Distance measures between type-2 intuitionistic fuzzy sets and their application to multicriteria decision-making process

Abstract

Type-2 fuzzy set (T2FS) is a generalization of the ordinary fuzzy set in which the membership value for each member of the set is itself a fuzzy set. However, it is difficult, in some situations, for the decision-makers to give their preferences towards the object in terms of single or exact number. For handling this, a concept of type-2 intuitionistic fuzzy set (T2IFS) has been proposed and hence under this environment, a family of distance measures based on Hamming, Euclidean and Hausdorff metrics are presented. Some of its desirable properties have also been investigated in details. Finally, based on these measures, a group decision making method has been presented for ranking the alternatives. The proposed measures has been illustrated with a numerical example.