An approach to multiple attribute decision making with combined weight information in interval-valued intuitionistic fuzzy environment

With respect to multiple attribute decision making problems with interval-valued intuitionistic fuzzy information, some operational laws of interval-valued intuitionistic fuzzy numbers, score function and accuracy function of interval-valued intuitionistic fuzzy numbers are introduced. A combined optimization model based on the deviation method, by which the attribute weights can be determined, is established. For special situations, in which information about attribute weights is completely unknown, we establish another combined optimization model. By solving this model, we get a simple and exact formula, which can be used to determine the attribute weights. We utilize the interval-valued intuitionistic fuzzy weighted averaging (IIFWA) operator to aggregate the intuitionistic fuzzy information corresponding to each alternative, and then rank the alternatives and select the most desirable one(s) according to the score and accuracy functions. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.