Interval-valued intuitionistic fuzzy continuous weighted entropy and its application to multi-criteria fuzzy group decision making

In this paper, we propose the interval-valued intuitionistic fuzzy continuous weighted entropy which generalizes intuitionistic fuzzy entropy measures defined by Szmidt and Kacprzyk on the basis of the continuous ordered weighted averaging (COWA) operator. It is shown that the continuous entropy of interval-valued intuitionistic fuzzy set is the average of the entropies of its interval-valued intuitionistic fuzzy values (IVIFVs). We also establish the programming model to determine optimal weight of criteria with the principle of minimum entropy. Furthermore, we investigate the multi-criteria group decision making (MCGDM) problems in which criteria values take the form of interval-valued intuitionistic fuzzy information. An approach to interval-valued intuitionistic fuzzy multi-criteria group decision making is given, which is based on the weighted relative closeness and the IVIFV attitudinal expected score function. Finally, emergency risk management (ERM) evaluation is provided to illustrate the application of the developed approach.