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

Abstract

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.

Keywords

• ordered fuzzy number
• fuzzy relation
• preorder
• strict order
• equivalence relation