## A formal study of linearity axioms for fuzzy orderings, Fuzzy Sets and Systems (2004)

Citations: | 2 - 2 self |

### BibTeX

@MISC{Bodenhofer04aformal,

author = {Ulrich Bodenhofer and Frank Klawonn},

title = {A formal study of linearity axioms for fuzzy orderings, Fuzzy Sets and Systems},

year = {2004}

}

### OpenURL

### Abstract

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 Łukasiewicz-type logics are considered. Key words: completeness, fuzzy ordering, fuzzy preference modeling, fuzzy relation,