Ranking type 2 fuzzy sets by parametric embedded representation

In this article, we propose a new and general approach of ranking a set of interval type 2 fuzzy sets (IT2FS). 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. In addition, the meaning of the specific IT2FS is defined by the decision maker relevant to the specific parameter function. Firstly, the parametric centroid function is calculated with respect to the embedded pessimistic, modal and optimistic functionals. Then, the centroid of the IT2FS is determined by taking the average of the parametric centroid function. In this manner, the IT2FSs are defuzzified and can be ranked by sorting the average centroids. A numerical example is presented for verifying the proposed method.