Interval-valued intuitionistic fuzzy multi-criteria decision making based on the generalized Shapley geometric Choquet integral

In practical decision-making, the independence of criteria is usually violated so it is unreasonable to aggregate the alternative values using additive measures. In order to reflect the interactions between combinations in a set, the generalized Shapley function is used to measure the importance of them, which is an expectation utility function with respect to a fuzzy measure. It is worth pointing out that the generalized Shapley function is also a fuzzy measure. Then, the generalized Shapley interval-valued intuitionistic fuzzy geometric Choquet operator is defined, which is also an interval-valued intuitionistic fuzzy value. Further, some important properties are investigated. Moreover, an approach to interval-valued intuitionistic fuzzy multi-criteria decision-making is developed. In the end, two practical examples are selected to show the presented procedure.