This paper deals with the problem of evaluating a fuzzy quantity. We call fuzzy quantity any non-normal and non-convex fuzzy set, defined as the union of two, or more, non-normal fuzzy numbers. In order to introduce either ranking or defuzzifing procedures, we propose a definition which arises from crisp set theory: it is based on a particular fuzzy number evaluation, weighted average value (WAV) that works on alpha-cuts levels and depends on two parameters, a real number A and an additive measure S; A is connected with the optimistic or pessimistic point of view of the decision maker, S allows the decision maker to choose evaluations in particular subsets of the fuzzy number support, according to his preference.