Multi-Criteria Decision-Making Method Based on Distance Measure and Choquet Integral for Linguistic Z-Numbers

Z-numbers are a new concept considering both the description of cognitive information and the reliability of information. Linguistic terms are useful tools to adequately and effectively model real-life cognitive information, as well as to characterize the randomness of events. However, a form of Z-numbers, in which their two components are in the form of linguistic terms, is rarely studied, although it is common in decision-making problems. In terms of Z-numbers and linguistic term sets, we provided the definition of linguistic Z-numbers as a form of Z-numbers or a subclass of Z-numbers. Then, we defined some operations of linguistic Z-numbers and proposed a comparison method based on the score and accuracy functions of linguistic Z-numbers. We also presented the distance measure of linguistic Z-numbers. Next, we developed an extended TODIM (an acronym in Portuguese of interactive and multi-criteria decision-making) method based on the Choquet integral for multi-criteria decision-making (MCDM) problems with linguistic Z-numbers. Finally, we provided an example concerning the selection of medical inquiry applications to demonstrate the feasibility of our proposed approach. We then verified the applicability and superiority of our approach through comparative analyses with other existing methods. Illustrative and comparative analyses indicated that the proposed approach was valid and feasible for different decision-makers and cognitive environments. Furthermore, the final ranking results of the proposed approach were closer to real decision-making processes. Linguistic Z-numbers can flexibly characterize real cognitive information as well as describe the reliability of information. This method not only is a more comprehensive reflection of the decision-makers' cognition but also is more in line with expression habits. The proposed method inherited the merits of the classical TODIM method and considers the interactivity of criteria; therefore, the proposed method was effective for dealing with real-life MCDM problems. Consideration about bounded rational and the interactivity of criteria made final outcomes convincing and consistent with real decision-making.