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• An interval type-2 possibilistic fuzzy clustering with local information is proposed. • Deep neighborhood window is used to enhance the adaptive ability of algorithm. • Local and non-local information is used to improve the robustness of algorithm. • Using structural similarity to enhance the influence of local spatial information. • Testing results show that the proposed algorithm has extremely good performance. Type-2 fuzzy set theory has certain potential advantage in processing high-order uncertainty, and has been more and more widely applied in pattern recognition, image processing, and system modeling. Although it has been introduced into robust fuzzy clustering modeling, most clustering methods based on type-2 fuzzy set theory have many obvious shortcomings, such as weak robustness against noise and high sensitivity to initial value. Therefore, this paper presents a novel single fuzzifier interval type-2 kernel-based possibilistic fuzzy local and non-local information c-means clustering, and it is driven by deep neighborhood information for image segmentation in the presence of high noise. Firstly, we construct the novel deep neighborhood window structure, which consists of local neighborhood window around current pixel and deep neighborhood window around the pixel in local neighborhood window around current pixel. Secondly, using the structural similarity between local neighborhood window and deep neighborhood window around current pixel, we construct a novel fuzzy local information factor to tune the impact of local neighborhood information on current pixel clustering. Thirdly, possibility theory and fuzzy local information factor are introduced into interval type-2 kernel-based fuzzy c-means clustering, and a novel single fuzzifier type-2 possibilistic fuzzy clustering with richer local and non-local information and kernel metric is proposed. Experimental results indicate that the proposed algorithm outperforms existing state-of-the-art robust fuzzy clustering-related algorithms, and significantly improve the robustness of robust fuzzy clustering algorithms against noise. [ABSTRACT FROM AUTHOR]