Relation "Greater than or Equal to” between Ordered Fuzzy Numbers

Krzysztof Piasecki


The ordered fuzzy number (OFN) is determined as an ordered pair of fuzzy number (FN) and its orientation. FN is widely interpreted as imprecise number approximating real number. We interpret any OFN as an imprecise number equipped with additional information about the location of the approximated number. This additional information is given as orientation of OFN. The main goal of this paper is to determine the relation “greater than or equal to” on the space of all OFNs. This relation is unambiguously defined as an extension of analogous relations on the space of all FN. All properties of the introduced relation are investigated on the basis of the revised OFNs’ theory. It is shown here that this relation is a fuzzy one. The relations “greater than” and “equal to” also are considered. It is proven that the introduced relations are independent on the orientation of the compared OFNs. This result makes it easier to solve optimization tasks using OFNs
Author Krzysztof Piasecki (WZ / KIiN)
Krzysztof Piasecki,,
- Department of Investment and Real Estate
Journal seriesApplied System Innovation, ISSN 2571-5577, (0 pkt)
Issue year2019
Publication size in sheets0.85
Keywords in Polishskierowana liczba rozmyta; relacja rozmyta; preorder; ścisły porządek; relacja równoważności
Keywords in Englishordered fuzzy number; fuzzy relation; preorder; strict order; equivalence relation
Languageen angielski
Score (nominal)5
Score sourcejournalList
ScoreMinisterial score = 5.0, 07-10-2020, ArticleFromJournal
Publication indicators WoS Citations = 1
Citation count*11 (2021-05-03)
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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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