The Generalized Probabilistic Weighted Averaging Operator and Its Application in Strategic Decision Making

We analyze different types of aggregation operators based on the use of probabilities, weighted averages (WAs) and generalized aggregation operators. We present the generalized probabilistic weighted averaging (GPWA) operator. It is a new aggregation operator that unifies the WA and the probability in the same formulation considering the degree of importance that each concept has in the analysis. Moreover, it also uses generalized means providing a more complete formulation. Its main advantage is that it includes a wide range of particular cases such as the probabilistic weighted averaging (PWA) operator, the probabilistic weighted geometric averaging (PWGA) operator, the probabilistic weighted quadratic averaging (PWQA) operator, the arithmetic weighted average, the arithmetic probabilistic aggregation, and a lot of other cases. We further generalize this approach by using quasi-arithmetic means obtaining the Quasi-PWA operator. We end the paper with an application of the GPWA in a decision making problem about selection of production strategies.