Weighted sums of aggregation operators

  1. Calvo Sánchez, Tomasa
  2. Baets, Bernard de
  3. Mesiar, Radko
Revista:
Mathware & soft computing: The Magazine of the European Society for Fuzzy Logic and Technology

ISSN: 1134-5632

Any de publicació: 1999

Volum: 6

Número: 1

Pàgines: 33-47

Tipus: Article

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Altres publicacions en: Mathware & soft computing: The Magazine of the European Society for Fuzzy Logic and Technology

Resum

The aim of this work is to investigate when a weighted sum, or in other words, a linear combination, of two or more aggregation operators leads to a new aggregation operator. For weights belonging to the real unit interval, we obtain a convex combination and the answer is known to be always positive. However, we will show that also other weights can be used, depending upon the aggregation operators involved. A first set of suitable weights is obtained by a general method based on the variation of the partial derivatives of the aggregation operators. When considering the combination of OWA operators only, all suitable weights can be determined. These results are described explicitly for the case of two aggregation operators, and also for the case of two and three OWA operators.

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