基于抽象相关关系的粗糙集研究

Abstract interdependency in rough sets

通过定义抽象相关关系这一概念来研究覆盖粗糙集.借助群论中的思想,在覆盖上进行抽象,从而在覆盖粗糙集中定义了元素与元素的抽象相关关系,元素与集合的依赖关系.进而在粗糙集上定义了独立集、基、秩函数等概念,并在此基础上研究覆盖粗糙集的约简等性质.把这些概念放在Pawlak粗糙集环境中进行讨论,所得到的结果与Pawlak粗糙集理论中已有的结论相吻合,如本文中用秩函数定义的闭包算子等于Pawlak粗糙集中的上近似算子.

Vagueness and incompleteness in information systems are important issues in data mining and information processing.Rough set theory is an efficient and effective tool to deal with these problems while covering-based rough set theory is an extension to classical rough sets.In this paper,we investigate Abstract interdependency in covering-based rough sets.Firstly,we propose several concepts such as base,rank function,and independent set to describe Abstract interdependency among elements of a covering in covering-based rough sets.Then we establish the relationships between these new concepts and other concepts already existing in covering-based rough sets such as reducible elements and approximation operators.Finally,we apply these concepts and results to classical rough sets.As a result,we get a conclusion that a closure operator defined with the rank function we proposed is equal to the upper approximation operator.