The relations “less or equal” and “less than” for ordered fuzzy numbers

Krzysztof Piasecki

Abstract

The ordered fuzzy number is defined as fuzzy number supplemented with orientation of number. Any positively oriented ordered fuzzy number is interpreted as an imprecise real number which may to increase. Any negatively oriented ordered fuzzy number is interpreted as an imprecise real number which may to decrease. The main goal of this paper is to introduce the preorder “less or equal” and the strict order “less than” on the space of all ordered fuzzy numbers. These relations are defined as an extension of analogous relations on the space of all fuzzy numbers. All properties of the introduced relations have been investigated on the basis of the revised Kosiński’s theory of ordered fuzzy numbers. It is shown here that in the above way these relations have been defined unambiguously as fuzzy ones. In addition, it is proven that the obtained relationships depend on the orientation of the difference between the compared numbers. The results obtained will be useful for formulating optimization tasks using numbers.
Author Krzysztof Piasecki (WZ / KIiN)
Krzysztof Piasecki,,
- Department of Investment and Real Estate
Pages32-39
Publication size in sheets0.5
Book Szkutnik Włodzimierz, Sączewska-Piotrowska Anna, Hadaś-Dyduch Monika, Acedański Jan (eds.): 10th International Scientific Conference: Analysis of International Relations 2018. Methods and Models of Regional Development. Summer Edition. Conference Proceedings, 2018, Wydawnictwo Uniwersytetu Ekonomicznego w Katowicach, ISBN 978-83-7875-456-5, [978-83-7875-455-8], 145 p.
Keywords in Englishordered fuzzy number, fuzzy relation, preorder, strict order
URL https://air.ue.katowice.pl/pdf/2018b/04_Piasecki.pdf
Languageen angielski
Score (nominal)20
Score sourcepublisherList
ScoreMinisterial score = 20.0, 24-06-2020, ChapterFromConference
Publication indicators WoS Citations = 1
Citation count*4 (2020-09-06)
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