不协调区间值决策系统中的α-上、下近似约简  

α-lower and upper approximation reductions in inconsistent interval-valued decision systems

作　　者：张晓雨 李同军 ZHANG Xiao-yu;LI Tong-jun(School of Information Engineering,Zhejiang Ocean University,Zhoushan 316022,Zhejiang,China;Key Laboratory of Oceanographic Big Data Mining&Application of Zhejiang Province,Zhoushan 316022,Zhejiang,China)

机构地区：[1]浙江海洋大学信息工程学院,浙江舟山316022 [2]浙江海洋大数据挖掘与应用重点实验室,浙江舟山316022

出　　处：《山东大学学报（理学版）》2022年第5期20-27,共8页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(61773349,61573321,61976194,41631179)。

摘　　要：研究了不协调区间值决策系统中基于α-容差关系的属性约简问题。针对一种常用的α-容差关系,给出了保持全部决策类的下近似不变的α-下近似约简和保持全部决策类的上近似不变的α-上近似约简的定义,证明了α-上近似约简与已有的α-广义决策约简和α-不确定性保持约简的等价性,以及α-下近似约简与已有的α-确定性保持约简的等价性。讨论了α-上近似约简和α-下近似约简之间的关系,并用例子加以验证。The focus is on the attribute reductions of inconsistent interval-valued decision systems based on α-tolerance relation. With respect to one kind of α-tolerance relations in inconsistent interval-valued decision systems, notions of α-lower and upper approximate reductions are defined, which keep the lower and upper approximations of all the decision classes unchanged, respectively. Subsequently, the equivalences among the α-upper approximate reduction and α-generalized decision reduction, α-uncertainty maintained reduction, and between α-lower approximate reduction and α-certainty maintained reduction are proved. Meanwhile, the relationships between α-lower approximate reduction and α-upper approximate reduction are discussed in detail, and verified by some examples.

关 键 词：粗糙集 不协调区间值决策系统 α-容差关系 α-上近似约简 α-下近似约简 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]