【作者】 杨丽；

【导师】 宋振明；

【作者基本信息】 西南交通大学 ， 应用数学， 2006， 硕士

【摘要】 概念格理论作为一种知识表示和数据分析的形式化工具，无论在理论研究还是在实际应用中都具有重要意义，它在众多的领域已经获得了成功的应用。然而，在对信息的不同存在方式和动态数据的处理分析以及对概念格的约简与修复方法等方面，概念格理论体系还有待于进一步探索与完善。 本文首先分析了概念格形成所依赖的形式背景，在现有的单值背景和多值背景的基础之上，根据多值背景中属性值取值类型的不同，分别提出了数值型多值背景、区间型多值背景以及语言型多值背景的定义，并讨论了不同类型多值背景转化为同一类型多值背景的方法；分析了多值背景中不断变化的属性值即动态数据产生的原因，针对形式背景中的对象集，阐述了每个对象并非孤立存在而是相互作用和相互影响的观点；定义了基于对象间相互作用的一系列与概念格理论相关的概念，使经典概念格模型得到了扩展；对于相互作用下不断变化的属性值，在属性权重信息完全已知、完全未知以及不完全已知的情况下，分别结合属性权重向量不同的获取方法，采取属性加权法，将动态多值背景转化为静态多值背景；并根据语言评估标度的特点，提出语言标度分割原理，实现了多值背景向单值背景的转化，从而为动态多值背景的研究提供了可行的数学方法。 其次，本文仍以形式背景为着眼点，对概念格的约简及其修复的方法进行了研究，提出了对象的属性空间和属性的对象空间的定义形式；根据所定义的空间各自之间关系的不同，依据属性约简和对象约简的定义，分别对形式背景中的属性集和对象集进行约简，相应地在约简过程中给出了属性约简定理和对象约简定理，最终得到了约简形式背景。 最后，借助于已有的建格算法，在构建的基于约简形式背景的约简概念格基础之上，依据采取约简定理的不同，提出了不同的概念格修复定理，使更多还原

【Abstract】 As a powerful formal tool for data organization and data analysis, the concept lattice theory is very important both in theories and actual application, and has been widely and successfully used in many fields. However, in the analysis of the dynamic data and in the concept lattice of reduction and reparation method, the development of the concept lattice theory system still not mature, need the further quest with perfect.This paper, at first, analyzed the formal context that the construction of concept lattice depends on. Based on the single-valued context and the many-valued context, and according to the concrete applied background and the different attribute values, put forward the definition of the number many-valued context, the interval many-valued context and the linguistic many-valued context respectively and discussed them method convert mutually. Analyze the output reason of the dynamic data . For the set of objects in the formal context, this paper presents a viewpoint that objects are interactive, not exist alone. A series of relative notions based on the interaction among objects are defined and the concept lattice model is extended. Then a weighting method of attributes is adopted to deal with the changeable attribute values. Put forward the linguistic assessments scaling theory, carrying out the transformation of the dynamic many-valued context the static single-valued context, thus providing the viable mathematics method for the research of the dynamic many-valued context.Furthermore, for the study of the reduction and preparation of concept lattice, this paper still focused on the formal context, after the definitions of attribute spaces of object and object spaces of attribute are proposed, the object set and the更多还原