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

• Under the general utility, we provide a new operator called GOWUPA operator.
• Under HARA utility, we present a new operator called the GOWUPA-HARA operator.
• We put forward an orness measure of the GOWUPA-HARA operator.
• We construct a new model for determining the weight of the GOWUPA-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 proportional averaging (GOWUPA) 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 proportional averaging-hyperbolic absolute risk aversion (GOWUPA-HARA) operator, and further investigate its families including a wide range of aggregation operators. To determine the GOWUPA-HARA operator weights, we put forward an orness measure of the GOWUPA-HARA operator and analyze its properties. Considering that different DMs may have different opinions towards decision-making and their opinions can be characterized by different orness measures, we construct a new nonlinear 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 GOWUPA-HARA operator, a method for multiple attribute group decision- making (MAGDM) is developed. Finally, an example is given to illustrate the application of the GOWUPA-HARA operator to the MAGDM.