{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,22]],"date-time":"2026-03-22T08:18:33Z","timestamp":1774167513632,"version":"3.50.1"},"reference-count":23,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2019,4,3]],"date-time":"2019-04-03T00:00:00Z","timestamp":1554249600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>From the perspective of each evaluation criterion, any decision alternative is evaluated by means of trapezoidal ordered fuzzy numbers (TrOFN). This approach is justified in the way that some criteria are linguistically evaluated. In this paper, decision alternatives are evaluated using oriented fuzzy Simple Additive Weighting (OF-SAW) scoring function. The ranking of alternatives may be defined by means of a nonincreasing sequence of defuzzified values of a scoring function. Any defuzzification procedure distorts ordered fuzzy numbers in a way that information on imprecision and orientation is lost. This undermines the credibility of the determined alternatives\u2019 ranking. The main purpose of this paper is to avoid the defuzzification stage in the OF-SAW method. Thus, the OF-SAW method is equipped with fuzzy scoring order. This OF-SAW method is described as a negotiation scoring system. We study an empirical example of the OF-SAW application and rank some negotiation offers. Here, we focus on the effects of replacing the defuzzified scoring function by a fuzzy one. The obtained conclusions are generalized for the case of any decision alternatives.<\/jats:p>","DOI":"10.3390\/sym11040482","type":"journal-article","created":{"date-parts":[[2019,4,4]],"date-time":"2019-04-04T03:13:42Z","timestamp":1554347622000},"page":"482","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":25,"title":["Simple Additive Weighting Method Equipped with Fuzzy Ranking of Evaluated Alternatives"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9629-4167","authenticated-orcid":false,"given":"Krzysztof","family":"Piasecki","sequence":"first","affiliation":[{"name":"Department of Investment and Real Estate, Pozna\u0144 University of Economics and Business, 61-875 Pozna\u0144, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2249-7217","authenticated-orcid":false,"given":"Ewa","family":"Roszkowska","sequence":"additional","affiliation":[{"name":"Faculty of Economy and Management, University of Bialystok, 15-062 Bialystok, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6011-7855","authenticated-orcid":false,"given":"Anna","family":"\u0141yczkowska-Han\u0107kowiak","sequence":"additional","affiliation":[{"name":"Institute of Finance, WSB University in Pozna\u0144, 61-895 Pozna\u0144, Poland"}]}],"member":"1968","published-online":{"date-parts":[[2019,4,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1007\/s10700-009-9065-2","article-title":"Computing with words in decision making: Foundations trends and prospects","volume":"8","author":"Herrera","year":"2009","journal-title":"Fuzzy Optim. 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