  Because of the efficiency of modeling fuzziness and vagueness, Z-number plays
an important role in real practice. However, Z-numbers, defined in the real
number field, lack 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.
