{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:45:42Z","timestamp":1760240742580,"version":"build-2065373602"},"reference-count":27,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2019,9,2]],"date-time":"2019-09-02T00:00:00Z","timestamp":1567382400000},"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>We examine some aspects of the use of Simple Additive Weighting method to evaluate decision alternatives. Decision alternative attributes may be evaluated by verbal assessments which by their nature are imprecise. This means that for the purposes of Simple Additive Weighting method, any verbal assessment is represented by a fuzzy number being an imprecise approximation of a number. In this paper, all verbal assessments are represented by ordered fuzzy numbers. This approach is justified in the way that any ordered fuzzy number is additionally equipped with orientation, i.e., information about the location of the approximated number. The family of all ordered fuzzy numbers is divided into centrally symmetric families of positively oriented fuzzy numbers and of negatively oriented fuzzy numbers. The main purpose of this paper is to examine the consequences of omitting orientation of criterion ratings. We restrict all considerations to the case of trapezoidal oriented fuzzy numbers. We prove the mathematical theorem that an orientation omission can result in an increase in risk when choosing the right decision alternative. We study an empirical example of the Simple Additive Weighting method application to rank some negotiation offers. From the discussion, it follows that an orientation omission results in an increase in risk.<\/jats:p>","DOI":"10.3390\/sym11091104","type":"journal-article","created":{"date-parts":[[2019,9,3]],"date-time":"2019-09-03T03:06:14Z","timestamp":1567479974000},"page":"1104","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Impact of the Orientation of the Ordered Fuzzy Assessment on the Simple Additive Weighted Method"],"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":[[2019,9,2]]},"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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