Interval Type 2 Intuitionistic Fuzzy Sets Ranking Method Based on the General Graded Mean Integration Representation with Application to Multiple Criteria Decision Making

The critical stage in multiple criteria decision making (MCDM) is to determine the priority. Most MCDM tasks are in the uncer-tain environment. Some judgments can be characterized by fuzzy sets or even better by interval type 2 fuzzy sets (IT2FS). The clas-sical fuzzy sets consider only the degrees of belongingness. The intuitionistic fuzzy sets introduced by Atanassov consider both the degrees of membership (belonging to) and the degrees of non-membership (not belonging to). The first contribution of this pa-per is to define the interval type 2 intuitionistic fuzzy sets (IT2IFS). Such kinds of mathematical functionals can be mapped to the lin-guistic judgments of the MCDM problems. The second contribution is to develop the IT2IFS ranking methodology based on the general graded mean integration representation (GGMIR). Such expressions can be directly utilized in MCDM problems involving IT2IFS criteria weights as well as IT2IFS alternative rates to prioritize alternatives. A numerical example of the MCDM with IT2IFS is performed for demonstrating the proposed methodology.