New distance measures between intuitionistic fuzzy sets and interval-valued fuzzy sets

Over the past several years, many studies have introduced distance and similarity measures between intuitionistic fuzzy sets (IFSs) and interval-valued fuzzy sets (IVFSs). This paper first reviews several widely used distance measures and then proposes two new distance measures. Moreover, the paper proves that the measures proposed satisfy the properties of the axiomatic definition for distance measures and introduces two corollaries. In addition, several numerical examples are provided to compare the second proposed distance measure with a number of existing distance measures. The results demonstrate that the second distance measure proposed can significantly overcome the drawback of information loss because it contains information regarding all of the points on the interval of a given IVFS. The paper concludes with suggestions for future research. (C) 2013 Elsevier Inc. All rights reserved.