Li and Cheng  and Hong and Kim  proposed several similarity measures between intuitionistic fuzzy sets and between vague sets, respectively. In this paper, by analyzing these similarity measures, we show that they are not reasonable in some cases. Some new methods for measuring the degree of similarity between intuitionistic fuzzy sets and between elements are proposed and their properties are discussed. These new methods turned out to be more reasonable by comparison. Finally, we use the same examples given by Li and Cheng  to show the application of the new measure methods in pattern recognition. © 2005 Elsevier Ltd. All rights reserved.
Liu, H. W. (2005). New similarity measures between intuitionistic fuzzy sets and between elements. Mathematical and Computer Modelling, 42(1–2), 61–70. https://doi.org/10.1016/j.mcm.2005.04.002