Development of new operators for expert opinions aggregation: Average-induced ordered weighted averaging operators

In this paper we propose a new induced ordered weighted averaging (IOWA) operator for expert opinions aggregation, namely, the average-induced OWA (AIOWA) operator. The AIOWA operator defines the order-induced variable as the similarity of each individual expert's opinion with respect to the average opinion of the group, as the average opinion is notably an important piece of information of the group opinion and often used as an approximate estimate of the group opinion with equal weights. The new operator facilitates to capture the distribution characteristics of the opinion data with respect to the consensus and constructs a nonlinear aggregation of individual opinions. Further, we extend the new operator to the situation where the experts' opinions are represented by probability density functions (PDFs). Last, we incorporate the entropy-orness optimization model into the proposed aggregation operator. The new operator makes the aggregation process more flexible in terms of application problems. Two case studies are conducted to show the effectiveness of the proposed operators. The result is promising.