Linearity axioms for fuzzy orderings: A formal review
B. De Baets
|Title||Linearity axioms for fuzzy orderings: A formal review|
|Booktitle||Principles of Fuzzy Preference Modelling and Decision Making|
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.