Aggregation of fuzzy opinions with an area between the centroid point and the original point under group decision making

It is an important issue to obtain the consensus opinion under group decision making. In this paper, we propose a new approach to aggregate the experts’ opinions which is based on the area between the centroid points of fuzzy numbers and the original point. The opinions of experts are represented by positive fuzzy numbers which include the normal and the non-normal trapezoidal fuzzy numbers as well as interval numbers. A new index that the consensus of each expert to others is constructed by using a similarity measure under the area. We also take into consideration the importance of each expert in the process of aggregation. The operational procedure is simple and the numerical examples show its reliability.