A New Similarity Measure between Intuitionistic Fuzzy Sets Based on a Choquet Integral Model

Several existing similarity measures between intuitionistic fuzzy sets (IFSs) and between vague sets are reviewed. A numerical example shows that these similarity measures are not always reasonable in some cases, and one reason is that inherent interactions among elements of a given universe are ignored. To overcome the drawbacks of these similarity measures, a new similarity measure of IFSs is proposed based on a Choquet integral model, where a generalized fuzzy measure is used to characterize interactions among elements of a given universe of IFSs or vague sets, and the Choquet integral model instead of a weighted average model is used to compute the new similarity measure. Further, properties of the new similarity measure are discussed, and numerical examples show that this new similarity measure is more reasonable than the existing similarity measures.