粗糙集的阶梯式近似

doi:10.16451/j.cnki.issn1003-6059.201907003

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摘要

首先,利用基于边界域粗糙近似算子,给出n阶边界集的定义,引入n阶粗糙近似算子的定义,构造粗糙集理论的一套阶梯式近似方法.然后,通过实例和相关证明表明,无论二元关系还是在覆盖环境中,总存在正整数n,对于任意对象集,n阶上下近似集完全等于该对象集,即该对象集是此意义下的精确集,或其n阶上下近似集趋近于某一固定的对象集,即n阶粗糙集总能使对象集合趋近于它本身或某一固定的集合.

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	马周明
	张海洋
	陈锦坤
	李进金

关键词 ： n阶粗糙集, 精确集, 近似算子, 边界域, 阶梯式近似方法

Abstract：

The definition of n-step boundary set is given based on rough approximation operator in boundary region. The definition of n-step rough approximation operator is introduced and a set of stepped approximation method of rough set theory is constructed. The examples and related proofs show that positive integers always exist in both binary relations and coverage environments, the n-step upper and lower approximation sets are exactly equal to the set of objects, and the object set is the exact set in this sense. Its n-step upper and lower approximation sets or approach a fixed set of objects. The n-step rough set can make an object set approach itself or a fixed set.

Key words： n-Step Rough Set Exact Set Approximation Operator Boundary Region Stepped Approximation Method

收稿日期: 2019-05-15

ZTFLH:

TP 18

基金资助:

国家自然科学基金项目(No.A011404,61573127,61672272,61603173,11701258)、福建省自然科学基金项目(No.2017J01507,2019J01748)资助

作者简介: 马周明(通讯作者),博士,副教授,主要研究方向为不确定性理论及其应用.E-mail:44842802@qq.com.张海洋,硕士研究生,主要研究方向为不确定性理论及其应用.E-mail:1913570847@qq.com.)陈锦坤,博士研究生,副教授,主要研究方向为粗糙集、概念格.E-mail:cjk99@163.com李进金,博士,教授,主要研究方向为拓扑学、概念格.E-mail:jinjinli@mnnu.edu.cn.

引用本文:

马周明,张海洋,陈锦坤,李进金. 粗糙集的阶梯式近似[J]. 模式识别与人工智能, 2019, 32(7): 600-606. MA Zhouming, ZHANG Haiyang, CHEN Jinkun, LI Jinjin. Stepped Approximation Method of Rough Sets. , 2019, 32(7): 600-606.

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http://manu46.magtech.com.cn/Jweb_prai/CN/10.16451/j.cnki.issn1003-6059.201907003 或 http://manu46.magtech.com.cn/Jweb_prai/CN/Y2019/V32/I7/600

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