A formal study of linearity axioms for fuzzy orderings, Fuzzy Sets and Systems

A formal study of linearity axioms for fuzzy orderings, Fuzzy Sets and Systems (2004)

by Ulrich Bodenhofer , Frank Klawonn

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Datum	Value	Source
TITLE	A formal study of linearity axioms for fuzzy orderings, Fuzzy Sets and Systems	INFERENCE
AUTHOR NAME	Ulrich Bodenhofer	SVM HeaderParse 0.2
AUTHOR AFFIL	Software Competence Center Hagenberg	SVM HeaderParse 0.2
AUTHOR ADDR	A-4232 Hagenberg, Austria	SVM HeaderParse 0.2
AUTHOR NAME	Frank Klawonn	SVM HeaderParse 0.2
AUTHOR AFFIL	Fachhochschule Braunschweig/Wolfenbüttel, Fachbereich Informatik	SVM HeaderParse 0.2
AUTHOR ADDR	D-38302 Wolfenbüttel, Germany	SVM HeaderParse 0.2
ABSTRACT	This contribution is concerned with a detailed investigation of linearity axioms for fuzzy orderings. Different existing concepts are evaluated with respect to three fundamental correspondences from the classical case—linearizability of partial orderings, intersection representation, and one-to-one correspondence between linearity and maximality. As a main result, we obtain that it is virtually impossible to simultaneously preserve all these three properties in the fuzzy case. If we do not require a one-to-one correspondence between linearity and maximality, however, we obtain that an implication-based definition appears to constitute a sound compromise, in particular, if Łukasiewicz-type logics are considered. Key words: completeness, fuzzy ordering, fuzzy preference modeling, fuzzy relation,	SVM HeaderParse 0.2
YEAR	2004	INFERENCE
VOLUME	145	INFERENCE
CITATIONS	35 found	ParsCit 1.0