Weighted sums of aggregation operators

Abstract

he 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.