Developing new similarity measures of generalized intuitionistic fuzzy numbers and generalized interval-valued fuzzy numbers from similarity measures of generalized fuzzy numbers

The main aim of this paper is to give a novel method to extend a similarity measure of generalized trapezoidal fuzzy numbers (GTFNs) to similarity measures of generalized trapezoidal intuitionistic fuzzy numbers (GTIFNs) and generalized interval-valued trapezoidal fuzzy numbers (GIVTFNs) such that the initial properties to be preserved. The first idea is to consider the similarity measure of GIVTFNs as a combination of similarity measure between the lower GTFNs with the similarity measure between the upper GTFNs. The second idea is to find a bijective correspondence between GTIFNs and GIVTFNs such that the similarity measures can be transferred in an obvious way. The results in the triangular case are immediate consequences.