An Approach to Decision Making with Interval-Valued Intuitionistic Hesitant Fuzzy Information Based on the 2-Additive Shapley Function

Interval-valued intuitionistic hesitant fuzzy sets (IVIHFSs) are useful to denote the decision makers' interval preferred, interval non-preferred and hesitant opinions simultaneously. Considering the application of IVIHFSs, this paper introduces a new decision-making method with interval-valued intuitionistic hesitant fuzzy information that extends the application scopes. To do this, the interval-valued intuitionistic hesitant fuzzy hybrid Shapley weighted averaging (IVIHFHSWA) operator and the interval-valued intuitionistic hesitant fuzzy hybrid Shapley weighted geometric (IVIHFHSWG) operator are defined to aggregate the collective attribute values of alternatives. To reflect the interactions and reduce the complexity of calculating the weights, the 2-additive measures are used to define these two hybrid Shapley weighted operators. To derive the exact weight information of attributes and ordered positions, the associated programming models for determining the optimal 2-additive measures are constructed that are based on the defined Hamming distance measure. To show the feasibility and efficiency of the new method, a practical decision-making problem is offered, which is also used to compare with the previous methods.