Abstract Fuzzy clustering is a classical method to produce soft partitions of data. Since its inception, the fuzzy clustering has been extensively studied and widely used in different applications, such as knowledge discovering, pattern recognition and image processing, by virtue of its fast convergence and straightforward implementation. To exploit more robust fuzzy clustering models, in this thesis we study different knowledge-based fuzzy clustering techniques for image segmentation and data clustering, respectively. Our main contributions are as follows: • Prior knowledge has been considered as valuable supplementary information in many image processing techniques. To embed some prior knowledge, we take the input image itself as the guidance prior and develop a novel fuzzy clustering algorithm to segment it by adding a new term to the objective function of Fuzzy C-Means. The new term comes from image guided filter for its capability in noise suppression and edge-preserving smoothing. As a result, the memberships derived from the new objective function incorporate the guidance information from the image to be segmented. In this way, the segmentation result retains more subtle details on the boundaries of segments. Experimental results demonstrate that the proposed method can efficiently handle image segmentation tasks especially for images with high noise rates. • Guided filter is a powerful edge preserving filter for image smoothing and enhancement. In this thesis, to integrate this filter in a new and easy way, we design a general framework to improve the fuzzy clustering based noisy image segmentation. Specifically, the fuzzy clustering is applied on the smoothed image to obtain more homogeneous segments, but the original noisy image is used as the guide of guided filter to post-process the fuzzy memberships in the iteration of clustering. By doing this, the information loss caused by beforehand image smoothing is remedied by the guidance of original noisy image that pulls back subtle details on the boundaries of partitions. In addition, we prove that the memberships post-processed by guided filter still retain the property usually required by fuzzy clustering: for each data point, the sum of its memberships is one. This property and the linear time complexity of guided filter make the proposed information integration framework an efficient way to enhance fuzzy clustering based image segmentation methods. Experiments on synthetic and real images show that the proposed framework can improve the state-of-the-art fuzzy clustering methods significantly with little run-time overhead. • Although non-local guided filter performs well for propagating the non-local information, it still suffers from preserving details in image smoothing process. The final results of the non-local models, such as no-local image restoration, are always a summation of all the data in the non-local window with non-local weight. So the non-local weight of image filter is of great importance. In the non-local image guided filter, the patches of guidance with high weight is more valuable than other patches in the non-local window to get a better final image. Such that, in this thesis, we propose two strategies to find a proper weight based on the fuzzy theory and shadow sets, respectively • In data mining, the straightforward assumption on fuzzy clustering is that the data points close to each other should also take similar membership vectors. Such constraints on the affinities of memberships are valuable prior knowledge that should be imposed to the objective function of fuzzy clustering for better performance. To this end, we introduce the membership affinity lasso for fuzzy clustering in this thesis. Utilizing alternating direction method of multipliers, an efficient approach is derived to optimize the general membership affinity lasso regularized fuzzy clustering model in offline manner. As illustrative examples, three new fuzzy clustering algorithms with the membership affinity lasso are proposed. Experiments on the synthetic and real data demonstrate the superiority and flexibility of the proposed algorithms.