A formal study of linearity axioms for fuzzy orderings
|Title||A formal study of linearity axioms for fuzzy orderings|
|Journal||Fuzzy Sets and Systems|
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.