An approach to interval-valued intuitionistic fuzzy decision making based on induced generalized symmetrical Choquet-Shapley operator

Interval-Valued Intuitionistic Fuzzy Variables (IVIFVs) are powerful tools to illustrate the preferred and non-preferred uncertainty degrees of decision-makers. Considering the application of IVIFVs in decision-making, this paper rst gives some new operations that can address the shortages of previous ones. Then, an Induced Generalized Symmetrical Interval-Valued Intuitionistic Fuzzy Choquet-Shapley (IG-SIVIFCS) operator is dened, which not only globally considers the importance of the elements, but also re ects their overall interactions. Afterwards, several desirable properties are brie y studied to provide assurance for success in application. In some situations, the weighting information of attributes is incompletely known. Considering this case, the Shapley function-based model for determining the optimal fuzzy measure on the attribute set is constructed. Furthermore, an approach to interval-valued intuitionistic fuzzy decision-making with incomplete weighting information and interactive characteristics is developed to provide a complete theoretical framework. Finally, a practical example is provided to show the concrete practicality and validity of the proposed procedure.