{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:03:33Z","timestamp":1760241813865,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2018,8,21]],"date-time":"2018-08-21T00:00:00Z","timestamp":1534809600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information"],"abstract":"<jats:p>Hesitant fuzzy sets (HFSs), which were generalized from fuzzy sets, constrain the membership degree of an element to be a set of possible values between zero and one; furthermore, if two or more decision-makers select the same value, it is only counted once. However, a situation where the evaluation value is repeated several times differs from one where the value appears only once. Multi-hesitant fuzzy sets (MHFSs) can deal effectively with a case where some values are repeated more than once in a MHFS. In this paper, the novel convex combination of multi-hesitant fuzzy numbers (MHFNs) is introduced. Some aggregation operators based on convex operation, such as generalized multi-hesitant fuzzy ordered weighted average (GMHFOWA) operator, generalized multi-hesitant fuzzy hybrid weighted average (GMHFHWA) operator, generalized multi-hesitant fuzzy prioritized weighted average (GMHFPWA) operator and generalized multi-hesitant fuzzy Choquet integral weighted average (GMHFCIWA) operator, are developed and corresponding properties are discussed in detail. Then, based on the proposed aggregation operators, a novel approach for multi-criteria decision-making (MCDM) problem is proposed for ranking alternatives. Finally, an example is provided to verify the developed approach and demonstrate its validity and feasibility and the study is supported by a sensitivity analysis and a comparison analysis.<\/jats:p>","DOI":"10.3390\/info9090207","type":"journal-article","created":{"date-parts":[[2018,8,21]],"date-time":"2018-08-21T11:12:42Z","timestamp":1534849962000},"page":"207","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Convex Aggregation Operators and Their Applications to Multi-Hesitant Fuzzy Multi-Criteria Decision-Making"],"prefix":"10.3390","volume":"9","author":[{"given":"Ye","family":"Mei","sequence":"first","affiliation":[{"name":"School of Electrical and Information Engineering, Hubei University of Automotive Technology, Shiyan 442002, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Juanjuan","family":"Peng","sequence":"additional","affiliation":[{"name":"School of Electrical and Information Engineering, Hubei University of Automotive Technology, Shiyan 442002, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Junjie","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Information Engineering, Lingnan Normal University, Zhanjiang 524048, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,8,21]]},"reference":[{"key":"ref_1","first-page":"529","article-title":"Hesitant fuzzy sets","volume":"25","author":"Torra","year":"2010","journal-title":"Int. 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