摘要
在粗糙集的代数方法研究中,一个重要的方面是从粗糙集的偶序对(<下近似集,上近似集>)表示入手,通过定义偶序对的基本运算,从而构造出相应的粗代数并发现R0-代数能够抽象刻画偶序对的性质。讨论了粗糙集代数与R0-代数的关系以及由粗糙集代数构造R0-代数的方法,借助近似代数上的原子及同余关系,证明了在适当选取蕴涵算子和余运算之后,粗糙集代数就成为R0-代数。
Description of the pairs〈low approximation upper approximation〉of rough set is an important aspect in the research of rough set theory by algebraic method. By defining some basic operators on the approximation pairs, rough algebras can be constructed and we find out residual lattice can be selected to describe the pairs of rough set. The relation between rough set algebra and R0-aigebra was studied, and the method of constructing R0-algebra from rough set algebra was presented. Based on the atoms and congruence of approximation algebra, it is proved that rough set algebra becomes R0-algebra if proper implication and compliment operators are selected.
出处
《四川理工学院学报（自然科学版）》
CAS
2006年第5期95-98,共4页
Journal of Sichuan University of Science & Engineering(Natural Science Edition)
基金
国家自然科学基金(60474022)
