Uniform fuzzy relations and fuzzy functions
type: Item
instance of: scholarly article
title: Uniform fuzzy relations and fuzzy functions
zbMATH Open document ID: 1188.03035
author: Miroslav Ćirić
author: Jelena Ignjatović
author: Stojan Bogdanović
published in: Fuzzy Sets and Systems
publication date: 2009-11-17T00:00:00Z
review text: In this paper, one of the approaches to the concept of a fuzzy function is presented. Diverse types of fuzzy functions are based on fuzzy equivalence relations. For example, such an approach was used in definitions of partial fuzzy functions and fuzzy functions presented by Klawonn, and of strong fuzzy functions and perfect fuzzy functions presented by Demirci. In this paper, a new approach, different from the ones mentioned above, is given. The authors present characterizations of partial and perfect fuzzy functions. They also define uniform fuzzy relations and give various characterizations of such relations. Some necessary and sufficient conditions for the existence of a uniform fuzzy relation of \(A\) to \(B\) which induces a given pair of fuzzy equivalences \(E\) on \(A\) and \(F\) on \(B\) are presented. One of them is the existence of a bijective function of the quotient set \(A/E\) onto the quotient set \(B/F\). Moreover, the concept of an \(F\)-function is developed. A partially uniform \(F\)-function is defined here as an \(F\)-function which is a partially uniform fuzzy relation, and a perfect \(F\)-function is defined as an \(F\)-function which is a perfect fuzzy function. Necessary and sufficient conditions for the existence of a uniform \(F\)-function from \(A\) to \(B\) which induces a given fuzzy equivalence on \(A\) and a given fuzzy equality on \(B\) are determined. Furthermore, two constructions of uniform \(F\)-functions are presented. Since relational composition of two partially uniform \(F\)-functions is not necessarily a partially uniform \(F\)-function, another kind of composition, which preserves the property to be a uniform \(F\)-function and the property to be a perfect \(F\)-function, is introduced. Except for the mentioned two types of compositions, a third one is also introduced and relationships between these three kinds of compositions are studied. The definition of a uniform \(F\)-function presented in this paper enables a mutual co…
reviewed by: Urszula Bentkowska
Mathematics Subject Classification ID: 03E72
Mathematics Subject Classification ID: 68T37
Mathematics Subject Classification ID: 93C42
zbMATH DE Number: 5634424
zbMATH Keywords: fuzzy function
zbMATH Keywords: partial fuzzy function
zbMATH Keywords: perfect fuzzy function
zbMATH Keywords: fuzzy relation
zbMATH Keywords: uniform fuzzy relation
zbMATH Keywords: fuzzy equivalence
zbMATH Keywords: fuzzy partition
zbMATH Keywords: complete residuated lattice
MaRDI profile type: Publication
full work available at URL: j.fss.2008.07.006
OpenAlex ID: W2057714840
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DOI: 10.1016/J.FSS.2008.07.006
description: scientific article; zbMATH DE number 5634424