A new generalized knowledge measure in multi-attribute group decision making under interval-valued intuitionistic fuzzy environment

In this paper, we discuss some revealed drawbacks of the existing measures for the interval-valued intuitionistic fuzzy sets (IvIFSs). Then, we propose a new generalized knowledge measure for IvIFSs and prove some its axiomatic properties. Based on the proposed knowledge measure we construct a new information entropy measure for IvIFSs. We show by some comparative examples, that the proposed measure is simple, easily interpreted and reasonable in discriminating the IvIFSs generally, IFSs and FSs particularly. Using the generalized knowledge measure, we develop a new approach to solve multi-attribute group decision making (MAGDM) problems under interval-valued intuitionistic fuzzy (IvIF) environment, with completely unknown weight information. To demonstrate the superiority of the proposed approach over the preceding ones, the comparative analysis is also conducted by utilizing them in solving the same decision making (DM) problems and showing the effectiveness of the proposed method in real life applications.