An approach to group decision making based on interval-valued intuitionistic fuzzy geometric distance measures

The interval-valued intuitionistic fuzzy set (IVIFS) theory, originated by Atanassov and Gargov [3], has been used in different types of applications such as decision making, pattern recognition and so on. However, so far there has been little investigation of the distance measures of IVIFSs and their applications. In this paper, at first, we develop some new geometric distance measures with interval-valued intuitionistic fuzzy information, including the interval-valued intuitionistic fuzzy weighted geometric distance (IVIFWGD) measure, the interval-valued intuitionistic fuzzy ordered weighted geometric distance (IVIFOWGD) measure and the interval-valued intuitionistic fuzzy hybrid weighted geometric distance (IVIFHWGD) measure. Also, several desirable properties of these new distance measures are studied and a numerical example is given to show application of the distance measure to pattern recognition problems. And then, based on the developed distance measures a consensus reaching process with interval-valued intuitionistic fuzzy preference information for group decision making is proposed. Finally, we apply the developed approach by an illustrative example to group decision making with interval-valued intuitionistic fuzzy information.