Linearity axioms for fuzzy orderings: A formal review

U. Bodenhofer, F. Klawonn. Linearity axioms for fuzzy orderings: A formal review. pages 1-14, 2003.

Autoren
  • Ulrich Bodenhofer
  • Frank Klawonn
Editoren
  • B. De Baets
  • F. Fodor
BuchPrinciples of Fuzzy Preference Modelling and Decision Making
TypIn Sammelband
VerlagAcademia Press
Noteinvited
ISBN90-382-0567-8
Jahr2003
Seiten1-14
Abstract This contribution is concerned with a review of linearity axioms for fuzzy orderings 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. 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 ?ukasiewicz-type logics are considered.