{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,31]],"date-time":"2026-01-31T03:36:20Z","timestamp":1769830580684,"version":"3.49.0"},"reference-count":27,"publisher":"SAGE Publications","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IFS"],"published-print":{"date-parts":[[2022,8,10]]},"abstract":"<jats:p>Fuzzy clustering is an important research field in pattern recognition, machine learning and image processing. The fuzzy C-means (FCM) clustering algorithm is one of the most common fuzzy clustering algorithms. However, it requires a given number of clusters in advance for accurate clustering of data sets, so it is necessary to put forward a better clustering validity index to verify the clustering results. This paper presents a ratio component-wise design method of clustering validity function based on FCM clustering method. By permutation and combination of six clustering validity components representing different meanings in the form of ratio, 49 different clustering validity functions are formed. Then, these functions are verified experimentally under six kinds of UCI data sets, and a clustering validity function with the simplest structure and the best classification effect is selected by comparison. Finally, this function is compared with seven traditional clustering validity functions on eight UCI data sets. The simulation results show that the proposed validity function can better verify the classification results and determine the optimal clustering number of different data sets.<\/jats:p>","DOI":"10.3233\/jifs-213481","type":"journal-article","created":{"date-parts":[[2022,5,17]],"date-time":"2022-05-17T12:27:00Z","timestamp":1652790420000},"page":"4691-4707","source":"Crossref","is-referenced-by-count":0,"title":["Ratio component-wise design method of fuzzy c-means clustering validity function"],"prefix":"10.1177","volume":"43","author":[{"given":"Guan","family":"Wang","sequence":"first","affiliation":[{"name":"School of Electronic and Information Engineering, University of Science and Technology Liaoning, Anshan, China"}]},{"given":"Jie-Sheng","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, University of Science and Technology Liaoning, Anshan, China"}]},{"given":"Hong-Yu","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, University of Science and Technology Liaoning, Anshan, China"}]},{"given":"Jia-Xu","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, University of Science and Technology Liaoning, Anshan, China"}]}],"member":"179","reference":[{"key":"10.3233\/JIFS-213481_ref1","doi-asserted-by":"crossref","first-page":"100193","DOI":"10.1016\/j.cosrev.2019.100193","article-title":"Data mining and information retrieval in the 21st century: A bibliographic review","volume":"34","author":"Liu, Jiaying","year":"2019","journal-title":"Computer Science Review"},{"key":"10.3233\/JIFS-213481_ref2","doi-asserted-by":"crossref","first-page":"128","DOI":"10.1002\/sam.10008","article-title":"Cluster ensemble selection","volume":"1.3","author":"Fern, Xiaoli","year":"2008","journal-title":"Statistical Analysis and Data Mining: The ASA Data Science Journal"},{"key":"10.3233\/JIFS-213481_ref3","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1016\/j.inffus.2020.03.009","article-title":"A multiple k-means clustering ensemble algorithm to find nonlinearly separable clusters","volume":"61","author":"Bai, Liang","year":"2020","journal-title":"Information Fusion"},{"key":"10.3233\/JIFS-213481_ref4","doi-asserted-by":"crossref","first-page":"641","DOI":"10.1016\/j.patrec.2003.12.018","article-title":"A clustering method based on boosting","volume":"25.6","author":"Frossyniotis","year":"2004","journal-title":"Pattern Recognition Letters"},{"key":"10.3233\/JIFS-213481_ref6","first-page":"231","article-title":"Density-based clustering","volume":"1.3","author":"Kriegel, Hans-Peter","year":"2011","journal-title":"Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery"},{"issue":"10","key":"10.3233\/JIFS-213481_ref7","doi-asserted-by":"crossref","first-page":"3364","DOI":"10.1016\/j.patcog.2010.04.021","article-title":"SEP\/COP: An efficient method to find the best partition in hierarchical clustering based on a new cluster validity index","volume":"43","author":"Gurrutxga, Ibai","year":"2010","journal-title":"Pattern Recognition"},{"issue":"1-2","key":"10.3233\/JIFS-213481_ref8","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1007\/s11222-014-9500-2","article-title":"Model-based clustering based on sparse finite Gaussian mixtures","volume":"26","author":"Malsiner-Walli, Gertraud","year":"2016","journal-title":"Statistics and Computing"},{"issue":"1","key":"10.3233\/JIFS-213481_ref9","first-page":"100","article-title":"A k-means clustering algorithm","volume":"28","author":"Hartigan","year":"1979","journal-title":"Journal of the Royal Statistical Society, Series C (Applied Statistics)"},{"issue":"4","key":"10.3233\/JIFS-213481_ref10","doi-asserted-by":"crossref","first-page":"1013","DOI":"10.1109\/TFUZZ.2016.2584644","article-title":"Extending information-theoretic validity indices for fuzzy clustering","volume":"25","author":"Lei","year":"2017","journal-title":"IEEE Transactions on Fuzzy Systems"},{"key":"10.3233\/JIFS-213481_ref11","doi-asserted-by":"crossref","first-page":"12386","DOI":"10.1109\/ACCESS.2019.2893063","article-title":"Brain image segmentation based on FCM clustering algorithm and rough set","volume":"7","author":"Huang, Hong","year":"2019","journal-title":"IEEE Access"},{"issue":"2\u20133","key":"10.3233\/JIFS-213481_ref13","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1016\/0098-3004(84)90020-7","article-title":"Full, William. 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