Oriented Fuzzy Numbers vs. Fuzzy Numbers

Krzysztof Piasecki and Anna Łyczkowska-Hanćkowiak
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Krzysztof Piasecki: Institute of Economy and Finance, WSB University in Poznan, ul. Powstańców Wielkopolskich 5, 61-895 Poznań, Poland
Anna Łyczkowska-Hanćkowiak: Institute of Economy and Finance, WSB University in Poznan, ul. Powstańców Wielkopolskich 5, 61-895 Poznań, Poland

Mathematics, 2021, vol. 9, issue 5, 1-27

Abstract: A formal model of an imprecise number can be given as, inter alia, a fuzzy number or oriented fuzzy numbers. Are they formally equivalent models? Our main goal is to seek formal differences between fuzzy numbers and oriented fuzzy numbers. For this purpose, we examine algebraic structures composed of numerical spaces equipped with addition, dot multiplication, and subtraction determined in a usual way. We show that these structures are not isomorphic. It proves that oriented fuzzy numbers and fuzzy numbers are not equivalent models of an imprecise number. This is the first original study of a problem of a dissimilarity between oriented fuzzy numbers and fuzzy numbers. Therefore, any theorems on fuzzy numbers cannot automatically be extended to the case of oriented fuzzy numbers. In the second part of the article, we study the purposefulness of a replacement of fuzzy numbers by oriented fuzzy numbers. We show that for a portfolio analysis, oriented fuzzy numbers are more useful than fuzzy numbers. Therefore, we conclude that oriented fuzzy numbers are an original and useful tool for modelling a real-world problems.

Keywords: ordered fuzzy number; oriented fuzzy number; Kosi?ski’s number; imprecision measure; portfolio diversification (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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