Similarity measures on intuitionistic fuzzy sets

Intuitionistic fuzzy sets (IFSs), proposed by Atanassov, have gained attention from researchers for their applications in various fields. Then similarity measures between IFSs were developed. In this paper, firstly, some existing measures of similarity are reviewed. Then some examples are applied to show that some existing similarity measures are not always effective in some cases. At the same time, several new similarity measures are proposed and the relationships between some similarity measures are proved. Finally a comparison is made to show the proposed similarity measures are more reasonable than some existing similarity measures in general cases. Therefore, the proposed similarity measures can provide a useful way for measuring IFSs more effectively. (C) 2003 Elsevier B.V. All rights reserved.