lattice are defined,the connections of the original concept lattice and the fuzzy classified concept lattice is studied,the relationships between fuzzy classified concept lattices under different thresholds are also explored.更多还原