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The design of high-performance gradient coils is essential for modern magnetic resonance imaging (MRI) applications. This work presents a new and alternative design methodology that explores three-dimensional (3-D) solution space by combining fuzzy membership functions to model and reshape the coil structure, given the magnetic field and electrical and mechanical constraints. The approach includes a stream function generator, a 3-D coil structure generator, and the evaluation of an objective function. An unconventional stream function for asymmetric transverse gradient coils is defined in terms of fuzzy sets. The method was applied to design a short, unshielded asymmetric gradient coil for breast imaging. The resulting dome-shape coil has superior gradient performance compared to a standard fingerprint coil. New quadrupolar gradient coil designs for breast imaging can also be obtained with the proposed method. The paper concludes with a study of the influence of a number of design parameters on the coil performance.