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The classification of very high-resolution remotely sensed images from urban areas is addressed. Previous studies have shown the interest of exploiting the local geometrical information of each pixel to improve the classification. This is performed using the derivative morphological profile (DMP) obtained with a granulometric approach, using opening and closing operators. For each pixel, this DMP constitutes the feature vector on which the classification is based. In this letter, we present an interpretation of the DMP in terms of a fuzzy measurement of the characteristic size and contrast of each structure. This fuzzy measure can be compared to predefined possibility distributions to derive a membership degree for a set of given classes. The decision is taken by selecting the class with the highest membership degree. This model is illustrated and validated in a classification problem using IKONOS images.