重叠函数和分组函数的加法与乘法生成子对的相互转化  

The Mutual Transformation Between Overlap,Grouping Functions and Their Additive and Multiplicative Generator Pairs

作　　者：张廷海[1] 覃锋[1] ZHANG Ting-hai;QIN Feng(College of Mathematics and Informatics,Jiangxi Normal University,Nanchang 330022,China)

机构地区：[1]江西师范大学数学与信息科学学院,江西南昌330022

出　　处：《安徽师范大学学报（自然科学版）》2019年第2期110-115,165,共7页Journal of Anhui Normal University(Natural Science)

基　　金：国家自然科学基金项目(61563020);江西省自然科学重点基金项目(20171ACB20010);江西省教育厅科技项目(60296)

摘　　要：重叠函数和分组函数是在图像处理、分类和决策等问题中有着重要作用的两类特殊聚合算子,在它们的表示方法中,加法和乘法生成子对是两种广泛存在的重要形式。本文找到了这两种生成子对之间的密切联系,使得这两类函数的两种生成子对之间可以相互转化,并给出了重叠函数和分组函数与其生成子对函数间关系的新结果。Overlap functions and grouping functions are two special kinds of aggregation operators that play an important role in image processing,classification and decision making problems.The important representation methods of them are additive and multiplicative generator pairs,which are widely existent.In this paper,we find the close connection between the two kinds of generator pairs.This leads to the mutual transformation of the two kinds of generator pairs of two functions.The new results about the relationships between the two kinds of functions and their generator pairs are obtained.

关 键 词：重叠函数 分组函数 加法生成子对 乘法生成子对 

分 类 号：O14[理学—数学] O17[理学—基础数学]