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.

With the rapid development of society and continual progress of science and technology, large-scale group decision-making (LSGDM) problems are very commonly encountered in real-life situations. Considering that the information required for decision-making and people's cognition processes is becoming more and more complex, double hierarchy linguistic preference relation (DHLPR) can be used to express complex linguistic information reasonably and intuitively. Sometimes experts in LSGDM unwillingly modify their preferences or even modify them on purpose in a contrary way to the other experts. Thus, differing opinions or minority preferences are often referred to as obstacles to decision-making. This article develops a consensus model to manage minority opinions and noncooperative behaviors in LSGDM with DHLPRs. In addition, to establish the consensus model, some basic tools, such as the clustering method, weights-determining method, and adjustment coefficients-determining method, are developed. Finally, a practical LSGDM problem is set up to prove that the proposed consensus model is feasible and effective, and some comparative analyses are made to highlight the advantages of these methods and models, as well as to analyze current deficiencies.