Interval-valued intuitionistic hesitant fuzzy Choquet integral based TOPSIS method for multi-criteria group decision making

Abstract

Inter-dependency among the decision criteria and difficulty of establishing a common membership grade are two important issues to be addressed in multi-criteria group decision making (MCGDM) problems in the environment of uncertainty. The main purpose of this paper is to define the Choquet integral operator for interval-valued intuitionistic hesitant fuzzy sets (IVIHFS) and to extend the technique for order preference by similarity to ideal solution (TOPSIS) method using Choquet integral operator in interval-valued intuitionistic hesitant fuzzy environment. In the present study we define interval-valued intuitionistic hesitant fuzzy Choquet integral (IVIHFCI) operator and extend the definition of hamming distance for the elements of IVIHFS. Using IVIHFCI operator and hamming distance for IVIHFS, we extend TOPSIS method for MCGDM for interval-valued intuitionistic hesitant fuzzy environment considering the interaction phenomena among the decision criteria. An illustrative example has also been taken in the present study to understand the proposed method.