In order to solve the problem that the traditional correlation coefficients between hesitant fuzzy sets are not conform to the statistics and the random process intuition

considering the more precise definition of correlation coefficient in mathematics we point out the drawbacks of the existing correlation coefficients and propose two correlation coefficient methods between hesitant fuzzy sets based on the variance and covariance of them.Meanwhile taking the attribute weight into account

we further extend the correlation coefficients into the weight correlation coefficients and apply them in multi-sensor decision-making problem.The validity of the proposed correlation coefficients to the decision making is illustrated in the simulation example and the capability of the two correlation coefficients as well as the influence of the attribute weight are also compared.