双论域多粒度模糊粗糙集近似的并交关系  

Union and Intersection Relationships of Approximations of Double-universes Multi-granularity Fuzzy Rough Sets

作　　者：陈江 张贤勇 莫智文 CHEN Jiang;ZHANG Xianyong;MO Zhiwen(School of Mathematical Sciences,Institute of Intelligent Information and Quantum Information,Sichuan Normal University,Chengdu 610066,Sichuan)

机构地区：[1]四川师范大学数学科学学院智能信息与量子信息研究所,四川成都610066

出　　处：《四川师范大学学报（自然科学版）》2021年第5期699-705,共7页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(61673285,11671284);四川省科技计划项目(2021YJ0085、2019YJ0529)。

摘　　要：模糊粗糙集是一种强健的不确定性处理模型,其拓展及相关性质具有重要意义.针对双论域多粒度模糊粗糙集,研究并交近似与近似并交的关系,得到悲观双近似算子与乐观双近似算子对于并交运算的保持性或拓展性,最后用一个医疗实例进行性质说明与有效验证.对于并交系统性质,其中的悲观模型与乐观模型分别具有与经典粗糙集模型的一致性与差异性,所得结果揭示出双论域多粒度模糊粗糙集的扩张特性.Fuzzy rough sets serve as a robust model of uncertainty processing,and their extension and relevant properties have fun-damental significance.Regarding double-universes multi-granularity fuzzy rough sets,relationships between the union/intersection approximation and approximation union/intersection are studied,and thus pessimistic and optimistic dual approximation operators acquire their preservation or extension on union and intersection operations.finally,the property illustration and effectiveness verification are implemented by a medical example.For systematic properties of union and intersection,the pessimistic and optimisticmodels respectively have uniformity and difference from the classical rough set model,and thus the obtained results reveal the expansion feature of double-universes multi-granularityfuzzy rough sets.

关 键 词：模糊粗糙集 多粒度 双论域 上下近似 并交运算 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]