Frank Klawonn, Ulrich Bodenhofer,
"A Formal Study of Linearity Axioms for Fuzzy Orderings"
, in Fuzzy Sets and Systems, Vol. 145, Nummer 3, Seite(n) 323-354, 2004
A Formal Study of Linearity Axioms for Fuzzy Orderings
Sprache des Titels:
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 Lukasiewicz-type logics are considered.