基于相容关系的局部粗糙集模型  

Local Rough Sets Based on Tolerance Relations

作　　者：周悦丽 林国平 ZHOU Yue-li;LIN Guo-ping(School of Mathematics and Statistics,Minnan Normal University,Zhangzhou 363000,China;Institute of Meteorological Big Data-Digital Fujian,Zhangzhou 363000,China)

机构地区：[1]闽南师范大学数学与统计学院,福建漳州363000 [2]数字福建气象大数据研究所,福建漳州363000

出　　处：《模糊系统与数学》2020年第6期43-54,共12页Fuzzy Systems and Mathematics

基　　金：国家青年科学基金资助项目(61603173,11871259,61379021);福建省高校新世纪优秀人才支持计划项目;浙江省海洋大数据挖掘与应用重点实验室开放课题(OBDMA201603)。

摘　　要：粗糙集模型作为一种重要的粒计算模型,是我们处理数据的重要工具。在实际生活中,由于数据来源的多样性,信息系统常出现集值型数据,经典的粗糙集理论显然不能处理此类数据,于是有学者提出基于相容关系的粗糙集来处理这种数据类型。为了对集值型数据进行有效的处理,本文基于局部粗糙集的概念,对粗糙集模型进行扩展,在集值信息系统中建立基于相容关系的局部粗糙集模型,首先给出局部相容粗糙集的定义,然后研究了其相关性质并给出下近似和上近似的算法的复杂度分析。同时将局部相容粗糙集的下近似算法与全局相容粗糙集的下近似算法进行比较。最后,基于对局部下近似的分析,对其属性约简进行讨论。As for an important granular computing model,rough set model is an important tool for us to deal with data.Information systems often have set-valued data because of the diversity of data sources in real life.The classical rough set theory can’t deal with this kind of data obviously,so some scholars put forward the rough sets based on the tolerance relation to deal with this type of data.In order to deal with set-valued data further effectively,this passage is based on the concept of local rough sets,then extends the types of rough sets and establishes the local rough sets based on the tolerance relation in set-valued information systems.Firstly,the definition of local rough sets based on the tolerance relation is introduced,and then the related properties are studied.In addition,the computational complexities of the proposed algorithms for the computations of lower and upper approximations are given.Meanwhile,we make a comparison between the algorithm of the computation of lower approximation on the local tolerance rough sets and that on the global tolerance rough sets.Finally,the attribute reductions are discussed based on the analysis of local lower approximation.

关 键 词：相容关系 局部粗糙集 属性约简 集值信息系统 

分 类 号：O159[理学—数学]