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. (C) 2012 Elsevier Ltd. All rights reserved.