Deriving the priority weights from hesitant multiplicative preference relations in group decision making

In this paper, we investigate the deviation of the priority weights from hesitant multiplicative preference relations (HMPRs) in group decision-making environments. As basic elements of HMPRs, hesitant multiplicative elements (HMEs) usually have different numbers of possible values. To correctly compute or compare HMEs, there are two principles to normalize them, i.e., the α-normalization and the β-normalization. Based on the α-normalization, we develop a new goal programming model to derive the priority weights from HMPRs in group decision-making environments. Based on the β-normalization, a consistent HMPR and an acceptably consistent HMPR are defined, and their desired properties are studied. A convex combination method is then developed to obtain interval weights from an acceptably consistent HMPR. This approach is further extended to group decision-making situations in which the experts evaluate their preferences as several HMPRs. Finally, some numerical examples are provided to illustrate the validity and applicability of the proposed models.     

Periodic autoregressive conditional duration

We propose an autoregressive conditional duration (ACD) model with periodic time-varying parameters and multiplicative error form. We name this model periodic autoregressive conditional duration (PACD). First, we study the stability properties and the moment structures of it. Second, we estimate the model parameters, using (profile and two-stage) Gamma quasi-maximum likelihood estimates (QMLEs), the asymptotic properties of which are examined under general regularity conditions. Our estimation method encompasses the exponential QMLE, as a particular case. The proposed methodology is illustrated with simulated data and two empirical applications on forecasting Bitcoin trading volume and realized volatility. We found that the PACD produces better in-sample and out-of-sample forecasts than the standard ACD.     

瑞利分布乘性噪声去除的非局部TV模型

基于局部算子的TV模型用于瑞利分布乘性噪声去除时往往存在边缘模糊、纹理模糊等问题。因此,将非局部TV算子应用于传统的局部TV模型,提出一种新模型来去除瑞利分布的乘性噪声,并通过引入辅助变量构造一个逼近的泛函,设计相应的分裂Bregman算法,加快了计算速度。实验结果表明,所提出的非局部TV模型在峰值信噪比、结构相似度和视觉效果方面都优于传统算法,对图像纹理、边缘等特征的保持能力更强。     

Higherorder singular value decomposition- and total variation- regularized multiplicative noise removal model

Smoothness, sparsity and self-similarity are the priors widely used in image denoising due to their importance in representing natural images. Motivated by the collaborative roles of higher order singular value decomposition and total variation regularization, a new approach that can simultaneously capture the above priors is proposed in this paper for removing the multiplicative noises. By taking advantages of local adaptiveness, sparsity and self-similarity realized by higher order singular value decomposition, the proposed approach starts with similar-patch-group-wise adaptive denoising on the log-transformed image, followed by the iterative optimization implemented by the total variation constraint which considers the prior of smoothness. Experiments demonstrate the advantages of the proposed approach in removing multiplicative noise and preserving the details near the edges and in the texture area.     

Multiplicative relative perturbation bounds of eigenvalues for diagonalizable matrices

In this paper, we present the general bounds of multiplicative relative perturbation for diagonalizable matrices, which are the improvement of recent results. The bounds gained here are sharper than those in related literatures. In addition, we obtain the multiplicative relative bounds for normal matrices, which are discussed first.     

On the hybrid multi-watermarking

Multi-watermarking is the technique to embed multiple messages into the same media content repeatedly. It can be used to identify media content's ownership or trace the illegal redistributors in media distribution. However, some performances of multiple watermark embedding, e.g., the distortion and security, are not considered carefully in the previous work. In this paper, the application scenario and framework of hybrid multi-watermarking are figured out, which show the secure media distribution model suitable for hierarchical media distribution. Additionally, the multi-watermarking based on hybrid multiplicative rule is firstly proposed and then analyzed theoretically with respect to two cases, i.e., the multi-embedding of same watermark sequence and the multi-embedding of different watermark sequences. The analysis emphasizes on four aspects, i.e., robustness, capacity, distortion and security, each of which considers two cases, i.e., the authorized embedding and unauthorized embedding. What is more, the locally optimum detector for multi-watermarking of hybrid multiplicative rule is reduced, and some potential attacks are investigated. Additionally, for each case, some suggestions are proposed to improve the system's performance. Finally, some comparative experiments are done, and results are given to show the validity of the theoretical analysis.     

Neutron flux characterization of the SM1 sub-critical multiplying complex of the Pavia University

SM1 is a thermal Sub-critical Multiplication complex located at the University of Pavia (Italy) and, since its installation in 1962, has been utilized mainly for radiochemistry research. This work focuses on the characterization, by means of the Monte Carlo code MCNP and direct measurements, of the neutron flux distribution inside the complex and on the calculation of the effective multiplicative coefficient (k_eff) in the current SM1 thermal configuration. For two specific irradiation channels, experimental measurements of the neutron fluxes were performed by foils activation technique and neutron spectrum de-convolution based on the SAND II code. Measurements have been compared with the simulation results showing a good agreement. Furthermore, a comparison between the preliminary results of the simulations of the SM1 plant in fast configuration, characterized by a solid lead diffuser, and the actual thermal configuration is also presented. The fast configuration of SM1, if implemented, will give the opportunity to carry out preliminary studies for the analysis of sub-critical fast-neutron installations and their applications.     

Optimal control with constrained total variance for Markov jump linear systems with multiplicative noises

We consider in this paper the stochastic optimal control problem of discrete-time linear systems subject to Markov jumps and multiplicative noises (MJLS-mn for short). Our objective is to present an optimal policy for the problem of maximising the system's total expected output over a finite-time horizon while restricting the weighted sum of its variance to a pre-specified upper-bound value. We obtain explicit conditions for the existence of an optimal control law for this problem as well as an algorithm for obtaining it, extending previous results in the literature. The paper is concluded by applying our results to a portfolio selection problem subject to regime switching.     

An approach to multiplicative linguistic group decision making based on possibility degrees

In order to compare two uncertain multiplicative linguistic variables, a possibility degree formula has been developed and its properties are also studied. Then a possibility degree matrix (also considered as a reciprocal preference relation) is constructed to compare a collection of uncertain multiplicative linguistic variables. Two models are further provided to derive the priority vector from the possibility degree matrix based on the additive consistency and multiplicative consistency. Especially, if the parameters are assigned specific values, then the models reduce to the existing ones. A group decision making method has been developed to deal with the situations where the preferences on alternatives are expressed by uncertain multiplicative linguistic variables. In this method, the possibility degree matrix is first constructed, from which the priority of alternatives is obtained using the developed models. At the end, an example is given to illustrate the proposed method.