Multi-attribute Group Decision Making under Interval-valued Intuitionistic Fuzzy Environment

In this paper, we investigate the multi-attribute group decision making (MAGDM) problem with incomplete attribute weight information under interval-valued intuitionistic fuzzy (IVIF) environment. Firstly, we propose a new axiomatic definition of the entropy on interval-valued intuitionistic fuzzy sets (IVIFSs) and a method to construct a set of entropies on IVIFSs. Secondly, we construct a decision making model based on aggregation operator and distance measures to solve the MAGDM problem under IVIF environment. In this model, we propose a method based on linear programming methodology using an accuracy function to choose the attribute weights for the decision making problem with partially known attribute weight information, and a method based on IVIF entropy to choose the attribute weights for the decision making problem with unknown attribute weight information. Finally, two numerical examples are given to demonstrate the feasibility and validity of the newly proposed MAGDM method by comparing it with other fuzzy MAGDM methods.