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Open AccessArticle

Impact of the Orientation of the Ordered Fuzzy Assessment on the Simple Additive Weighted Method

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(9), 1104; https://doi.org/10.3390/sym11091104
Received: 28 July 2019 / Revised: 17 August 2019 / Accepted: 21 August 2019 / Published: 2 September 2019
(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems)
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. View Full-Text
Keywords: ordered fuzzy number; linguistic order scale; Simple Additive Weighting method; disorientation; fuzzy ranking; decision alternative; negotiation problem ordered fuzzy number; linguistic order scale; Simple Additive Weighting method; disorientation; fuzzy ranking; decision alternative; negotiation problem
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MDPI and ACS Style

Piasecki, K.; Roszkowska, E.; Łyczkowska-Hanćkowiak, A. Impact of the Orientation of the Ordered Fuzzy Assessment on the Simple Additive Weighted Method. Symmetry 2019, 11, 1104.

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