梯度豪斯道夫度量及其应用(英文)  

GRADUAL HAUSDORFF METRIC AND ITS APPLICATIONS

作　　者：周彩丽 陈欣 ZHOU Cai-li;CHEN Xin(College of Mathematics and Information Science,Hebei University,Baoding 071002,China)

机构地区：[1]河北大学数学与信息科学学院

出　　处：《数学杂志》2019年第4期486-492,共7页Journal of Mathematics

基　　金：Supported by the Natural Science Foundation of China(61572011);Natural Science Foundation of Hebei University(799207217073);Youth Scientific Research Foundation of Education Department of Hebei Province(QN2015005);Special Funds for One University of One Province of Hebei University

摘　　要：本文研究了Zhou和Zhang引入的梯度豪斯道夫度量的性质及其应用问题.利用梯度数和模糊数之间的关系,证明了(Fc(R),dH)是一个梯度度量空间,并把梯度豪斯道夫度量应用到模糊随机变量,获得了模糊随机变量的新的强大数定律.本文所得结果丰富和深化了模糊数及模糊随机变量相关理论.This paper is devoted to study of gradual Hausdorff metric introduced by Zhou and Zhang and its application. By means of relationships between gradual numbers and fuzzy numbers, we prove that (Fc(R);~ dH) is a gradual metric space. And then, we apply gradual Hausdorff metric to fuzzy random variables and obtain new strong law of large numbers for fuzzy random variables, which enrich and deepen the theory of fuzzy numbers and fuzzy random variables.

关 键 词：梯度数 梯度豪斯道夫度量 模糊随机变量 强大数定律 

分 类 号：O159[理学—数学]