Quantum computing as a new computational theory model is becoming the focus of information study. To realize the effective fusion of fuzzy morphology and quantum computing model,a fuzzy morphological structuring element based on quantum state model is proposed. Inspired by quantum signal processing theory,the structuring element is denoted by quantum bit system,a degree of membership function denotes a probability of quantum state. A fuzzy structuring element is collapsed as a clear structuring element through quantum measurement. Simulation analysis shows the feasibility of the quantum state model,and morphological filter can effectively remove noise and keep the detail information by using the collapsed structuring element.
Quantum computing as a new computational theory model is becoming the focus of information study. To realize the effective fusion of fuzzy morphology and quantum computing model,a fuzzy morphological structuring element based on quantum state model is proposed. Inspired by quantum signal processing theory,the structuring element is denoted by quantum bit system,a degree of membership function denotes a probability of quantum state. A fuzzy structuring element is collapsed as a clear structuring element through quantum measurement. Simulation analysis shows the feasibility of the quantum state model,and morphological filter can effectively remove noise and keep the detail information by using the collapsed structuring element.
Fuzzy model theory is an alternative approach to formalizing uncertainty and/or incompleteness of knowledge to the formalization using fuzzy sets proposed by Lotfi Zadeh. This approach to information processing is also applied in quantum computing. All quantum computations are conducted under the assumption of incomplete knowledge and only at the last stage the measurement (i.e. digitization) of the obtained results is performed. The paper describes a model-theoretic formalization of a pure quantum system in the language of fuzzy model theory. It is shown that the fuzzy model can be considered as a generalization of the concept of quantum system. One of the central concepts of quantum computing is quantum entanglement. A quantum system is considered to be non-entangled or separable if the results of measurements of some elements of the system do not depend on measurements of other elements. The paper introduces the concept of entangled and partially entangled fuzzy system, formulates and proves the criteria of entanglement of a fuzzy system.
Recent development of computer technology may lead to the quantum image algorithms becoming a hotspot. Quantum information and computation give some advantages to our quantum image algorithms, which deal with the limited problems that cannot be solved by the original classical image algorithm. Image processing cry out for applications of quantum image. Most works on quantum images are theoretical or sometimes even unpolished, although real-world experiments in quantum computer have begun and are multiplying. However, just as the development of computer technology helped to drive the Technology Revolution, a new quantum image algorithm on constrained least squares filtering computation was proposed from quantum mechanics, quantum information, and extremely powerful computer. A quantum image representation model is introduced to construct an image model, which is then used for image processing. Prior knowledge is employed in order to reconstruct or estimate the point spread function, and a non-degenerate estimate is obtained based on the opposite processing. The fuzzy function against noises is solved using the optimal measure of smoothness. On the constraint condition, determine the minimum criterion function and estimate the original image function. For some motion blurs and some kinds of noise pollutions, such as Gaussian noises, the proposed algorithm is able to yield better recovery results. Additionally, it should be noted that, when there is a noise attack with very low noise intensity, the model based on the constrained least squares filtering can still deliver good recovery results, with strong robustness. Subsequently, discuss the simulation analysis of the complexity of implementing quantum circuits and image filtering, and demonstrate that the algorithm has a good effect on fuzzy recovery, when the noise density is small.
Among clustering algorithms, fuzzy clustering stands out for its ability to offer a nuanced representation of the data by assigning degrees of membership to clusters, providing a more flexible and adaptive approach than the rigid partitioning of hard clustering algorithms. This has proved highly advantageous, particularly for image segmentation problems. Numerous approaches have been proposed to improve the Fuzzy C-means (FCM) algorithm using quantum computing, some are quantum-inspired and others can be run on quantum simulators. In this paper, a study was conducted on Quantum Fuzzy Means (QFCM) approaches. Then, a novel QFCM algorithm is introduced to address the challenges associated with these current algorithms, particularly in handling large datasets and incorporating genuine fuzzy system principles. Using concepts from quantum computing, our approach aims to improve distance calculations between data points by using a quantum distance measure. This method enables significant acceleration of the clustering process especially when dealing with extensive datasets. Moreover, our proposed algorithm integrates a structured fuzzy system framework into the membership matrix calculation, enhancing the precision and interpretability of the clustering results. Furthermore, unlike other FCM algorithms, which often lack explicit representation of fuzzy logic principles, our approach incorporates a well-defined fuzzy system to capture the inherent uncertainty and ambiguity in real-world data.
In this paper, an attempt is made to synthesize fuzzy mathematics and quantum mechanics. By using the method of fuzzy mathematics to blur the probability (wave) of quantum mechanics, the concept of fuzzy wave function is put forward to describe the fuzzy quantum probability. By applying the non-fuzzy formula of fuzzy quantity and Schrödinger wave equation of quantum mechanics, the membership function equation is established to describe the evolution of the fuzzy wave function. The concept of membership degree amplitude is introduced to calculate fuzzy probability amplitude. Some important concepts in fuzzy mathematics are also illustrated.
The goal of this study is to integrate fuzzy mathematics and quantum mechanics to seek deeper cosmic principles. The concept of fuzzy wave function is proposed to represent the fuzzy quantum probability by utilizing fuzzy mathematics to blur the probability (wave) of quantum mechanics. By applying the non-fuzzy formula of fuzzy quantity and the Schrödinger wave equation of quantum mechanics, the membership function equation is constructed to describe the evolution of the fuzzy wave function. The concept of membership degree amplitude is introduced to calculate fuzzy probability amplitude, and the membership degree amplitude equation is derived. Some important concepts in fuzzy mathematics are also illustrated.
The goal of this study is to extend quantum theory to the field of fuzzy phenomena. Using the idea and method of fuzzy mathematics, the quantum probability theory of fuzzy event is proposed, with the form of fuzzy event route integral, membership degree amplitude, fuzzy field function, Green function, physical quantity and fuzzy diagram. This theory changes quantum mechanics, making it a special instance of the former. Under some conditions, this theory breaches unitarity, gauge invariance, probability conservation, and information conservation, rendering these concepts approximate. This new theory, which does not require renormalization and can naturally produce meaningful results that are consistent with the experiments, is the proper theory for describing microscopic high-speed phenomena, whereas quantum mechanics is only a proper theory for describing microscopic low-speed phenomena. Because this theory is not divergent under the conditions that there is no renormalization and an infinite number of offsetting terms, it can constitute the theoretical framework required for gravity quantization.