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In this paper, we focus on the similarity measures of Fermatean fuzzy sets. The definitions of the Fermatean fuzzy sets similarity measures and its weighted similarity measures on discrete and continuous universes are given in turn. Then, the basic properties of the presented similarity measures are discussed. Afterward, a decision-making process under the Fermatean fuzzy environment based on TOPSIS method is established, and a new method based on the proposed Fermatean fuzzy sets similarity measures is designed to solve the problems of medical diagnosis. Ultimately, an interpretative multi-criteria decision making example and two medical diagnosis examples are provided to demonstrate the viability and effectiveness of the proposed method. Through comparing the different methods in the multi-criteria decision making and the medical diagnosis application, it is found that the new method is as efficient as the other methods. These results illustrate that the proposed method is practical in dealing with the decision making problems and medical diagnosis problems.<\/jats:p>","DOI":"10.3233\/jifs-201557","type":"journal-article","created":{"date-parts":[[2021,10,22]],"date-time":"2021-10-22T12:20:06Z","timestamp":1634905206000},"page":"5847-5863","source":"Crossref","is-referenced-by-count":16,"title":["Multi-criteria decision making and pattern recognition based on similarity measures for Fermatean fuzzy sets"],"prefix":"10.1177","volume":"41","author":[{"given":"Changlin","family":"Xu","sequence":"first","affiliation":[{"name":"School of Mathematics and Information Science, North Minzu University, Yinchuan, Ningxia, China"},{"name":"The Key Laboratory of Intelligent Information and Big Data Processing of Ningxia Province, North Minzu University, Yinchuan, Ningxia, China"}]},{"given":"Juhong","family":"Shen","sequence":"additional","affiliation":[{"name":"School of Mathematics and Information Science, North Minzu University, Yinchuan, Ningxia, China"}]}],"member":"179","reference":[{"issue":"5","key":"10.3233\/JIFS-201557_ref1","first-page":"878","article-title":"Big data for intelligent decision making","volume":"46","author":"Yu","year":"2020","journal-title":"Acta Automatica Sinica"},{"key":"10.3233\/JIFS-201557_ref2","doi-asserted-by":"crossref","first-page":"1749","DOI":"10.1007\/s13042-020-01070-1","article-title":"A q-rung orthopair fuzzy multicriteria group decision making method for supplier selection based on a novel distance measure","volume":"11","author":"Pinar","year":"2020","journal-title":"Int J Mach Learn Cybern"},{"key":"10.3233\/JIFS-201557_ref3","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","article-title":"Fuzzy sets","volume":"8","author":"Zadeh","year":"1965","journal-title":"Inf Control"},{"issue":"1","key":"10.3233\/JIFS-201557_ref4","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/S0165-0114(86)80034-3","article-title":"Intuitionistic fuzzy sets","volume":"20","author":"Atanassov","year":"1986","journal-title":"Fuzzy Sets Syst"},{"key":"10.3233\/JIFS-201557_ref5","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1016\/0165-0114(89)90215-7","article-title":"More on intuitionistic fuzzy sets","volume":"33","author":"Atanassov","year":"1989","journal-title":"Fuzzy Sets Syst"},{"key":"10.3233\/JIFS-201557_ref6","doi-asserted-by":"crossref","unstructured":"Atanassov K.T. 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