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\iteman{io-port 06089566}
\itemau{Gong, Zengtai; Wang, Liangliang}
\itemti{The Henstock-Stieltjes integral for fuzzy-number-valued functions.}
\itemso{Inf. Sci. 188, 276-297 (2012).}
\itemab
Summary: We firstly define and discuss the Henstock-Stieltjes integral for fuzzy-number-valued functions which is an extension of the usual fuzzy Riemann-Stieltjes integral. In addition, several necessary and sufficient conditions of the integrability for fuzzy-number-valued functions are given by means of the Henstock-Stieltjes integral of real-valued functions and Henstock integral of fuzzy-number-valued functions. Secondly, the continuity and the differentiability of the primitive for the fuzzy Henstock-Stieltjes integral are discussed. Thirdly, we introduce some quadrature rules for the fuzzy Henstock-Stieltjes integral by giving error bounds for the mappings of bounded variation and of Lipschitz type. We also consider the generalization of classical quadrature rules, such as midpoint-type, trapezoidal and Simpson's quadrature. Finally, we propose the concept of weak equi-integrability for sequences of fuzzy Henstock-Stieltjes integrable functions.
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\itemut{fuzzy number; fuzzy Henstock integral; Stieltjes integral; differentiability; numerical calculate; convergence theorem}
\itemli{doi:10.1016/j.ins.2011.11.024}
\end