广义粗集的拓扑结构、方法及应用研究

项目名称： 广义粗集的拓扑结构、方法及应用研究

项目编号： No.61272031

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 自动化技术、计算机技术

项目作者： 刘贵龙

作者单位： 北京语言大学

项目金额： 60万元

中文摘要： 粗集是智能信息处理的重要工具，在知识发现等领域的作用日益显著。拓扑结构是粗集最重要、最基础的结构之一，是知识提取与知识表达的重要基础，本项目拟利用拓扑理论描述粗空间的结构。所指的广义粗集包括经典粗集的各种推广与发展，但主要指由一般二元关系诱导的粗集、模糊粗集和覆盖粗集。在理论方面，用布尔矩阵或模糊矩阵的方法，深入研究一般二元关系诱导的粗集的拓扑结构、模糊粗集确定的模糊拓扑结构及在一定条件限制下的覆盖粗集的拓扑结构；研究对应的闭包扩展成拓扑闭包的变化规律，考虑具有附带条件的覆盖粗集的拓扑结构与二元关系粗集的拓扑结构的相互转化问题；通过对广义粗集拓扑结构的研究，以拓扑为方法，以矩阵为工具，考虑复杂信息系统（或决策表）的知识约简问题，给出简单的约简算法。在应用方面主要考虑（1）应用模糊粗集诱导的拓扑的闭集的性质研究模糊离散动力系统中的平衡态问题。（2）应用模糊粗集的方法研究模糊综合评判问题。

中文关键词： 广义粗集；拓扑；属性约简；覆盖；上下近似

英文摘要： Rough set theory, proposed by Pawlak in 1982, is a powerful tool to describe the dependences among attributes,evaluate the significance of attributes, and derive decision rules. It has attracted the interesting of researchers and practitioners in various fields of science and technology. The concept of topological structures and their generalizations are one of the most powerful notion in system analysis. It is also one of the most important structure of rough sets. Studies of topological structure not only can provide more insight into and a full understanding of rough set theory but also can find new applications. In this project, the generalized rough sets include rough sets induced by general binary relations, fuzzy relations, and coverings. The aims of the project is to study topological structures of generalized rough sets and their applications by means of matrix approaches. First, we study three types of topological structures induced by binary relations, fuzzy relations and coverings, respectively. In general, for a binary relation R, the upper approximation induced by R is a closure, however, the upper approximation may be not a topological closure. We can extened the closure to topological closure. We consider the relationship between the closure and topological closure. We also study similar prob

英文关键词： Generalized rough set；Topology；Attribute reduction；Covering；lower and upper approximation