Interval-Valued Intuitionistic Hesitant Uncertain Linguistic Set and Choquet Integral Based TOPSIS Method to MCGDM Problems

We define a new class of interval-valued intuitionistic hesitant uncertain linguistic set (IVIHULS) in this study to combine uncertainty, fuzziness and hesitancy in decision making problems both qualitatively and quantitatively. This new class of set is an extension of both uncertain linguistic term set (ULTS) and interval-valued intuitionistic hesitant fuzzy set (IVIHFS). We have developed TOPSIS method based on Choquet integral for multi-criteria group decision making (MCGDM) with IVIHUL environment considering interactive characteristics among decision criteria and preferences of decision makers. For this, we have defined Choquet averaging and geometric mean operators for IVIHULS. Some properties of proposed Choquet integral operators are obtained. Definitions of Choquet integral based Hamming and Euclidean distance measures are defined for IVIHULS. A numerical example is undertaken to clarify the newly developed method with a validity test.