The weighted average operator is often used to assign a value v(a) to entities a from performances xj(a), j=1,…,n. This operator makes intervene specific weights wj as multipliers of the performance relative to the jth component. This induces possibilities of compensation of the worst performances by the better ones. Such compensation can be judged as unacceptable in some concrete contexts. So as to soften these possibilities of compensation, we can make intervene a second weighting using weights of rank qr. The new weights modify the role which plays, in the definition of v(a), the performance xj(a) according to rank r it has in a ranking from the best values to the worst ones. I will start by describing three examples coming from real contexts in which this double weighting is useful. Then, I will successively present a first operation I have introduced in 1990, namely ‘moyenne ordonnée doublement pondérée (MO2P)’, and a second one proposed in 1997 by Torra, namely ‘weighted ordered weighted average (WOWA)’. These two operators being significant only if the performances xj(a) are situated on a same interval scale E, I will end by suggesting a new type of operator likely to be suitable when E is a purely ordinal scale.
