A formal study of linearity axioms for fuzzy orderings

  • Bodenhofer U
  • Klawonn F
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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. © 2003 Elsevier B.V. All rights reserved.

Author-supplied keywords

  • Completeness
  • Fuzzy ordering
  • Fuzzy preference modeling
  • Fuzzy relation
  • Linearity
  • Szpilrajn theorem

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