In this paper an automatic procedure to perform the optimal sizing of a stand-alone solar electrical system with battery storage is developed by a fuzzy logic based multi-objective optimization approach. The procedure aims at finding the configuration that yields the best compromise for the two considered objectives: the long-term average performance and the overall cost of the generating system. In particular, the objectives of the optimization problem are: the maximization of the Supplied Load Fraction, that is the fraction of the actual electrical load that can be supplied by the system, and the minimization of the Relative Unit Electricity Cost, that is the net cost of generating each kWh during the lifetime of the stand-alone solar electrical system referred to the UEC calculated in case of loads supplied by the grid. The control variables are the solar cell array surface, the tilt angle of the modules, and the storage system capacity. The fuzzy multi-objective optimization procedure is described and the application results are presented considering different configurations characterized by some parameters, such as the electrical load, the yearly power demand, the distance from the utility grid, and the solar cells unit cost.