Generalized ordered weighted utility averaging-hyperbolic absolute risk aversion operators and their applications to group decision-making

• Under the general utility, we provide a new operator called GOWUA operator.
• Under HARA utility, we present a new operator called the GOWUA-HARA operator.
• We put forward an orness measure of the GOWUA-HARA operator.
• We construct a new model for determining the weight of the GOWUA-HARA operator.
• We develop a new approach for multiple attributes group decision-making.

This paper develops a new class of aggregation operator based on utility function, which introduces the risk attitude of decision makers (DMs) in the aggregation process. First, under the general framework of utility function, we provide a new operator called the generalized ordered weighted utility averaging (GOWUA) operator, and study its properties which are suitable for any utility function. Then, under the hyperbolic absolute risk aversion (HARA) utility function, we propose another new operator named as the generalized ordered weighted utility averaging-hyperbolic absolute risk aversion (GOWUA-HARA) operator, and further investigate its families including a wide range of aggregation operators. To determine the GOWUA-HARA operator weights, we put forward an orness measure of the GOWUA-HARA operator and analyze its properties. Considering that different DMs may have different opinions toward decision-making and their opinions can be characterized by different orness measures, we construct a new optimization model to determine the optimal weights which can aggregate all the individual sets of weights into an overall set of weights. Furthermore, based on the GOWUA-HARA operator, a method for the multiple attribute group decision-making (MAGDM) is developed. Finally, an example is given to illustrate the application of the GOWUA-HARA operator to the MAGDM.