Novel correlation coefficients for hesitant fuzzy sets and their applications to supplier selection and medical diagnosis

Hesitant fuzzy set theory provides an effective technique for researchers and engineers to cope with vagueness and uncertainty. In recent years, to explore the correlation between hesitant fuzzy sets, traditional correlation measure in statistics has been constantly studied in hesitant fuzzy environments. In this study, extant studies of correlation measures in hesitant fuzzy contexts are recalled and analyzed. In view of the forgoing analysis, we find out that the extant correlation coefficients have some limitations. Moreover, a few correlation coefficients are not in line with the traditional definition of correlation coefficients. In order to address the flaws of the existing proposals, a novel hesitant fuzzy correlation coefficient is proposed in this study. The new proposal of this study can not only overcome the flaws of the old hesitant fuzzy correlation coefficients, but it also shows several desirable characteristics. The weighted form of the newly defined correlation coefficient and its features are also investigated. Finally, three numerical examples concerning supplier selection and medical diagnosis are examined using the developed correlation coefficients to demonstrate their applicability. Comparison analyses with existing proposals highlight the efficiency of our proposals.