This paper presents a novel support vector machine classifier designed for sub-pixel image classification (pixel/spectral unmixing). The proposed classifier generalizes the properties of SVMs to the identification and modeling of the abundances of classes in mixed pixels by using fuzzy logic. This results in the definition of a fuzzy-input fuzzy-output support vector machine (F2SVM) classifier that can: i) process fuzzy information given as input to the classification algorithm for modeling the sub-pixel information in the learning phase of the classifier, and ii) provide a fuzzy modeling of the classification results, allowing a relation many-to-one between classes and pixels. The presented binary F2SVM can address multicategory problems according to two strategies: the fuzzy one-against-all (FOAA) and the fuzzy one-against-one strategies (FOAO). These strategies generalize to the fuzzy case techniques based on ensembles of binary classifiers used for addressing multicategory problems in crisp classification problems. The effectiveness of the proposed F2SVM classifier is tested on three problems related to image classification in presence of mixed pixels having different characteristics. Experimental results confirm the validity of the proposed sub-pixel classification method.