模糊测度的零连续性  

Null-Continuity of Fuzzy Measures

作　　者：谭浔晓 张承坤 徐鹤萍 李军[1] TAN Xun-xiao;ZHANG Cheng-kun;XU He-ping;LI Jun(School of Data Science and Intelligent Media,Communication University of China,Beijing 100024,China)

机构地区：[1]中国传媒大学数据科学与智能媒体学院,北京100024

出　　处：《中国传媒大学学报（自然科学版）》2020年第2期36-43,49,共9页Journal of Communication University of China：Science and Technology

基　　金：国家自然科学基金资助项目(No.11571106)。

摘　　要：本文将研究模糊测度的零连续性的一些性质。在模糊测度为零连续性的条件下,我们分别证明Choquet积分和基于泛运算的泛积分具有积分的唯一性。作为这些结果的特殊情形,我们得到了Sugeno积分(即模糊积分)和Shilkret积分的相应结果。我们还要讨论零连续性与模糊测度的其它几个结构特性之间的关系,并且利用可测函数的收敛性刻画模糊测度的零连续性。In this note we discuss some properties of null-continuity of fuzzy measures.Under the condition of null-continuity we show that the Choquet integral and the Pan-integral with respect to pan-operations possess the uniqueness of integral.As a special case,we obtain the results corresponding to the Sugeno integral and the Shirlkret integral.We shall discuss the relationships among the null-continuity and other structure characteristics of fuzzy measures,and by using the convergence of measurable functions we shall describe characteristics of null-continuity.

关 键 词：模糊测度 零连续性 泛积分 模糊积分 CHOQUET积分 

分 类 号：O159[理学—数学]