An improved MULTIMOORA with CRITIC weights based on new equivalent transformation functions of nested probabilistic linguistic term sets

The majority of real-life decision-making problems often require the analysis and evaluation of multiple factors. The nested probabilistic linguistic term set is a good tool for describing multidimensional uncertain information because it contains a collection of inner-layer and outer-layer terms and expresses both ordinal and nominal terminologies. In order to avoid losing information in the process of converting linguistic terms into numerical values, this paper proposes a series of new equivalent transformation functions for nested probabilistic linguistic term sets and defines the corresponding comparison rules. The criteria importance through inter-criteria correlation (CRITIC) method is conducted to calculate the objective weights of attributes. Using equivalent transformation functions and the weighting approach with the nested probabilistic linguistic information, this paper combines the weighted MULTIMOORA method with dominance-directed graph to solve the doctor–patient shared decision-making problem. In addition, the results of comparative analysis show that the proposed method is reasonable and effective, and it is applicable to other decision-making scenarios.