集值模糊测度的自连续性  

Autocontinuity of Set-valued Fuzzy Measures

作　　者：高娜[1] 李艳红[2] 王贵君[1] 

机构地区：[1]天津师范大学数学科学学院,天津300387 [2]辽东学院师范学院数学系,辽宁丹东118000

出　　处：《四川师范大学学报（自然科学版）》2008年第4期386-389,共4页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(70571056)资助项目

摘　　要：在m维正欧式空间的子集类上引入一种新的序结构.定义了集合列依序收敛的概念,讨论了集值模糊测度的自连续、一致自连续、逆自连续和一致逆自连续性,给出了逆零可加、逆自连续、一致逆自连续等定义,进而研究它们的蕴涵关系,从而丰富了集值模糊测度和集值模糊积分的理论.By introducing a new order structure in the class of subsets of an m dimensional positive Euclid space, the concept of convergence （in respect to the order） of set sequences is defined. Then autocontinuity, uniform autocontinuity, converse-autocontinuity and uniform converse-autocontinuity for the set-valued fuzzy measure are discussed. The definitions for the so-called converse-null-additivity, converse-autocontinuity, and uniform converse-autocontinuity are presented. The implication relationship among them is studied. The obtained results enrich the theory of set-valued fuzzy measures and set-valued fuzzy integrals.

关 键 词：集值模糊测度 自连续 一致自连续 逆零可加 一致逆自连续 

分 类 号：O159[理学—数学]