A generalized and unified approach to the approximation of fuzzy numbers and its arithmetic and characteristics Berenguer Maldonado, María Isabel Gámez Domingo, Domingo Garralda Guillén, Ana Isabel Ruiz Galán, Manuel Fuzzy number Schauder bases Approximation of functions In this paper we propose a general method for the approximation of an arbitrary fuzzy number. This method, which is constructive, recovers and properly extends some well-known approximations such as those obtained in terms of polygonal fuzzy numbers or simple fuzzy numbers. We prove the convergence of the general method and study the properties of the approximation operator, such as its compatibility with arithmetic operations of fuzzy numbers and with some of their important characteristics. In addition to this, we illustrate the method with some particularly interesting cases by providing algorithms, of great simplicity for practical use and apply them to some numerical examples. Furthermore, the approximations we construct are particularly simple from the point of view of fuzzy arithmetic and preserve some of their most important characteristics. 2023-12-20T10:05:40Z 2023-12-20T10:05:40Z 2023-09-22 journal article M.I. Berenguer , D. Gámez, A.I. Garralda-Guillem, M. Ruiz Galán. A generalized and unified approach to the approximation of fuzzy numbers and its arithmetic and characteristics. Fuzzy Sets and Systems 473 (2023) 108727 https://hdl.handle.net/10481/86364 https://doi.org/10.1016/j.fss.2023.108727 eng http://creativecommons.org/licenses/by-nc-nd/3.0/ embargoed access Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License Elsevier B.V.