The generalized hybrid averaging operator and its application in decision making

We present the generalized hybrid averaging (GHA) operator. It is a new aggregation operator that generalizes the hybrid averaging (HA) operator by using the generalized mean. Thus, we are able to generalize a wide range of mean operators such as the HA, the hybrid geometric averaging (HGA), the hybrid quadratic averaging (HQA), the generalized ordered weighted averaging (GOWA) operator and the weighted generalized mean (WGM). A key feature in this aggregation operator is that it is able to deal with the weighted average and the ordered weighted averaging (OWA) operator in the same formulation. We further generalize the GHA by using quasi-arithmetic means obtaining the quasi-arithmetic hybrid averaging (Quasi-HA) operator. We conclude the paper with an example of the new approach in a financial decision making problem.