Correlation Coefficient of Probabilistic Hesitant Fuzzy Soft Set and Its Applications in Decision Making

In this study, some concepts are developed such as probabilistic hesitant fuzzy soft set (PHFSS), a combination of probabilistic hesitant fuzzy set and soft set. PHFSS can be used to describe the uncertainty and complexity in practical evaluation problems. Herein, the relationships between any two PHFSSs are proposed, including the relation of inclusion, equivalence and complement. Considering that correlation coefficient is one of the most important tools in data analysis and decision making, we develop a novel correlation coefficient formulation to measure the interrelationship between the PHFSSs. Meanwhile, the mean and the variance of a PHFSS are defined. The properties of the proposed correlation coefficient are also discussed. Finally, a numerical evaluation example in business environment satisfaction is proposed to illustrate the feasibility and rationality of the given correlation coefficient between PHFSSs.