Ulrich Bodenhofer,
"A Similarity-Based Generalization of Fuzzy Orderings Preserving the Classical Axioms"
, in International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, Vol. 8, Nummer 5, Seite(n) 593-610, 10-2000, ISSN: 0218-4885
Original Titel:
A Similarity-Based Generalization of Fuzzy Orderings Preserving the Classical Axioms
Sprache des Titels:
Englisch
Original Kurzfassung:
Equivalence relations and orderings are key concepts
of mathematics. For both types of relations, formulations
within the framework of fuzzy relations have been
proposed already in the early days of fuzzy set theory.
While similarity (indistinguishability) relations have
turned out to be very useful tools, e.g. for the
interpretation of fuzzy partitions and fuzzy
controllers, the utilization of fuzzy orderings is still
lagging far behind, although there are a lot of possible
applications, for instance, in fuzzy preference modeling
and fuzzy control. The present paper is devoted to this
missing link. After a brief motivation, we will
critically analyze the existing approach to fuzzy
orderings. In the main part, an alternative approach to
fuzzy orderings, which also takes the strong connection
to gradual similarity into account, is proposed and
studied in detail, including several constructions and
representation results.
Sprache der Kurzfassung:
Englisch
Journal:
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
Forschungs-