Intuitionistic Fuzzy Interaction Hamy Mean Operators and Their Application to Multi-attribute Group Decision Making

The Hamy mean (HM) operator, as a useful aggregation tool, is capable of capturing the correlations among multiple integrated parameters. In this paper, we expand HM operator to integrate intuitionistic fuzzy numbers (IFNs) on the basis of interaction operational rules of IFNs, and develop intuitionistic fuzzy interaction HM (IFIHM) operator and intuitionistic fuzzy weighted interaction HM (IFWIHM) operator. Moreover, we discuss some properties and particular cases of the IFIHM operator and the IFWIHM operator in detail. In addition, in real applications, there are many decision making problems with the interactions among multiple attributes, so we present a multi-attribute group decision making (MAGDM) method based on the IFWIHM operator. At the same time, the applicability and validity of the proposed MAGDM method is illustrated clearly by using an example concerning the evaluation of scenic spots. Finally, comparing with the existing approaches, the merits of the proposed MAGDM method are demonstrated, i.e., it can deal with MAGDM problems by considering the interactions among multiple attributes based on the IFWIHM operator which is a generalization of most existing operators, and it can also overcome the weaknesses existed in the traditional operational laws of IFNs.