CAJ | 학술논문

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.
조집이론중적핵심개념——하근사화상근사적경전정의시이불가분변관계위기출적,저충정의방식괄합우처리명의속성.연이,허다현실문제기포괄정성속성야포괄정량속성,인차유필요대불가분변관계진행범화.수선재단개속성층차상근거괄합적상사성측도정의료이원관계,대저사이원관계진행취합성위속성집합층차상적전국이원관계.결책류병집적조조근사화변계역칙정의재전국이원관계적기출상.연후정의료조조근사화변계역적운산,종이가이묘술학정성、가능성화부의성적지식,병차증명료저사운산만족적조조포함성、호보성、변계역항등성화단조성.저충신적조집방법가이묘술포함정성속성화정량속성적결책표중포함적불일치성.
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.