Probabilities in the OWA operator

We analyze the use of the probability in the ordered weighted average (OWA). We introduce the probabilistic OWA (POWA) operator. It is an aggregation operator that provides a parameterized family of aggregation operators between the minimum and the maximum that considers the degree of importance that the probability and the OWA operator have in the aggregation. We study some of its main properties and particular cases. We also study the construction of interval and fuzzy numbers with POWA operators. We study the applicability of the POWA operator and we see that it is very broad because all the previous studies that use the probability can be revised with this new approach. We develop an application in a group decision making problem regarding investment selection.