Paper Info
Title
A formal study of linearity axioms for fuzzy orderings
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.
Year
DOI
Venue
2004
10.1016/S0165-0114(03)00128-3
Fuzzy Sets and Systems
Keywords
Field
DocType
Completeness,Fuzzy ordering,Fuzzy preference modeling,Fuzzy relation,Linearity,Szpilrajn theorem
Discrete mathematics,Information processing,Axiom,Fuzzy logic,Linearity,Fuzzy set,Fuzzy control system,Completeness (statistics),Partially ordered set,Mathematics
Journal
Volume
Issue
ISSN
145
3
0165-0114
Citations 
PageRank 
References 
19
1.36
10
Authors
2
Name
Order
Citations
PageRank
Ulrich Bodenhofer170568.02
Frank Klawonn2705101.95