Combined weighted geometric averaging operator and its application

A combined weighted geometric averaging (CWGA) operator is presented and both the well known weighted geometric averaging (WGA) operator and the ordered weighted geometric averaging (OWGA) operator are proved to be the special cases of the CWGA operator. The fundamental aspect of the CWGA operator is that it takes the importance degrees of both individual argument and its relative position into account. Finally, a method based on the WGA and CWGA operators for multi-attribute group decision-making problems is proposed, and an illustrative example is given to verify the developed method and to demonstrate its reasonability and effectiveness.