基于阶梯均值vague集的粗糙集模型及其不确定性度量  

Rough Set Model and Its Uncertainty Measures Based on Average-step-vague Set

作　　者：王潇雪 张贤勇 WANG Xiao-xue;ZHANG Xian-yong(School of Mathematical Sciences,Sichuan Normal University,Chengdu 610066;Laurent Math Center,Sichuan Normal University,Chengdu 610066;Institute of Intelligent Information and Quantum Information,Sichuan Normal University,Chengdu 610066,China)

机构地区：[1]四川师范大学数学科学学院,四川成都610066 [2]四川师范大学Laurent数学中心,四川成都610066 [3]四川师范大学智能信息与量子信息研究所,四川成都610066

出　　处：《模糊系统与数学》2024年第1期145-155,共11页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金项目(6167325811671284);四川省自然科学基金项目(2022NSFSC0929);四川省科技计划项目(2021YJ0085)。

摘　　要：Vague集和粗糙集都是处理不确定性的数学工具,它们的结合具有研究意义.基于阶梯均值vague集构造一种新型粗糙集模型,并研究相关的模糊度、粗糙度等不确定性度量.定义阶梯均值vague粗糙集,确定上下近似与三支区域,研究该模型近似算子的并、交、补等运算性质.提出相应的模糊度、精确度、粗糙度、近似精度、近似质量,并得到关于论域剖分与层次集成的性质。提供数据实例,计算上下近似、三支区域、模糊度、粗糙度等概念,并验证相关性质.所得vague粗糙集及其不确定度量有利于深入不确定性处理。Both vague sets and rough sets are mathematical tools for dealing with uncertainty,and their combination has research significance.A new rough set model is constructed based on the averagestep-vague set,and its uncertain-ty measures such as ambiguity and roughness are studied.At first,the average-step-vague rough set is defined to de-termine its dual approximations and three-way regions,and u-nion,intersection and complement properties of approxi-mation operators are studied.Then,corresponding ambiguity,accuracy,roughness,approximate precision and quality are proposed,and their properties on universe division and hierarchy integration are obtained.Finally,data examples are provided to calculate related notions of dual approximation,three-way regions,ambiguity,roughness,and thus cor-responding properties are verified.The obtained vague rough set and its uncertainty measures profit in-depth uncer-tainty processing.

关 键 词：VAGUE集 粗糙集 Vague粗糙集 近似算子 三支决策 粗糙度 模糊度 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程] O159[自动化与计算机技术—控制科学与工程]