The classical Power Average (PA) operator proposed by Yager implicitly restricts itself to an assumption that unduly high or low arguments are conceived as “false” or “biased” perceptions, thereby being assigned smaller weights for aggregation. However, on many occasions, these kinds of inputs to a great extent may be of significant importance to the accuracy of the aggregation outcomes, particularly when different sources of information are taken into consideration. The primary purpose of this paper is to adapt the PA operator to model generally various decision making settings where outliers are treated with different aggregation significance. The concept of Extended PA (EPA) operator is therefore proposed to effectively capture heterogeneous interrelationships among aggregation inputs. Several desirable properties of the EPA operator are investigated and their usefulness in practical decision making problems is highlighted. The choice of appropriate values for parameters associated with the EPA operator is likewise investigated. The proposed EPA operator is applied to develop an approach for multi-attribute decision making in which the interrelationships among the attributes and the inputs themselves are simultaneously taken into consideration. Finally, a case study in emergency response plan selection of civil aviation and a comparison analysis are provided to illustrate the feasibility and effectiveness of the proposed method.