A multi-attribute decision-making framework for Chinese medicine medical diagnosis with correlation measures under double hierarchy hesitant fuzzy linguistic environment

In order to meet the increasingly complex and changeable decision-making needs, the double hierarchy hesitant fuzzy linguistic term set (DHHFLTS) expresses linguistic information through two independent linguistic term sets, which is a powerful tool for expressing complex linguistic information. Therefore, the research on the DHHFLTS has great theoretical and practical significance. Considering that correlation measures are not only the theoretical basis for solving linguistic decision-making problems, but also the cornerstone of many multi-attribute decision-making (MADM) methods. Therefore, this paper is devoted to the research on the correlation measure of DHHFLTSs. Based on the equivalent transformation functions of the double hierarchy hesitant fuzzy linguistic element (DHHFLE), we propose the mean and hesitancy degree of DHHFLEs and the mean and variance of DHHFLTSs. Then, this paper proposes the hesitancy degree-based correlation and correlation coefficient of DHHFLTSs. In addition, on the one hand, considering that hesitation is a key feature of the DHHFLTS, this paper gives the upper and lower bounds of the above correlation coefficient. On the other hand, taking into account the weighting factors in the actual problem, the weighted correlation coefficient and the ordered weighted correlation measure are proposed. Then, a general framework for applying the correlation measures proposed in this paper to practical MADM problems is given. Finally, taking the diagnosis of traditional Chinese medicine as an example, it proves that this method is scientific and feasible, and compares and analyzes this method with the existing related correlation measure methods.