Many applications of Fuzzy Power Flow have been proposed not only for operational purposes considering uncertainties, but also for planning exercises with high level of intermittent sources, interconnection presence and, more recently, electric vehicles load. However, their use in real systems is not usual, mainly where the uncertainty level can be significant. This is due to the low accuracy of the results related to the classical methods, and the computational burden needed to achieve a high level of accuracy in the symmetric approaches. This paper aims to present a linearization of the Symmetric Fuzzy Power Flow in order to reduce the computational effort and make it possible for it to achieve high levels of accuracy when applied to real systems. With the purposes of demonstrating the applicability of the proposed approach, several IEEE test systems and a planning configuration of the Portuguese Transmission System will be studied.