Frank Klawonn, Ulrich Bodenhofer,
"Linearity axioms for fuzzy orderings: a formal review"
, in B. De Baets and J. Fodor: Principles of Fuzzy Preference Modelling, Academia Press, Gent, Seite(n) 1-14, 2003, ISBN: 90-382-0567-8
Linearity axioms for fuzzy orderings: a formal review
Sprache des Titels:
Principles of Fuzzy Preference Modelling
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 Lukasiewicz-type logics are considered.