基于结构元的模糊值函数R-S积分  

Riemann-Stieltjes Integral of Fuzzy Valued Functions Based on the Fuzzy Structured Element

作　　者：郭元伟[1] 吕振伟[1] 闫喜红[2] GUO Yuan-wei;LV Zhen-wei;YAN Xi-hong(Basic Course Department,Taiyuan University,Taiyuan 030009,China;Department of Mathematics,Taiyuan Normal University,Jinzhong 030619,China)

机构地区：[1]太原学院基础部,山西太原030009 [2]太原师范学院数学系,山西晋中030619

出　　处：《数学的实践与认识》2021年第8期219-226,共8页Mathematics in Practice and Theory

基　　金：山西省自然科学基金(201801D121022)。

摘　　要：定义和讨论了区间值函数关于实值增函数的Riemann-Stieltjes积分及其性质,给出了区间值Riemann-Stieltjes可积的充分必要条件;同时利用实值RiemannStieltjes积分的单调收敛定理给出了区间值Riemann-Stieltjes积分收敛的必要条件.其次,定义了模糊值函数Riemann-Stieltjes积分,研究了基于结构元的模糊值函数Riemann-Stieltjes积分性质.最后讨论了模糊Riemann-Stieltjes积分收敛的必要条件.The Riemann-Stieltjes integral for interval-valued functions was defined and characterized.In addition,a necessary and sufficient condition of the interval-valued RiemannStieltjes integral was given by means of monotone convergence theorem.Furthermore,it gave the definition and some properties of Riemann-Stieltjes integral for fuzzy-valued functions.Finally,an convergence theorem for Riemann-Stieltjes was presented.

关 键 词：模糊数 结构元 模糊数值函数 RIEMANN-STIELTJES积分 

分 类 号：O172.2[理学—数学]