This article investigates new score and accuracy functions for ranking interval-valued intuitionistic fuzzy numbers (IVIFNs). The novelty of these functions is that they allow the comparison of IVIFNs by taking into account of the decision makers’ attitudinal character. The new attitudinal expected score and accuracy functions extend Xu and Chen's score and accuracy degree functions, and verify the following set of properties: (1) boundedness; (2) monotonicity; (3) commutativity; and (4) symmetry. These novel functions are used to propose a total order on the set of IVIFNs, and to develop an interval-valued intuitionistic fuzzy multi-attribute decision making selection process in which the final result depends on the decision maker's risk attitude. In addition, a ranking sensitivity analysis with respect to the risk attitude is provided. 
A risk attitudinal ranking method for interval-valued intuitionistic fuzzy numbers based on novel attitudinal expected score and accuracy functions