关于有界变差函数的模糊Henstock-Stieltjes积分  

The fuzzy Henstock-Stieltjes integral with regard to bounded variation functions

作　　者：邵亚斌[1] 巩增泰[2] 

机构地区：[1]重庆邮电大学理学院,重庆400065 [2]西北师范大学数学与统计学院,兰州730070

出　　处：《模糊系统与数学》2017年第1期57-65,共9页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金项目(No.11161041;No.61472056;No.11461062);重庆市科委项目(cstc2015jcyjA00015);重庆邮电大学博士启动基金项目(A2014-90)

摘　　要：定义和讨论了模糊数值函数关于实值有界变差函数的Henstock-Stieltjes积分及其性质,并得到了模糊Henstock-Stieltjes可积的充分必要条件;同时给出了模糊数值函数列关于实值有界变差函数的Henstock-Stieltjes积分以及模糊数值函数关于有界变差函数列的模糊Henstock-Stieltjes积分的收敛定理.最后,讨论了模糊Henstock-Stieltjes积分原函数的绝对连续性.In this paper, we define the Henstock-Stieltjes integral for fuzzy-number-valued functions with regard to boundel Variation funtims. In addition,a necessary and sufficient condition of the fuzzy Henstock-Stieltjes integrability for fuzzy-number-valued functions was given. Furthermore, we give some convergence theorems of fuzzy Henstock-Stieltjes integrals with regard to bounded variation functions. Finally, the absolute continuityof the primary functions of the fuzzy Henstock-Stieltjes integral were discussed.

关 键 词：模糊数 有界变差 模糊Henstock-Stieljtjes积分 收敛定理 

分 类 号：O159[理学—数学] O172.1[理学—基础数学]