Novel correlation coefficient between hesitant fuzzy sets with application to medical diagnosis

As an extension of the fuzzy set, the hesitant fuzzy set (HFS) is an effective tool for handling uncertainty and vagueness in decision making problems. Considering that the correlation coefficient (CC) has a strong ability to process and analyze data, we are developing a novel CC to measure the strength of the relationship between HFSs in this article. The CC presented between the HFSs has more desirable properties than the current ones. It relaxes limits on the length of the hesitant fuzzy elements (HFEs) and can be used to determine whether the HFSs are negatively or positively correlated. More importantly, it can ensure that the CC between two HFSs is equal to one (minus one) if and only if the two HFSs are the same (complement each other), and thus avoid the achievement of counter-intuitive decision results by inappropriate calculation approaches. The motivation of re-visiting the CC between HFSs is that a more effective CC between HFSs should be developed in order to significantly improve decision-making performance. To demonstrate the effectiveness of the proposed method, a case study on medical diagnosis is offered and the comparative analyses with other methods are also conducted.