Double hierarchy hesitant fuzzy linguistic term set and MULTIMOORA method: A case of study to evaluate the implementation status of haze controlling measures

In recent years, hesitant fuzzy linguistic term sets (HFLTSs) have been studied by many scholars and are becoming gradually mature. However, some shortcomings of HFLTS also emerged. To describe the complex linguistic terms or linguistic term sets more accurately and reasonably, in this paper, we introduce the novel concepts named double hierarchy linguistic term set (DHLTS) and double hierarchy hesitant fuzzy linguistic term set (DHHFLTS). The operational laws and properties of the DHHFLTSs are developed as well. Afterwards, we investigate the multiple criteria decision making model with double hierarchy hesitant fuzzy linguistic information. We develop a double hierarchy hesitant fuzzy linguistic MULTIMOORA (DHHFL-MULTIMOORA) method to solve it. Furthermore, we apply the DHHFL-MULTIMOORA method to deal with a practical case about selecting the optimal city in China by evaluating the implementation status of haze controlling measures. Some comparisons between the DHHFL-MULTIMOORA method and the hesitant fuzzy linguistic TOPSIS method are provided to show the advantages of the proposed method.