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In this paper, a generalized multiple-kernel fuzzy C-means (FCM) (MKFCM) methodology is introduced as a framework for image-segmentation problems. In the framework, aside from the fact that the composite kernels are used in the kernel FCM (KFCM), a linear combination of multiple kernels is proposed and the updating rules for the linear coefficients of the composite kernel are derived as well. The proposed MKFCM algorithm provides us a new flexible vehicle to fuse different pixel information in image-segmentation problems. That is, different pixel information represented by different kernels is combined in the kernel space to produce a new kernel. It is shown that two successful enhanced KFCM-based image-segmentation algorithms are special cases of MKFCM. Several new segmentation algorithms are also derived from the proposed MKFCM framework. Simulations on the segmentation of synthetic and medical images demonstrate the flexibility and advantages of MKFCM-based approaches.