多粒度近似空间的模糊粗糙集模型  

A Fuzzy Rough Set Model in Multi-granulation Spaces

作　　者：胡谦 秦克云[2] HU Qian;QIN Keyun(School of Information Science and Technology, Southwest Jiaotong University, Chengdu 611756, China;School of Mathematics, Southwest Jiaotong University, Chengdu 611756, China)

机构地区：[1]西南交通大学信息科学与技术学院,四川成都611756 [2]西南交通大学数学学院,四川成都611756

出　　处：《郑州大学学报（理学版）》2020年第4期60-66,共7页Journal of Zhengzhou University:Natural Science Edition

基　　金：国家自然科学基金项目(61976130)。

摘　　要：粗糙集理论是一种处理不完备、不确定性数据的有效数学工具。多粒度的提出可以很好地解决描述粒计算理论中多视角的概念,但是原始的多粒度模型中上、下近似定义里的条件过于严苛或过于松弛且无法区分不同粒度的重要性。为使多粒度模型更适用于实际数据,更好地考虑不同粒度的重要性,提出一种处理数据的方法,可以从多粒度近似空间中得到基于对象的不同粒度的重要度,进而构建对象之间的相似度,然后得到上、下近似。最后讨论了多粒度近似空间中用该方法得到的上、下近似与其他形式的多粒度上、下近似之间的关系。Rough set theory was an effective mathematical tool to deal with incomplete and uncertain data.The proposal of multi-granulation could well describe the multi-view in granular computing theory,but the conditions of the upper and lower approximate definitions in the original multi-granulation model were too strict or too coarse to the importance of different granularities.In order to make the multi-granulation model more suitable for actual data and consider the importance of different granularities,a method for processing data was proposed.The importance of different granularities was obtained in the multi-granulation approximation space based on the objects.The similarity between the objects was constructed and then the upper and lower approximations were obtained.Finally,the relationship between the upper and lower approximations obtained by this method with other forms of multi-granularity upper and lower approximations was discussed in the multi-granulation approximation space.

关 键 词：粗糙集 模糊集 多粒度近似空间 多粒度上、下近似 模糊粗糙集 

分 类 号：TP182[自动化与计算机技术—控制理论与控制工程]