A Novel Multi-Attribute Group Decision-Making Method and Its Application in Solving the Downward Referral Problem in the Hierarchical Medical Treatment System in China

China has made many achievements in health care industry since the establishment of hierarchical medical treatment system, but also exposed a lot of problems, such as the problem of “easy to upward-referral, hard to downward-referral”, which occurred in the implementation process of two-way referral. Recently, the appearance of “hard to downward-referral” have gotten more and more attention from scholars. The key step in solving the problem of “downward-referral” is to classify hospitals at different levels evaluated by the professional doctors. This paper proposes a framework to solve the problem where evaluation values of the hospital are given as q-rung orthopair fuzzy uncertain linguistic variables (q-ROFULVs). Considering Schweizer-Sklar t-conorm and t-norm (SSTT) can make the information aggregation process more flexible, and Hamy Mean operator can consider the correlation between hospital indicators. In order to take full advantage of these two kinds of operators, firstly, we extend SSTT to q-ROFULVs and define Schweizer-Sklar operational rules of q-ROFULVs. Secondly, we combine the Hamy Mean operator with Schweizer-Sklar t-conorm and t-norm, and propose the q-rung orthopair fuzzy uncertain linguistic Schweizer-Sklar Hamy mean aggregation operators and q-Rung orthopair fuzzy uncertain linguistic Schweizer-Sklar weighted Hamy Mean respectively. Afterwards, q-rung orthopair fuzzy uncertain linguistic Schweizer-Sklar dual Hamy mean operator and its weighted form are also developed. Then, we have studied in detail some of the ideal properties of these operators. Furthermore, a novel multi-attribute group decision-making approach based on proposed operators is introduced. Finally, we apply the new approach to solve the problem about the downward conversion in the hierarchical medical treatment system. This is of great significance for integrating the medical resources of the whole society and improving the service efficiency of the medical service system.