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Open AccessArticle

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

Department of Investment and Real Estate, Poznań University of Economics and Business, Niepodległości 10, 61-875 Poznań, Poland
Appl. Syst. Innov. 2019, 2(3), 26; https://doi.org/10.3390/asi2030026
Received: 13 July 2019 / Revised: 26 July 2019 / Accepted: 1 August 2019 / Published: 3 August 2019
(This article belongs to the Special Issue Fuzzy Decision Making and Soft Computing Applications)
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. View Full-Text
Keywords: ordered fuzzy number; fuzzy relation; preorder; strict order; equivalence relation ordered fuzzy number; fuzzy relation; preorder; strict order; equivalence relation
MDPI and ACS Style

Piasecki, K. Relation “Greater than or Equal to” between Ordered Fuzzy Numbers. Appl. Syst. Innov. 2019, 2, 26.

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