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However, it is sometimes a complicated task, especially when these pixels are at the edges of regions, where there is a gradient and it is difficult to decide to which region to assign it. Hesitating fuzzy sets (HFS) better describe these situations, allowing to have multiple possible values for each element, giving more flexibility. This type of sets has been mainly applied in decision-making problems, obtaining better results than other types of fuzzy sets. This research proposes a fast and automatic method based on fuzzy hesitant clustering (FAHFC), which does not require parameters since it is capable of determining the number of clusters, using the Calinski-Harabasz index, in which the segmentation is performed, solving the initialization problem in clustering; it also proposes an alternative to construct the HFS through the use of fuzzy relations. The experiments show superiority in terms of clustering quality and convergence over some selected state-of-the-art algorithms.<\/jats:p>","DOI":"10.3233\/jifs-219370","type":"journal-article","created":{"date-parts":[[2024,3,29]],"date-time":"2024-03-29T12:39:30Z","timestamp":1711715970000},"page":"526-538","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["Fast and automatic hesitant fuzzy clustering applied to image segmentation"],"prefix":"10.1177","volume":"50","author":[{"given":"Virna V.","family":"Vela-Rinc\u00f3n","sequence":"first","affiliation":[{"name":"Tecnol\u00f3gico Nacional de M\u00e9xico\/CENIDET, Cuernavaca, Morelos, M\u00e9xico"}]},{"given":"Dante","family":"M\u00fajica-Vargas","sequence":"additional","affiliation":[{"name":"Tecnol\u00f3gico Nacional de M\u00e9xico\/CENIDET, Cuernavaca, Morelos, M\u00e9xico"}]},{"given":"Antonio","family":"Luna-\u00c1lvarez","sequence":"additional","affiliation":[{"name":"Tecnol\u00f3gico Nacional de M\u00e9xico\/CENIDET, Cuernavaca, Morelos, M\u00e9xico"}]},{"given":"Andr\u00e9s Antonio","family":"Arenas Mu\u00f1iz","sequence":"additional","affiliation":[{"name":"Tecnol\u00f3gico Nacional de M\u00e9xico\/CENIDET, Cuernavaca, Morelos, M\u00e9xico"}]},{"given":"Luis A.","family":"Cruz-Prospero","sequence":"additional","affiliation":[{"name":"Universidad Polit\u00e9cnica de Tapachula"}]}],"member":"179","published-online":{"date-parts":[[2024,3,27]]},"reference":[{"key":"e_1_3_3_2_1","unstructured":"DeJ.V. 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