Summary: We study the differentiability, integral, and calculus of linear fuzzy-number-valued functions. Special emphasis is placed on the linear fuzzy-number-valued function \(\widetilde{F}(t) = \widetilde{u}_1 f_1(t) + \widetilde{u}_2 f_2(t) + \cdots + \widetilde{u}_m f_m(t)\), where \(\widetilde{u}_1, \widetilde{u}_2, \ldots, \widetilde{u}_m\) denote fuzzy \(n\)-cell numbers and \(f_1, f_2, \ldots, f_m\) 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 L. T. Gomes and L. C. Barros [ibid. 280, 142–145 (2015; Zbl 1373.26033)], 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 \(\widetilde{F}(t) = \widetilde{u}_1 f_1(t) + \widetilde{u}_2 f_2(t) + \cdots + \widetilde{u}_m f_m(t)\) is derived.