On the correspondence between reciprocal relations and strongly complete fuzzy relations

Fuzzy relations and reciprocal relations are two popular tools for representing degrees of preference. It is important to note that they carry a different semantics and cannot be equated directly. We propose a simple transformation based on implication operators that allows to establish a one-to-one...

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Veröffentlicht in:	Fuzzy sets and systems 2017-09, Vol.322, p.19-34
Hauptverfasser:	Martinetti, Davide, Montes, Susana, Díaz, Susana, De Baets, Bernard
Format:	Artikel
Sprache:	eng
Schlagworte:	Bipolar/unipolar scale Cycle-transitivity Fuzzy relation Implication operator Mathematics Reciprocal relation Statistics
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container_title	Fuzzy sets and systems
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creator	Martinetti, Davide Montes, Susana Díaz, Susana De Baets, Bernard
description	Fuzzy relations and reciprocal relations are two popular tools for representing degrees of preference. It is important to note that they carry a different semantics and cannot be equated directly. We propose a simple transformation based on implication operators that allows to establish a one-to-one correspondence between both formalisms. It sets the basis for a common framework in which properties such as transitivity can be studied and definitions belonging to different formalisms can be compared. As a byproduct, we propose a new family of upper bound functions for cycle-transitivity. Finally, we unveil some interesting equivalences between types of transitivity that were left uncompared till now.
doi_str_mv	10.1016/j.fss.2017.03.004
format	Article
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subjects	Bipolar/unipolar scale Cycle-transitivity Fuzzy relation Implication operator Mathematics Reciprocal relation Statistics
title	On the correspondence between reciprocal relations and strongly complete fuzzy relations
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