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 denote the uncertain preferred and non-preferred degrees of decision makers. Considering the application of IVIFVs in decision making, this paper first 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 defined, which not only globally considers the importance of the elements but also overall reflects their interactions. After that, several desirable properties are briefly studied to provide assurance 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 completed theoretical framework. Finally, a practical example is provided to show the concrete practicality and validity of the proposed procedure.