双精度容差关系的粗糙集拓展模型及约简

Extension rough set model and reduction of dual-variable precision tolerance relation

研究了不完备区间值信息系统,提出新的改进模型.首先给出了基于相离度的相似度定义,使得模型可以处理属性值大多数相交但不具备包含关系以及含多个连续值的情形.其次,将容差关系进行拓展,提出了基于相似度和相似率的双精度容差关系,进而建立了适用于不完备区间值信息系统的粗糙集拓展模型.再次,为解决双精度容差关系在划分论域时的不足,提高近似精度,又求出了双精度极大相容类,据此来得到上下近似集,并给出了极大分类约简算法.最后,通过实例分析验证模型和算法的有效可行性.结果表明,所提出的粗糙集拓展模型适用的不完备区间值数据类型更为广泛,可用于处理一般的不完备区间值信息系统,拓展了粗糙集的适用范围.

The information system with incomplete interval value was investigated to propose a new improved model. The definition of similarity was provided based on deviation degree to deal with the situations that most attribute values were intersected but not included and contained multiple continuous values. The tolerance relation was extended to establish dual-variable precision tolerance relation based on similarity and similar rate. The extension rough set model was set up for incomplete interval-valued infor- mation system. To solve the shortage of dual-variable precision tolerance relation in dividing domain and improve approximation quality, the dual-variable precision maximal consistent classes were found out. The upper and lower approximation sets were obtained to propose the maximal classification reduction algorithm. The effective feasibility of the model and algorithm was verified by real example analysis. The results show that the proposed model is suitable for incomplete interval value date type, and can be used to deal with general incomplete interval value information system and expand the scope of rough set.