n维模糊数值函数Henstock-Stieltjes积分原函数的可导性与导函数的可积性  

Differentiability of Integral Primitive for n Dimensional Fuzzy Henstock-Stieltjes Integral and Integrability of Derivative

作　　者：肖志勇 王欣欣 XIAO Zhiyong;WANG Xinxin(College of Mathematics and Statistics,Longdong University,Qingyang 745000,Gansu)

机构地区：[1]陇东学院数学与统计学院,甘肃庆阳745000

出　　处：《四川师范大学学报（自然科学版）》2020年第5期637-641,共5页Journal of Sichuan Normal University（Natural Science）

基　　金：甘肃省高校项目(2017A-099)。

摘　　要：为了完善n维模糊数值函数微积分理论,首先,定义模糊数值函数α-导数和α-支撑导数;其次,讨论α-导数和α-支撑导数的关系、模糊数值函数Henstock-Stieltjes积分与实值函数Henstock-Stieltjes积分的关系;最后,利用n维模糊数支撑函数研究n维模糊数值函数Henstock-Stieltjes积分原函数的可导性与导函数的可积性.In order to complete the theory of fuzzy integrals,theα-derivative andα-support-derivative for n dimension fuzzy-valued functions are defined.Then we study the relationships between theα-derivative,and theα-support-derivative,and the fuzzy Henstock-Stieltjes integral for n dimension fuzzy-valued functions and the integral for real-valued functions.Moreover,we discuss the differentiability of integral primitive for n dimensional fuzzy Henstock-Stieltjes integral and the integrability of derivative by using support function of n dimensional fuzzy number.

关 键 词：模糊数 模糊数值函数Henstock-Stieltjes积分 模糊数值函数的α-导数 

分 类 号：O159[理学—数学]