2008•International Journal of Uncertainty Fuzziness and Knowledge-Based SystemsRequires access
AN OVERVIEW OF DISTANCE AND SIMILARITY MEASURES OF INTUITIONISTIC FUZZY SETS
Zeshui Xu, J. CHEN
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Abstract
The Intuitionistic Fuzzy Sets (IFSs), originated by Atanassov [1], is a useful tool to deal with vagueness and ambiguity. In the short time since their first appearance, many different distance and similarity measures of IFSs have been proposed, but they are scattered through the literature. In this paper, we give a comprehensive overview of distance and similarity measures of IFSs. Based on the weighted Hamming distance, the weighted Euclidean distance, and the weighted Hausdorff distance, respectively, we define some continuous distance and similarity measures for IFSs. We also utilize geometric distance model to define some continuous distance and similarity measures for IFSs, which are the various combinations and generalizations of the weighted Hamming distance, the weighted Euclidean distance and the weighted Hausdorff distance. Then we extend these distance and similarity measures for Interval-Valued Intuitionistic Fuzzy Sets (IVIFSs).