The relation "greater thanor equalto" for trapezoidal ordered fuzzy numbers
Krzysztof Piasecki , Anna Łyczkowska-Hanćkowiak , Aleksandra Wójcicka-Wójtowicz
AbstractThe ordered fuzzy number(OFN)is defined as a pair of fuzzy number and its orientation. Any OFNis interpreted as imprecise number with additional information about the location of the approximated number. Eachpositively oriented OFNis interpreted as an imprecise real numberdescribed by the linguistic variable “about or slightly above”.Eachnegatively oriented OFNis interpreted as an imprecise real number described by the linguistic variable “about or slightly below”.Here, we restrict our considerations to the case of trapezoidal OFN(TrOFN).The main goal of this paper is to introduce the preorder “greater than or equal to”on the space of all TrOFNs. This relation isdefined as an extension of analogous relations on the space of all fuzzy numbers. All properties of the introduced relationhave been investigated on the basis of the revised Kosiński’stheory of OFNs. It is shown here that in the above way this relation hasbeen defined unambiguously as fuzzy ones. In addition, it is proventhat the obtained relationshipis independenton the orientation of the compared OFNs. The results obtained will be useful for formulating optimization tasks using TrOFNs.
|Publication size in sheets||0.5|
|Book||Houda Michal, Remeš Radim (eds.): 37th International Conference Mathematical Methods in Economics MME 2019 : Conference Proceedings, 2019, University of South Bohemia in České Budějovice, Faculty of Economics, ISBN 978-80-7394-760-6, 598 p.|
|Keywords in Polish||skierowana liczba rozmyta, rozmyta relacja, preporządek, ścisły porządek|
|Keywords in English||ordered fuzzy number, fuzzy relation, preorder, strict order|
|Score||= 5.0, 11-02-2020, ChapterFromConference|
|Citation count*||2 (2020-07-09)|
* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.