摘要
定义和讨论了模糊数值函数关于实值增函数的模糊Henstock-Stieltjes积分及其性质,并利用实值Henstock-Stieltjes积分的单调收敛定理得到了模糊Henstock-Stieltjes可积的充分必要条件;同时给出了模糊Henstock-Stieltjes积分的可积函数类,发现模糊Henstock-Stieltjes积分是对模糊Riemann-Stieltjes积分的真推广.其次,讨论了模糊Henstock-Stieltjes积分原函数的连续性、可导性以及积分转化定理.最后通过一具体实例说明对于一般的模糊Henstock-Stieltjes可积的模糊数值函数其积分原函数未必α-可导.
The Henstock-Stieltjes integral for fuzzy-number-valued functions was defined and characterized and the result shows that the definition is an extension of the fuzzy Riemann-Stieltjes integral. In addition, a necessary and sufficient condition of the fuzzy Henstock-Stieltjes integrability for fuzzy-number-valued functions was given by means of the monotone convergence theorem of Henstock-Stieltjes integral for realvalued functions proposed in this paper. Furthermore, the continuity and the differentiability of the primary functions of the fuzzy Henstock-Stieltjes integral were discussed. It was found that there exists a fuzzynumber-valued function which is fuzzy Henstock-Stieltjes integrable, but its primitive is not α-differentiable. Finally, an integral transformation theorem for the fuzzy Henstock-Stieltjes integral was presented.
出处
《兰州大学学报（自然科学版）》
CAS
CSCD
北大核心
2010年第4期89-96,共8页
Journal of Lanzhou University(Natural Sciences)
基金
国家自然科学基金项目(10771171)
甘肃省自然科学基金项目(0803RJZA108)
西北师范大学知识创新工程项目(NWNU-KJCXGC-03-61)
