A modified class of correlation coefficients of hesitant fuzzy information

Due to the importance of correlation coefficient in data analysis, researchers have shown interest in the concept of correlation coefficient for the extensions of fuzzy sets, in particular, for a recent established extension known as hesitant fuzzy set (HFS). Most of the existing correlation coefficients 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 the decision-making viewpoint. Moreover, some of the existing correlation coefficients were undefined in the case that the two objects are the same. To overcome such drawbacks, we propose an approach for deriving the modified correlation coefficients of HFSs based on hesitancy degree and then extend the approach to that of interval-valued hesitant fuzzy sets. Furthermore, we put forward a number of new correlation coefficients for HFSs based on Jaccard’s and Dice’s similarity criteria. Then, we give a practical example to illustrate the application of the improved correlation coefficients for HFSs in medical diagnosis. However, comparing the results of the proposed correlation coefficients with those of the other existing definitions shows that the diagnosis results may be quite different, and this is due to their orientation.