Induced Atanassov's interval-valued intuitionistic fuzzy hybrid Choquet integral operators and their application in decision making

Based on the Choquet integral and the generalized Shapley function, two new induced Atanassov's interval-valued intuitionistic fuzzy hybrid aggregation operators are defined, which are named as the induced generalized Shapley Atanassov's interval-valued intuitionistic fuzzy hybrid Choquet arithmetical averaging (IGS-IVIFHCAA) operator and the induced generalized Shapley Atanassov's interval-valued intuitionistic fuzzy hybrid Choquet geometric mean (IGS-IVIFHCGM) operator. These operators do not only globally consider the importance of elements and their ordered positions, but also overall reflect the correlations among them and their ordered positions. Meantime, some important cases are examined, and some desirable properties are studied. Furthermore, if the information about the weighting vectors is incompletely known, the models for the optimal -fuzzy measures on attribute set and ordered set are established, respectively. Moreover, an approach to multi-attribute decision making under Atanassov's interval-valued intuitionistic fuzzy environment is developed. Finally, a numerical example is provided to illustrate the proposed procedure.