Susanne Saminger, Ulrich Bodenhofer, Radko Mesiar,
"Domination of aggregation operators and preservation of transitivity"
, in International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, Vol. 10, Nummer Suppl., Seite(n) 11-35, 12-2002, ISSN: 0218-4885
Original Titel:
Domination of aggregation operators and preservation of transitivity
Sprache des Titels:
Englisch
Original Kurzfassung:
Aggregation processes are fundamental in any discipline where the fusion of information
is of vital interest. For aggregating binary fuzzy relations such as equivalence relations
or fuzzy orderings, the question arises which aggregation operators preserve specific properties
of the underlying relations, e.g. T-transitivity. It will be shown that preservation of T-transitivity
is closely related to the domination of the applied aggregation operator over the corresponding
t-norm T. Furthermore, basic properties for dominating aggregation operators, not only in the
case of dominating some t-norm T, but dominating some arbitrary aggregation operator, will be
presented. Domination of isomorphic t-norms and ordinal sums of t-norms will be treated. Special
attention is paid to the four basic t-norms (minimum t-norm, product t-norm, £ukasiewicz t-norm,
and the drastic product).
Sprache der Kurzfassung:
Englisch
Journal:
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems