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

Krzysztof Piasecki , Ewa Roszkowska , Anna Łyczkowska-Hanćkowiak

Abstract

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.
Author Krzysztof Piasecki (WZ / KIiN)
Krzysztof Piasecki,,
- Department of Investment and Real Estate
, Ewa Roszkowska - Uniwersytet w Białymstoku, MNiSW [80]
Ewa Roszkowska,,
-
, Anna Łyczkowska-Hanćkowiak - Wyższa Szkoła Bankowa w Poznaniu
Anna Łyczkowska-Hanćkowiak,,
-
Journal seriesSymmetry-Basel, [Symmetry], ISSN 2073-8994, (N/A 70 pkt)
Issue year2019
Vol11
No9
Pages1-22
Publication size in sheets1.05
Article number1104
Keywords in Polishskierowana liczba rozmyta; lingwistyczna skala porządkowa; metoda SAW; dezorientacja; ranking rozmyty; problem negocjacyjny
Keywords in Englishordered fuzzy number; linguistic order scale; SAW method; disorientation; fuzzy ranking; decision alternative; negotiation problem
ASJC Classification1601 Chemistry (miscellaneous); 1701 Computer Science (miscellaneous); 2600 General Mathematics; 3101 Physics and Astronomy (miscellaneous)
DOIDOI:10.3390/sym11091104
URL https://www.mdpi.com/2073-8994/11/9/1104
Languageen angielski
Score (nominal)70
Score sourcejournalList
ScoreMinisterial score = 70.0, 16-06-2020, ArticleFromJournal
Publication indicators WoS Citations = 0; Scopus SNIP (Source Normalised Impact per Paper): 2016 = 0.64; WoS Impact Factor: 2018 = 2.143 (2) - 2018=2.041 (5)
Citation count*1 (2020-09-18)
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* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.
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