QZNs: Quantum Z-numbers

Because of the efficiency of modeling fuzziness and vagueness, Z-numbers play an important role in real practice. However, Z-number and its existing fuzzy operations are defined in the real number field, which lacks the ability to process the quantum information in quantum environment. It is reasonable to generalize Z-number into its quantum counterpart. In this paper, we propose quantum Z-numbers (QZNs), which are the quantum generalization of Z-numbers. In addition, seven basic quantum fuzzy operations of QZNs and their corresponding quantum circuits are presented and illustrated by numerical examples. Moreover, based on QZNs, a novel quantum multi-attributes decision making (MADM) algorithm is proposed and applied in medical diagnosis. The results show that, with the help of quantum computation, the proposed algorithm can make diagnoses correctly and efficiently.