Generalized Z-numbers with hesitant fuzzy linguistic information and its application to medicine selection for the patients with mild symptoms of the COVID-19.

Fuzzy set theory and a series of theories derived from it have been widely used to deal with uncertain phenomena in multi-criterion decision-making problems. However, few methods except the Z-number considered the reliability of information. In this paper, we propose a multi-criterion decision-making method based on the Dempster-Shafer (DS) theory and generalized Z-numbers. To do so, inspired by the concept of hesitant fuzzy linguistic term set, we extend the Z-number to a generalized form which is more in line with human expression habits. Afterwards, we make a bridge between the knowledge of Z-numbers and the DS evidence theory to integrate Z-valuations. The identification framework in the DS theory is used to describe the generalized Z-numbers to avoid ambiguity. Then, the knowledge of Z-numbers is used to derive the basic probability assignment of evidence and the synthetic rules in the DS theory are used to integrate evaluations. An illustrative example of medicine selection for the patients with mild symptoms of the COVID-19 is provided to show the effectiveness of the proposed method.