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Syst."],"published-print":{"date-parts":[[2023,4]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Orthopair fuzzy sets are fuzzy sets in which every element is represented by a pair of values in the unit interval, one of which refers to membership and the other refers to non-membership. The different types of orthopair fuzzy sets given in the literature are distinguished according to the proposed constrain for membership and non-membership grades. The aim of writing this manuscript is to familiarize a new class of orthopair fuzzy sets called \u201c(2,1)-Fuzzy sets\u201d which are good enough to control some real-life situations. We compare (2,1)-Fuzzy sets with IFSs and some of their celebrated extensions. Then, we put forward the fundamental set of operations for (2,1)-Fuzzy sets and investigate main properties. Also, we define score and accuracy functions which we apply to rank (2,1)-Fuzzy sets. Moreover, we reformulate aggregation operators to be used with (2,1)-Fuzzy sets. Finally, we develop the successful technique \u201caggregation operators\u201d to handle multi-criteria decision-making (MCDM) problems in the environment of (2,1)-Fuzzy sets. To show the effectiveness and usability of the proposed technique in MCDM problems, an illustrative example is provided.<\/jats:p>","DOI":"10.1007\/s40747-022-00878-4","type":"journal-article","created":{"date-parts":[[2022,10,7]],"date-time":"2022-10-07T02:05:21Z","timestamp":1665108321000},"page":"1687-1705","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":82,"title":["(2,1)-Fuzzy sets: properties, weighted aggregated operators and their applications to multi-criteria decision-making methods"],"prefix":"10.1007","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8074-1102","authenticated-orcid":false,"given":"Tareq M.","family":"Al-shami","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,10,7]]},"reference":[{"key":"878_CR1","doi-asserted-by":"publisher","first-page":"106","DOI":"10.1016\/j.ins.2019.12.008","volume":"514","author":"JCR Alcantud","year":"2020","unstructured":"Alcantud JCR, Khameneh AZ, Kilicman A (2020) Aggregation of infinite chains of intuitionistic fuzzy sets and their application to choices with temporal intuitionistic fuzzy information. 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