二元关系聚合与粗糙近似  

Binary relation aggregation and rough approximations

作　　者：安利平[1] 陈增强[2] 仝凌云[3] 

机构地区：[1]南开大学商学院,天津300071 [2]南开大学信息技术科学学院,天津300071 [3]河北工业大学管理学院,天津300130

出　　处：《系统工程理论与实践》2011年第10期1949-1959,共11页Systems Engineering-Theory & Practice

基　　金：国家自然科学基金(71071079;70601013);中央高校基本科研业务费专项基金(NKZXB10097)

摘　　要：粗集理论中的核心概念——下近似和上近似的经典定义是以不可分辨关系为基础的,这种定义方式适合于处理名义属性.然而,许多现实问题既包括定性属性也包括定量属性,因此有必要对不可分辨关系进行泛化.首先在单个属性层次上根据适合的相似性测度定义了二元关系,对这些二元关系进行聚合成为属性集合层次上的全局二元关系.决策类并集的粗糙近似和边界域则定义在全局二元关系的基础上.然后定义了粗糙近似和边界域的运算,从而可以描述确定性、可能性和怀疑性的知识,并且证明了这些运算满足的粗糙包含性、互补性、边界域恒等性和单调性.这种新的粗集方法可以描述包含定性属性和定量属性的决策表中包含的不一致性.Classical definitions of lower and upper approximations,which are core concepts of rough sets theory,are based on indiscernibility relations.This relation is well suited in the case of nominal attributes.However,many real-world problems often involve both qualitative and quantitative attributes. It is necessary to generalize indiscernibility relation by using some other binary relations.The binary relations defined from some similarity measures at the level of any single attribute are considered.These relations are aggregated into the global binary relations at the level of the set of attributes.Then,the rough approximations and the boundaries of the unions of decision classes are defined using the global binary relations.And,the operations of approximations and boundaries are defined to describe the certain, possible and doubtful knowledge.The operations satisfy the properties of rough inclusion,complementarity, identity of boundaries,and monotonicity.The new rough set approach can detect the inconsistency which may occur when in the decision table there are both qualitative and quantitative attributes.

关 键 词：二元关系 粗集 下近似 上近似 不一致性 

分 类 号：N94[自然科学总论—系统科学]