New similarity measures between intuitionistic fuzzy sets and between elements

Li and Cheng [1] and Hong and Kim [2] 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 [1] to show the application of the new measure methods in pattern recognition. (c) 2005 Elsevier Ltd. All rights reserved.