A formal study of linearity axioms for fuzzy orderings

Autoren Ulrich Bodenhofer
Frank Klawonn
TitelA formal study of linearity axioms for fuzzy orderings
TypArtikel
JournalFuzzy Sets and Systems
Nummer3
Band145
ISSN0165-0114
Jahr2004
Seiten323-354
SCCH ID#302
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 betweenlinearity and maximality. As a main result, we obtain that it is virtually impossible to simultaneously preserve allthese three properties in the fuzzy case. If we do not require a one-to-one correspondence between linearity andmaximality, however, we obtain that an implication-based definition appears to constitute a sound compromise, inparticular, if Lukasiewicz-type logics are considered.