区间粗糙数覆盖粗糙集模型  

Interval Rough Number Covering Rough Set Model

作　　者：何莹莹 张玉 程林海 吕跃进[2,3] HE Ying-ying;ZHANG Yu;CHENG Lin-hai;LV Yue-jin(College of Eletrical Engineering,Guangxi University,Nanning 530004,China;College of Mathematics and Information Science,Guangxi University,Nanning 530004,China;Liuzhou Institute of Technology,Liuzhou 545616,China)

机构地区：[1]广西大学电气工程学院,广西南宁530004 [2]广西大学数学与信息科学学院,广西南宁530004 [3]柳州工学院,广西柳州545616

出　　处：《模糊系统与数学》2020年第3期79-88,共10页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(71361002)

摘　　要：现有覆盖粗糙集仅讨论了属性值为实数、区间数或有限集值的情况,对属性值为区间粗糙数的讨论尚未见到。为此,文章提出了基于区间粗糙数的覆盖粗糙集模型。在定义了区间粗糙数距离的基础上,结合参数α和γ定义了相容度的概念,提出了相容关系和相容类的定义;然后定义了集合离散度的概念,对以相容类作为近似算子的上下近似进行了改进,提出了基于ξ阈值的集合离散度的上下近似和基于最小集合离散度的上下近似,证明了这两种上下近似的定义均提高了原有模型的精确度;最后讨论了基于最小集合离散度覆盖粗糙集模型的一些性质。At present,the existed covering rough sets only discussed the case where the elements in the domain are valued as real numbers,interval numbers or finite set-values.The discussion on the value of the interval rough numbers has not been seen.For this kind of situation,the covering rough set model based on interval rough numbers is proposed.Firstly,on the basis of the interval rough number the concept of the compatibility is defined by the parametersαandγ,and further put forward the definition of the compatible relation and the compatible classes.Then the concept of set dispersion is introduced to improve the upper and lower approximation which is defined by similar classes,and then the upper and lower approximation based onξset dispersion and the minimum set dispersion are proposed,and it is prove that the fidelity of the model is increased.Finally the accuracy of the minimum set dispersion based model is discussed.

关 键 词：覆盖粗糙集模型 区间粗糙数 相容度 相容关系 集合离散度 

分 类 号：O159[理学—数学]