Improved correlation measures for hesitant fuzzy sets

Most of the existing correlation measures for fuzzy sets return the value one to reflect a perfect linear relationship between objects, but they do not give us sufficient information about the scale with that the objects are correlated. This can be regarded as a disadvantage from decision making view point. Moreover, some of the existing correlation measures are surprisingly undefined in the case that the two objects are the same. To overcome such drawbacks, we propose an approach for deriving the modified correlation measures of hesitant fuzzy sets (HFSs) based on hesitancy degree. We also put forward some new correlation measures for HFSs based on Jaccard and Dice correlation measures defined on the vector space.