A robust correlation coefficient measure of dual hesitant fuzzy soft sets and their application in decision making

The objective of this work is to present novel correlation coefficients for measuring the relationship between two dual hesitant fuzzy soft set (DHFSSs). In the existing studies of fuzzy and intuitionistic fuzzy sets, the uncertainties which are present in the data are handled without considering the parameterizations factor of each expert during the process, which may lose some useful information of alternatives and hence affect the decision results. On the other hand, soft set theory handles the uncertainties by considering both the parameterizations as well as criteria during the evaluation of the object. Thus, motivated by this, we develop correlation coefficient and weighted correlation coefficients under the DHFSS environment in which pairs of membership, non-membership are to be considered as vector representation during the formulation and to investigate their properties. Further, under this environment, a multicriteria decision making method based on the proposed correlation coefficients are presented. Three numerical examples, one from the selection procedure and other from the medical diagnosis and pattern recognition, are taken to demonstrate the efficiency of the proposed approach and compared their results with the several existing approaches results.