基于平均型聚合函数的多粒度模糊粗糙集  

Multi-granulation Fuzzy Rough Set Based on Average Aggregation Functions

作　　者：于鹏[1] 王圣智 YU Peng;WANG Shengzhi(School of Mathematics and Data Science,Shaanxi University of Science&Technology,Xi′an 710021,China)

机构地区：[1]陕西科技大学数学与数据科学学院,陕西西安710021

出　　处：《郑州大学学报（理学版）》2024年第4期65-71,共7页Journal of Zhengzhou University:Natural Science Edition

基　　金：国家自然科学基金项目(12171294);陕西省自然科学基础研究计划项目(2022JQ-064)。

摘　　要：多粒度模糊粗糙集(multi-granulation fuzzy rough set,MGFRS)是一种重要的粗糙集模型。乐观多粒度模糊粗糙集和悲观多粒度模糊粗糙集分别给出了被描述对象的两种极端描述。从数据聚合角度看,将不同粒度值合并为单一粒度值时,乐观MGFRS采用的是取小算子,悲观MGFRS采用的是取大算子。将取小与取大算子拓展为一般的平均型聚合算子,提出了一种新的多粒度模糊粗糙集模型:基于平均型聚合函数的多粒度模糊粗糙集(multi-granulation fuzzy rough set model on the base of average aggregate function,MFA)模型。研究了MFA模型的基本性质,给出了MFA模型与乐观和悲观多粒度模糊粗糙集的关系。同时,基于MFA模型,提出了基于平均型聚合算子的粗糙近似集模型。Multi-granulation fuzzy rough set(MGFRS)was an important rough set model.Two extreme approximations of described objects could be given by optimistic and pessimistic multi-granulation fuzzy rough sets.From the perspective of data aggregation,when different granularity values were aggregated into a single one,the minimum and maximum operators were usually applied in optimistic and pessimistic MGFRS,respectively.A new multi-granulation fuzzy rough set model on the base of average aggregate function(MFA)model was proposed by extending the minimum and maximum operators to general aver-age aggregate operators.And then,its basic properties and the relationship between MFA model and opti-mistic and pessimistic multi-granulation fuzzy rough sets were explored.Finally,a new rough approximate set mode based on average aggregation operator was proposed in view of MFA model.

关 键 词：聚合函数 粗糙集 多粒度模糊粗糙集 近似集 

分 类 号：O41[理学—理论物理] O06[理学—物理]