Generalized Multiple Averaging Operators and their Applications to Group Decision Making

In this paper, we present a new operator called the generalized ordered weighted multiple averaging (GOWMA) operator based on a minimization problem with penalty function, which unifies the geometric mean and the generalized ordered weighted averaging operator with the generalized ordered weighted harmonic averaging operator in the same formulation. We study different properties and families of the GOWMA operator and develop a generalization of this operator called the generalized hybrid multiple averaging operator. To determine the GOWMA operator weights, we propose the generalized least squares method which does not follow a regular distribution. Finally, we give a numerical example of an investment selection to illustrate the application of the GOWMA operator to multiple attribute group decision making.