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In zoning-based classification, a membership function defines the way a feature influences the different zones of the zoning method. This paper presents a new class of membership functions, which are called fuzzy-membership functions (FMFs), for zoning-based classification. These FMFs can be easily adapted to the specific characteristics of a classification problem in order to maximize classification performance. In this research, a real-coded genetic algorithm is presented to find, in a single optimization procedure, the optimal FMF, together with the optimal zoning described by Voronoi tessellation. The experimental results, which are carried out in the field of handwritten digit and character recognition, indicate that optimal FMF performs better than other membership functions based on abstract-level, ranked-level, and measurement-level weighting models, which can be found in the literature.