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arXiv:2104.05190

QZNs: Quantum Z-numbers

Jixiang Deng, Yong Deng

Published Apr 12, 2021• 0 citations
arXivHTMLPDF

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.

DOI
10.48550/arxiv.2104.05190

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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.
Quantum computation has attracted numerous attentions and develops rapidly in the recent decades. To against the decoherence and the control errors upon the qubits, quantum error corrections are adopted. Such approaches require lots of redundant qubits, accurate measurement and timely feedback. Here we investigate a new framework of quantum computation that is associated with fuzzy processing. It will benefit significantly from three aspects: the fuzzy recognition of qubit states reduce the required gate fidelity; the fuzzy encoding encodes the information of the qubits into a distribution of probability, suppressing the fluctuations in the output of long quantum circuits; the fuzzy feedback offers a more efficient way to control the qubits when precision information of quantum states are absent. Furthermore, the fuzzy processing can be integrated into quantum error correction, eliminating the need for immediate correction operations. The proposed scheme will be fairly suitable for the solution of decision problems, which has significant applications in the optimization problems and control problems.
The combination of Quantum Technologies and Artificial Intelligence (AI) is shaping a new approach in life sciences and healthcare. The growing complexity of biomedical data, along with the demand for quick and precise decision-making, has led to the exploration of new computing methods beyond traditional systems. AI has shown great success in medical diagnosis, disease prediction, drug discovery, and healthcare analytics. However, traditional AI models have drawbacks when it comes to optimization, scalability, and computational efficiency. Quantum technologies offer new computing principles based on quantum mechanics, allowing for parallel processing and better optimization. This review provides a detailed look at recent progress in quantum technologies and AI applications within life sciences and healthcare. The paper examines the basics of quantum computing, quantum-inspired algorithms, and hybrid quantum-AI frameworks, emphasizing their uses in disease diagnosis, medical imaging, genomics, molecular modeling, and drug discovery. It also discusses current challenges, practical limitations, and future research directions. This review aims to give researchers, students, and practitioners a clear understanding of the developing quantum-AI landscape and its potential effects on future healthcare systems.
A general approach describing quantum decision procedures is developed. The approach can be applied to quantum information processing, quantum computing, creation of artificial quantum intelligence, as well as to analyzing decision processes of human decision makers. Our basic point is to consider an active quantum system possessing its own strategic state. Processing information by such a system is analogous to the cognitive processes associated to decision making by humans. The algebra of probability operators, associated with the possible options available to the decision maker, plays the role of the algebra of observables in quantum theory of measurements. A scheme is advanced for a practical realization of decision procedures by thinking quantum systems. Such thinking quantum systems can be realized by using spin lattices, systems of magnetic molecules, cold atoms trapped in optical lattices, ensembles of quantum dots, or multilevel atomic systems interacting with electromagnetic field.
In this article we investigate a way in which quantum computing can be used to extend the class of fuzzy sets. The core idea is to see states of a quantum register as characteristic functions of quantum fuzzy subsets of a given set. As the real unit interval is embedded in the Bloch sphere, every fuzzy set is automatically a quantum fuzzy set. However, a generic quantum fuzzy set can be seen as a (possibly entangled) superposition of many fuzzy sets at once, offering new opportunities for modeling uncertainty. After introducing the main framework of quantum fuzzy set theory, we analyze the standard operations of fuzzification and defuzzification from our viewpoint. We conclude this preliminary paper with a list of possible applications of quantum fuzzy sets to pattern recognition, as well as future directions of pure research in quantum fuzzy set theory.
Optimal query distribution in information systems plays a crucial role in minimizing delays, balancing workload, and ensuring system stability. Considering multi-factor parameters such as server capacity, network latency, and service rate, the fuzzy logic approach proves effective in handling uncertainty during decision-making. However, an increase in the number of linguistic variables leads to exponential growth of the fuzzy rule base, thereby increasing computational complexity and limiting real-time performance. Traditional optimization methods, including genetic algorithms, are constrained by slow convergence and a tendency to fall into local extrema in large search spaces. This paper proposes a multi-objective quantum optimization approach aimed at reducing the number of fuzzy rules in query distribution processes. By applying Grover's quantum algorithm, the search for optimal rules is significantly accelerated, and the search space is significantly reduced. Experimental results demonstrate reduced response time and improved load balancing. The proposed approach is evaluated as a promising quantum-intelligent mechanism for enhancing load management efficiency in cloud computing environments.