Ranking interval type 2 fuzzy sets using parametric graded mean integration representation

In this paper, we develop the parametric graded mean integration representation (PGMIR) for the interval type 2 fuzzy sets (IT2FS). The PGMIR value can be served as the type reduced or defuzzification of an IT2FS. A set of IT2FSs can then be ordered by the corresponding PGMIR values. Firstly, the parametric representation of the embedded fuzzy sets is defined for the general IT2FS. The IT2FS is characterized by the set of embedded fuzzy sets induced from the parametric function. Then, the graded mean integration representation (GMIR) of a type 1 fuzzy set (T1FS) is extended to the IT2FS through the parametric form of an IT2FS. The GMIR of the parametric embedded T1FS is defined and is called the PGMIR. In this manner, the IT2FSs are defuzzified and can be ranked by sorting the PGMIR values. The average value of the PGMIR is used to determine IT2FS ranking. A numerical example is presented to show that the proposed approach is superior to the ranking method from IT2FS centroid.