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Open AccessArticle

Simple Additive Weighting Method Equipped with Fuzzy Ranking of Evaluated Alternatives

1
Department of Investment and Real Estate, Poznań University of Economics and Business, 61-875 Poznań, Poland
2
Faculty of Economy and Management, University of Bialystok, 15-062 Bialystok, Poland
3
Institute of Finance, WSB University in Poznań, 61-895 Poznań, Poland
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(4), 482; https://doi.org/10.3390/sym11040482
Received: 27 February 2019 / Revised: 21 March 2019 / Accepted: 28 March 2019 / Published: 3 April 2019
(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems)
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’ 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. View Full-Text
Keywords: ordered fuzzy number; linguistic order scale; Simple Additive Weighting method; defuzzification; fuzzy ranking; decision alternative; negotiation problem ordered fuzzy number; linguistic order scale; Simple Additive Weighting method; defuzzification; fuzzy ranking; decision alternative; negotiation problem
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Piasecki, K.; Roszkowska, E.; Łyczkowska-Hanćkowiak, A. Simple Additive Weighting Method Equipped with Fuzzy Ranking of Evaluated Alternatives. Symmetry 2019, 11, 482.

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