基于两种新型算子的粗糙集运算  

Operations in Rough Set Theory Based on Two New Operators

作　　者：张化光[1] 梁洪力[1] 

机构地区：[1]东北大学信息科学与工程学院,辽宁沈阳110004

出　　处：《东北大学学报（自然科学版）》2003年第11期1021-1024,共4页Journal of Northeastern University(Natural Science)

基　　金：国家自然科学基金资助项目(60274017);沈阳市自然科学基金资助项目(1022033 1 07).

摘　　要：定义了基本致粗因子和基本致粗相关因子,将边界域划分为两部分·并以这两个因子为基础,定义了确定增量算子和不确定减量算子,给出并证明了这两类新型算子的一些重要性质和定理·进一步讨论了基于这两类新型算子的粗糙集运算·利用这两种新型算子可将对粗糙集理论影响较大的两个不等式转化为等式·同时,粗糙集的并、交、补运算被重新定义·这些新定义的运算在运算过程中不会丢失任何信息且具有良好的运算性质,特别是这些运算满足互补律和德摩根律·这使得粗糙集理论中的许多方面都得到了改善,进而拓宽了粗糙集的应用·Defining the basic roughnessinducing factor and correlated basic roughnessinducing factor of the rough set X, the boundary region is divided into two parts,i.e., the roughnessinducing region and correlated roughnessinducing region. Based on the two factors, the definite increment operator and indefinite decrement operator are defined with some important properties and theorems proved to give them. Then,the operations in the rough set are discussed on the basis of the two newly defined operators. It will thus be possible to transform the two inequalities which have important effects on the rough set theory (RST) into equalities. The transformation can be used to redefine the operations for union, intersection and complementation with good operational reliability provided and without information missed. In particular these operations satisfy both the law of complementation and De Morgans law. The work will improve many aspects of the rough set theory and, further, provide more applicable fields for the theory.

关 键 词：粗糙集理论 基本致粗因子 基本致粗相关因子 确定增量算子 不确定减量算子 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]