Firstly, we study some integrable properties for this system such as Hamiltonian structures, Liouville integrability and conservation laws. This paper investigates a relativistic Toda lattice system with an arbitrary parameter that is a very remarkable generalization of the usual Toda lattice system, which may describe the motions of particles in lattices. Simulation experiments and various security analyses show that this algorithm has a good effect on encryption, high time efficiency, and can effectively resist brute force attacks, statistical attacks, chosen-plaintext attacks, and differential attacks. The generation of the intermediate secret keys is related to the sum of the image DNA code, and the ciphertext feedback mechanism of the DNA encoding image is introduced in the diffusion procedure. The dynamic DNA coding mechanism is introduced by using the chaotic sequence. The encryption algorithm consists of line-by-line scrambling and diffusion of DNA encoding characters. In addition, a novel hyperchao-based image encryption scheme with dynamic DNA coding is proposed. The complexity of chaotic time series is tested with various measurement tools, such as the scale index, the multiscale sample entropy and approximate entropy, TESTU01, and NIST test. We make a quantitative analysis of the complexity of the conservative hyperchaotic system from several different aspects, such as phase diagrams, bifurcation diagrams, Lyapunov exponents, and Kaplan–Yorke dimension. In the current paper, a new conservative hyperchaotic system is proposed. Finally, an investment example is used to verify the effectiveness of our method, and the superiority of the method is proved by comparing with other methods. Then, we propose a method to deal with MSDM problems and give the specific steps to solve the problem. Furthermore, considering the influence of attribute weight on the results, we introduce the weighted SVNULMSM operator and weighted SVNULGMSM operator. First of all, according to the neutrosophic set and uncertain linguistic numbers, we propose the single-valued neutrosophic uncertain linguistic numbers and give some operating rules. In this paper, we combine the MSM operator with the singled-valued neutrosophic uncertain linguistic set and propose some MSM operators based on single-valued neutrosophic uncertain linguistic environment, such as single-valued neutrosophic uncertain linguistic Maclaurin symmetric mean(SVNULMSM) operator and single-valued neutrosophic uncertain linguistic generalized Maclaurin symmetric mean(SVNULGMSM) operator. It can capture the relationships between multiple input parameters, and the neutrosophic uncertain linguistic numbers can well represent some indeterminate and incomplete information. The Maclaurin symmetric mean (MSM) operator has a good aggregation effect.
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