Impact of the Orientation of the Ordered Fuzzy Assessment on the Simple Additive Weighted Method
Krzysztof Piasecki , Ewa Roszkowska , Anna Łyczkowska-Hanćkowiak
AbstractWe 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.
|Journal series||Symmetry-Basel, [Symmetry], ISSN 2073-8994, (N/A 70 pkt)|
|Publication size in sheets||1.05|
|Keywords in Polish||skierowana liczba rozmyta; lingwistyczna skala porządkowa; metoda SAW; dezorientacja; ranking rozmyty; problem negocjacyjny|
|Keywords in English||ordered fuzzy number; linguistic order scale; SAW method; disorientation; fuzzy ranking; decision alternative; negotiation problem|
|ASJC Classification||; ; ;|
|Score||= 70.0, 16-06-2020, ArticleFromJournal|
|Publication indicators||= 0; : 2016 = 0.64; : 2018 = 2.143 (2) - 2018=2.041 (5)|
|Citation count*||1 (2020-09-18)|
* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.