An approach to aggregating interval numbers into interval-valued intuitionistic fuzzy information for group decision making

In this paper, we investigate the multiple attribute group decision making (MAGDM) problems, of which the attribute values in the group decision matrices provided by each decision maker (DM) is characterized by interval numbers. First, we define the concepts of attribute satisfactory interval and attribute dissatisfactory interval, respectively, according to each attribute values. Then we develop an approach for aggregating attribute satisfactory interval and attribute dissatisfactory interval into the collective attribute interval-valued intuitionistic fuzzy number (IVIFN), and then we obtain the collective interval-valued intuitionistic fuzzy decision matrix for group decision making. Next, we use the interval-valued intuitionistic fuzzy weighted averaging operator to aggregate all attribute values characterized by interval-valued intuitionistic fuzzy information to get the overall IVIFNs of alternatives. And then we use the score function and accuracy function to calculate the score and accuracy degree of each alternative value, and then rank the alternatives according to the score and accuracy degree of each alternative and select the most desirable one(s). And finally, we give an example for comprehensive pre-evaluation of air quality in Guangzhou, China during 16th Asian Olympic Games to illustrate in detail the decision process by the developed approach.