Correlation coefficient of dual hesitant fuzzy sets and its applications

Correlation between two variables or parameters plays a very significant role in statistics. Furthermore, the accuracy in the measurement of the correlation depends upon the data collected for the set of discourse. It is quite evident that in many cases the data collected for various statistical measures are full of uncertainties. A dual hesitant fuzzy set (DHFS) is a generalized form of a hesitant fuzzy set (HFS) and negates the effects of uncertainty inherent in the collected data. In the present paper, the concept of HFS has been replaced with DHFS and the correlation between two DHFSs is obtained. A formula for the correlation coefficient between two DHFSs has been derived. The proposed method was used to determine the coefficient of correlation between different parameters of water in four different lakes in Rajasthan, India.