Abstract
Double hierarchy hesitant fuzzy linguistic term set (DHHFLTS) can be used to express complex linguistic information by combining two hierarchy linguistic term sets with 2-tuple linguistic structures. In decision-making processes, experts' assessment information may often be represented by some possible double hierarchy hesitant fuzzy linguistic elements (DHHFLEs) or some DHHFLEs with probability information, and we cannot ignore these probabilities when they are directly provided or aggregated by the experts' assessments. As we are aware that representing probability information is a new improvement and challenge for DHHFLTSs, this paper defines a novel and more general concept named probabilistic double hierarchy linguistic term set (PDHLTS). Then, to propose some more reasonable operations and a distance measure of PDHLTSs, we develop an adjustment method to ensure that two PDHLTSs have same probability distribution. Additionally, this paper develops an extended probabilistic double hierarchy linguistic VIKOR method by improving the traditional VIKOR method. Moreover, the advantages and practicality of the proposed method are demonstrated by applying it to solve a practical multiple criteria decision-making problem involving smart healthcare. Finally, we make some comparative analyses, as well as discussing possible directions for future studies.