An approach to multi-criteria decision-making under interval-valued intuitionistic fuzzy values and interval fuzzy measures

In this paper, we first define some operations of interval-valued intuitionistic fuzzy sets (IVIFSs) with respect to intervals. Then, the concept of interval fuzzy measure is introduced, which is used to measure the interval important degrees of criteria. To better reflect the interval important degrees of criteria, we apply the Shapley function to calculate their interval importance based on the restricted subtraction operation on intervals, which is simply called the restricted interval Shapley function. Meanwhile, two aggregation operators for IVIFSs with respect to the restricted interval Shapley function are proposed. It is worth pointing out that most of the existing intuitionistic fuzzy aggregation operators are special cases of our operators. Moreover, an approach to interval-valued intuitionistic fuzzy multi-criteria decision-making with respect to the restricted interval Shapley function is developed. Finally, a numerical example is provided to illustrate the developed procedure.

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