{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T20:16:22Z","timestamp":1771013782128,"version":"3.50.1"},"reference-count":70,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2017,12,26]],"date-time":"2017-12-26T00:00:00Z","timestamp":1514246400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The aim of this paper is to present a trade-off ranking method in a fuzzy multi-criteria decision-making environment. The triangular fuzzy numbers are used to represent the imprecise numerical quantities in the criteria values of each alternative and the weight of each criterion. A fuzzy trade-off ranking method is developed to rank alternatives in the fuzzy multi-criteria decision-making problem with conflicting criteria. The trade-off ranking method tackles this type of multi-criteria problems by giving the least compromise solution as the best option. The proposed method for the fuzzy decision-making problems is compared against two other fuzzy decision-making approaches, fuzzy Technique for Order Preference by Similarity to the Ideal Solution (TOPSIS) and fuzzy VlseKriterijuska Optimizacija I Komoromisno Resenje (VIKOR), used for ranking alternatives.<\/jats:p>","DOI":"10.3390\/axioms7010001","type":"journal-article","created":{"date-parts":[[2017,12,26]],"date-time":"2017-12-26T11:13:23Z","timestamp":1514286803000},"page":"1","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["A Fuzzy Trade-Off Ranking Method for Multi-Criteria Decision-Making"],"prefix":"10.3390","volume":"7","author":[{"given":"Nor","family":"Jaini","sequence":"first","affiliation":[{"name":"School of Mechanical, Aerospace and Civil Engineering, The University of Manchester, Sackville Street, Manchester M13 9PL, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sergey","family":"Utyuzhnikov","sequence":"additional","affiliation":[{"name":"School of Mechanical, Aerospace and Civil Engineering, The University of Manchester, Sackville Street, Manchester M13 9PL, UK"},{"name":"Moscow Institute of Physics and Technology, 141700 Dolgoprudny, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,12,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"180","DOI":"10.1287\/mnsc.12.3.180","article-title":"Weighting Multiple Criteria","volume":"12","author":"Eckenrode","year":"1965","journal-title":"Manag. 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