基于公理模糊集与粒化认知机理的形式概念分析研究

In the field of knowledge engineering, knowledge acquisition from complex data has become one main tasks to formal concept analysis, in which complexity of data is one of key challenges. Following the human's granulation cognition mechanism, within the axiomatic fuzzy set (AFS) theory, we look forward to developing novel theories and methods to improve the ability of formal concept analysis to acquiescing knowledge from complex data. There are three key problems to solved as follows: for complex formal contexts, we can get some granulations and their AFS logical semantical descriptions via granulation mechanism, by which we can establish granulation concept lattice and multigranulation concept lattice with granulation (AFS logical smentical description) allowed as extent (intent); uniform formula, reduction and rules extraction of the above mentioned models will be established; some theorems on composition and decomposition of granulation concept lattice and semantic-based concept approximation are obtained from the piont of AFS algebra, which can further explore algebric structure properties of granular space.. This project can form a system method of formal concept analysis based on the human's granulation cognition mechanism, which has important theoretical significance and practical application values for knowledge discovery and representation in complex data.

应用形式概念分析从复杂数据获取知识是当前知识工程领域一项重要任务，而数据的复杂性又是所面临的主要困难之一。本项目从人类的粒化认知机理出发，依据公理模糊集（AFS理论）建立一套处理复杂形式背景的理论与方法，提高形式概念分析从复杂数据中获取知识的能力。具体内容：对复杂形式背景进行粒化并求出粒的AFS语义描述，分别以粒及其语义描述为外延与内涵构造粒概念格及多粒度概念格；研究它们的粒描述逻辑框架、约简以及其上的规则提取问题；从AFS代数角度分析粒概念格的合成、分解和概念语义逼近等过程，进一步揭示粒空间的结构特征。.本项目的研究将初步形成一个基于粒化机理的形式概念分析理论与方法体系，对面向复杂数据的知识表示与发现有着重要的理论意义和应用价值。

本项目从模拟人的思维方式出发，对复杂系统的知识发现、获取与评价方法开展研究。在概念格理论方面，通过引入"强度"定义建立决策形式背景的规则提取方法，有效去除冗余的蕴含关系；建立AFS多粒度概念格，并通过构造映射从原始数据直接确定对象对属性的隶属度。在概念格应用方面，基于概念格建立本体快速查询方法和构建需求模型，并系统研究它们的优势所在，使其更有效地从复杂数据中表示和处理知识。在粒的语义描述方面，构建时空数据粒研究方法和多粒度邻近全局聚类算法。针对群决策问题，在公理模糊集（AFS）和语言值模糊理论框架内分别建立基于描述语义的群决策模型，将所改进的模型应用于多种实际决策问题，并测试了它的应用性和有效性。