QZNs: Quantum Z-numbers

TL;DR

This paper introduces quantum Z-numbers (QZNs), a quantum generalization of classical Z-numbers, along with quantum fuzzy operations and a quantum MADM algorithm for medical diagnosis, demonstrating improved efficiency and accuracy.

Contribution

The paper proposes the first quantum generalization of Z-numbers, develops quantum fuzzy operations, and applies a quantum MADM algorithm to medical diagnosis.

Findings

Quantum Z-numbers enable processing of quantum information.

Quantum fuzzy operations are effectively implemented with quantum circuits.

The quantum MADM algorithm achieves accurate and efficient medical diagnoses.

Abstract

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.