## Ordered fuzzy numbers vs fuzzy numbers - the first observations

### Krzysztof Piasecki , Anna Łyczkowska-Hanćkowiak

#### Abstract

An imprecise number is an approximation of fixed value crisp number. A commonly accepted model of imprecise number is the fuzzy number, defined as a fuzzy subset of the real line.Any ordered fuzzy number is defined as imprecise number with additional information about the location of the approximated number.The main purpose of this article is to compare the basics of ordered numbers and the theory of fuzzy numbers.Both theories differ in the definition of the unary operator “minus”. For this reason, we will place focus on comparison of the arithmetic of fuzzy numbers with the arithmetic of orderedfuzzy numbers.We have shown here that, despite the identical membership functions, fuzzy numbers cannot be considered as positively oriented fuzzy numbers.For the convenience of reasoning in this article, we will limit ourselves to the case, we restrictour considerations to the case of trapezoidal fuzzy numbers. Nevertheless, all obtained conclusions may be easily generalized for case of any ordered fuzzy numbers.
 Author Krzysztof Piasecki (WZ / KIiN) Krzysztof Piasecki,, - Department of Investment and Real Estate , Anna Łyczkowska-Hanćkowiak - Wyższa Szkoła Bankowa w Poznaniu Anna Łyczkowska-Hanćkowiak,, - Pages 44-52 Publication size in sheets 0.5 Book Szkutnik Włodzimierz, Sączewska-Piotrowska Anna, Hadaś-Dyduch Monika, Acedański Jan (eds.): 12th International Scientific Conference: Analysis of International Relations 2019. Methods and Models of Regional Development. Summer Edition. Conference Proceedings, 2019, Wydawnictwo Uniwersytetu Ekonomicznego w Katowicach, ISBN 978-83-7875-555-5, [978-83-7875-554-8], 97 p. Keywords in Polish skierowane liczby rozmyte, liczby rozmyte, dezorientacja, arytmetyka rozmyta Keywords in English ordered fuzzy number, fuzzy number, disorientation, fuzzy arithmetic URL https://air.ue.katowice.pl/pdf/2019b/4_Piasecki.pdf Language en angielski Score (nominal) 20 Score source publisherList Score Ministerial score = 20.0, 24-06-2020, ChapterFromConference Citation count*
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