We study the differentiability, integral, and calculus of linear fuzzy-number-valued functions. Special emphasis is placed on the linear fuzzy-number-valued function $\tilde{F}(t)={\tilde{u}}_1{f}_1(t)+{\tilde{u}}_2{f}_2(t)+\cdots +{\tilde{u}}_m{f}_m(t)$, where ${\tilde{u}}_1,{\tilde{u}}_2,\dots ,{\tilde{u}}_m$ denote fuzzy n-cell numbers and $f_1,f_2,\dots ,f_m$ represent real functions of a real variable. The concepts of the limit and continuity of fuzzy n-cell-number-valued functions are defined, which are the basis for studying the calculus of linear fuzzy-number-valued functions. Using the fuzzy generalized difference introduced by Gomes and Barros (Fuzzy Sets Syst. 280 (2015) 142–145), we define a generalized difference for fuzzy n-cell numbers. Then a generalized differentiability of fuzzy n-cell-number-valued functions is proposed, and a sufficient condition for generalized differentiability of linear fuzzy-number-valued functions is given by means of real function theory. Furthermore, a Riemann integral of fuzzy n-cell-number-valued functions is introduced, and some properties of the integral are discussed. Finally, the relationship between generalized differentiability and the Riemann integral of the linear fuzzy-number-valued function $\tilde{F}(t)={\tilde{u}}_1{f}_1(t)+{\tilde{u}}_2{f}_2(t)+\cdots +{\tilde{u}}_m{f}_m(t)$ is derived.

我们研究线性模糊数值函数的可微性，积分和演算。重点放在线性模糊数值函数上$\stackrel{〜}{F}（Ť）={\stackrel{〜}{ü}}_{\mathrm{1个}}{F}_{\mathrm{1个}}（Ť）+{\stackrel{〜}{ü}}_2{F}_2（Ť）+\cdots +{\stackrel{〜}{ü}}_{米}{F}_{米}（Ť）$，在哪里 ${\stackrel{〜}{ü}}_{\mathrm{1个}}，{\stackrel{〜}{ü}}_2，\dots ，{\stackrel{〜}{ü}}_{米}$表示模糊n元数，并且$F_{\mathrm{1个}}，F_2，\dots ，F_{米}$表示实变量的实函数。定义了模糊n元数值函数的极限和连续性的概念，为研究线性模糊数值函数的演算奠定了基础。使用Gomes和Barros引入的模糊广义差（Fuzzy Sets Syst。280（2015）142–145），我们定义了模糊n元数的广义差。然后提出了模糊n元数值函数的广义可微性，并利用实函数理论给出了线性模糊数值函数的广义可微性的充分条件。此外，模糊n的黎曼积分介绍了-cell-number-valued函数，并讨论了积分的一些属性。最后，广义可微性与线性模糊数值函数的黎曼积分之间的关​​系$\stackrel{〜}{F}（Ť）={\stackrel{〜}{ü}}_{\mathrm{1个}}{F}_{\mathrm{1个}}（Ť）+{\stackrel{〜}{ü}}_2{F}_2（Ť）+\cdots +{\stackrel{〜}{ü}}_{米}{F}_{米}（Ť）$ 派生。