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MCDM Prioritization Based on Interval Type 2 Intuitionistic Fuzzy Sets Ranking with Parametric General Graded Mean Integration Representation

This paper defines the interval type 2 intuitionistic fuzzy sets (IT2IFS) which combines the advantages of interval type 2 fuzzy sets (IT2FS) and intuitionistic fuzzy sets (IFS). Not only can IT2IFS include uncertain or incomplete information, but it is capable of containing both the positive and non-positive judgments. Mostly, multiple criteria decision making (MCDM) problems are under uncertain environment or lack complete information. It is better to model with IT2FS. In addition, IFS takes into account membership (belongs) and non-membership (does not belong) degrees, which is appropriate to allow experts to express positive and non-positive judgments. It is critical in MCDM to determine the priority. An IT2IFS ranking methodology based on the general graded mean integration representation (GGMIR) is developed. The decomposition process of IT2IFS with two IT2FS is presented to formulate the IT2IFS GGMIR. The IT2IFS GGMIR is served as a well-defined partial ordering. Additionally, the IFS type reduction and defuzzification process can be achieved by leveraging the IT2IFS GGMIR. The effectiveness of the proposed methodology is demonstrated by an IT2IFS MCDM problem.