基于拟阵方法的粗糙集理论研究

项目名称： 基于拟阵方法的粗糙集理论研究

项目编号： No.61202178

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 计算机科学学科

项目作者： 李小南

作者单位： 西安电子科技大学

项目金额： 23万元

中文摘要： 运用其他数学工具研究粗糙集一直是粗糙集理论研究的热点。本项目拟采用一种新的数学工具，拟阵理论，来研究粗糙集并侧重于理论研究。拟阵抽象了图、向量空间中的独立结构，和图论、代数、格论、组合优化等数学学科有着密切联系，拟阵的这些性质为本项目的进行提供了丰富的研究背景。本项目首先研究各种粗糙集扩展模型的拟阵结构，从拟阵的角度去理解各种粗糙集扩展模型之间的异同，研究基于拟阵理论中典型格的抽象近似空间模型。其次，利用粗糙集扩展模型导出拟阵的可线性表示性或可图性质给出相应模型的图或矩阵表示。第三，研究模糊粗糙集中的模糊拟阵结构，在此基础上给出模糊近似算子的公理化刻画。最后，建立信息系统属性约简的拟阵刻画，研究拟阵理论中经典算法和运算在信息系统背景下的意义，探寻基于拟阵方法的属性约简新算法。本项目预期在理论上有突破，从而促进拟阵理论和粗糙集理论的融合在应用研究方面的发展。

中文关键词： 粗糙集；拟阵；三支决策；格；

英文摘要： Using various mathematical tools to study rough sets are always hot topics in the research of rough sets. This project is expected to use a new tool, matroid theory, to study rough sets and focus on the theoretical aspect. Matroids abstract independent structures of graphs and vector spaces, and connect intimately with other mathematical branches such as graph theory, algebra, lattice theory and combinatorial optimization, etc. These properties of matroids provide rich research context for this project. First, we study the matroidal structures of generalized rough set models, point out similarities and differences of these models from matroidal viewpoint, and establish abstract approximation spaces based on classical lattices in matroid theory. Second, we give graphical and matric representations of generalized rough set models using representability of induced matroids of corresponding models. Third, based on the study of structure properties of fuzzy rough sets concerning fuzzy matroids, sets of axioms are proposed to characterize fuzzy approximation operators. Finally, we characterize attribute reduction from matroidal viewpoint, investigate the meanings of classical algorithms and operations in matroid theory in the context of information systems and explore new algorithms to attribute reduction using m

英文关键词： rough sets；matroids；three-way decisions；latttices；