基于相关族的偏覆盖粗糙集约简理论及方法

Widely applied to natural sciences and social sciences, rough set theory ，a tool of data mining,enjoys its unique advantages in various areas. As important developments of Pawlak's rough sets, covering generalized rough sets and binary relation generalized rough sets are getting more attention recently. Current researches regarding rough sets mainly focus on two aspects: generalizations of rough sets, design of its reduction algorithm. Between them, the reduction of rough sets is no doubt the most important, special, and widely applied theory. Compared with various generalized approximate operators, the research on attribute reduction theory is far from being developed. Partial covering(which is also called neighberhood system) is a generalization shared by covering and binary relation.. This program will study the reduction theory of partial covering rough sets which includes two respects. (1)To classify several generalized rough set models by the reduction algorithm to aviod repitition of study on one type.(2)To find necessary and sufficient conditions of attribute reduction and relative attribute reduction of several covering rough set models respectively. Moreover, attribute reduction algorithms and relative attribute reduction algorithms will be designed based on related family method. As a result, high performance heuristic algorithms will be designed on the basis of these research. This Program aims to establish a relatively complete reduction system of generalized rough sets, including stable and efficient heuristic algorithms. This research will improve the application of rough sets in fields of data mining, feature extraction and so on.

偏覆盖（也称领域系统）粗糙集是覆盖粗糙集和二元关系粗糙集的共同推广，其属性约简是粗糙集理论中最重要的内容之一。而偏覆盖粗糙集属性约简算法的研究存在重复设计和缺失等问题。相关族，是由本项目负责人专门针对覆盖粗糙集约简特点而提出的一种新型约简工具。它可以解决区分矩阵无法解决的覆盖粗糙集属性约简问题，并能以之为基础设计出高性能的启发式算法。本项目将在相关族的基础上从两方面解决偏覆盖粗糙集约简问题：（1）以约简类型为依据将多种广义粗糙集模型进行分类，避免重复研究；（2）给出多种广义粗糙集属性约简和相对属性约简的充要条件，基于相关族方法设计属性约简和相对属性约简算法，并以此为基础设计高性能的启发式算法。本项目旨在建立起一个相对完善的偏覆盖粗糙集约简理论体系，为模糊粗糙集的约简提供新的理论铺垫，并促进粗糙集理论在数据约简和特征提取等领域的应用。

偏覆盖（也称领域系统）粗糙集是覆盖粗糙集和二元关系粗糙集的共同推广，其属性约简是粗糙集理论中最重要的内容之一。而偏覆盖粗糙集属性约简算法的研究存在重复设计和缺失等问题。本项目的主要贡献就是结束了覆盖粗糙集属性约简领域同时存在的算法缺失和重复研究的混乱局面，建立起一个相对完善的偏覆盖粗糙集约简理论体系。相关族，是由本项目负责人专门针对覆盖粗糙集约简特点而提出的一种新型约简工具。它可以解决区分矩阵无法解决的覆盖粗糙集属性约简问题，并能以之为基础设计出高性能的启发式算法。本项目的主要研究内容为三个方面：（1）以约简类型为依据将多种广义粗糙集模型进行分类，避免重复研究；（2）给出多种广义粗糙集属性约简和相对属性约简的充要条件，基于相关族方法设计属性约简和相对属性约简算法，并以此为基础设计高性能的启发式算法。这项工作不仅奠定了偏覆盖粗糙集约简的理论基础，为模糊粗糙集的约简提供了新的理论铺垫，还提出了新的属性约简工具--相关族方法，为数据挖掘，模式识别，特征提取等领域提供了直接可用的新工具，而且拓宽了粗糙集的应用范围，能够深化和拓展粗糙集技术在各个领域的应用，具有理论和实际的双重意义。