Some aggregating operators based on the Choquet integral with fuzzy number intuitionistic fuzzy information and their applications to multiple attribute decision making

With respect to multiple attribute decision making (MADM) problems in which attribute values take the form of fuzzy number intuitionistic fuzzy values, a new decision making analysis method is developed. First, some operational laws of fuzzy number intuitionistic fuzzy values, score function and accuracy function of fuzzy number intuitionistic fuzzy values are introduced. Then, we have developed two fuzzy number intuitionistic fuzzy Choquet integral aggregation operators: fuzzy number intuitionistic fuzzy Choquet ordered averaging (FNIFCOA) operator and fuzzy number intuitionistic fuzzy Choquet ordered geometric mean (FNIFCOGM) operator. The prominent characteristic of the operators is that they can not only consider the importance of the elements or their ordered positions, but also reflect the correlation among the elements or their ordered positions. We have studied some desirable properties of the FNIFCOA and FNIFCOGM operators, such as commutativity, idempotency and monotonicity, and applied the FNIFCOA and FNIFCOGM operators to multiple attribute decision making with fuzzy number intuitionistic fuzzy information. Finally an illustrative example has been given to show the developed method.