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On distance and correlation measures of hesitant fuzzy information

A hesitant fuzzy set, allowing the membership of an element to be a set of several possible values, is very useful to express people's hesitancy in daily life. In this paper, we define the distance and correlation measures for hesitant fuzzy information and then discuss their properties in detail. These measures are all defined under the assumption that the values in all hesitant fuzzy elements (the fundamental units of hesitant fuzzy sets) are arranged in an increasing order and two hesitant fuzzy elements have the same length when we compare them. We can find that the results, by using the developed distance measures, are the smallest ones among those when the values in two hesitant fuzzy elements are arranged in any permutations. In addition, the derived correlation coefficients are based on different linear relationships and may have different results. © 2011 Wiley Periodicals, Inc.