A common approach in the multiple criteria decision making is to obtain the overall evaluation by aggregating the partial evaluations. For this, a member of a large family of aggregation operators is used. Many of these operators commonly employed in decision making (weighted average, ordered weighted average, minimum, maximum, ...) can be used only when criteria are independent. On the other hand, the Choquet integral, a generalization of the aforementioned operators, can be used even when some interactions between criteria occur. We present a fuzzified Choquet integral capable of dealing not only with fuzzy partial evaluations (first level fuzzification), but also with fuzzy weights (second level fuzzification). We also provide an effective way to evaluate the fully fuzzified integral, which allows its straightforward application to decision making problems with inherent uncertainty.
The weighted average is a well-known aggregation operator that is widely applied in various mathematical models. It possesses some important properties defined for aggregation operators, like monotonicity, continuity, idempotency, etc., that play an important role in practical applications. In the paper, we reveal whether and in which way such properties can be observed also for the fuzzy weighted average operator where the weights as well as the weighted values are expressed by noninteractive fuzzy numbers. The usefulness of the obtained results is discussed and illustrated by several numerical examples.