Method for multiple attribute decision making based on incomplete linguistic judgment matrix

With respect to the multiple attribute decision making problems with linguistic preference relations on alternatives in the form of incomplete linguistic judgment matrix, a method is proposed to analyze the decision problem. The incomplete linguistic judgment matrix is transformed into incomplete fuzzy judgment matrix and an optimization model is developed on the basis of incomplete fuzzy judgment matrix provided by the decision maker and the decision matrix to determine attribute weights by Lagrange multiplier method. Then the overall values of all alternatives are calculated to rank them. A numerical example is given to illustrate the feasibility and practicality of the proposed method.     

Blind reconstruction of linear scrambler

An algorithm based on eigenanalysis technique and Walsh-Hadamard transform （WriT） is proposed. The algorithm contains two steps. Firstly, the received sequence is divided into temporal windows, and a covariance matrix is computed. The linear feedback shift register （LFSR） sequence is reconstructed from the first eigenvector of this matrix. Secondly, equations according to the recovered LFSR sequence are constructed, and the Walsh spectrum corresponding to the equations is computed. The feedback polynomial of LFSR is estimated from the Walsh spectrum. The validity of the algorithm is verified by the simulation result. Finally, case studies are presented to illustrate the performance of the blind reconstruction method.     

基于群体AHP的仿真可信度评估方法研究

群体层次分析法（Group AHP）是由多个具有相关领域不同知识和经验的专家参与的群决策方法,提出了基于该方法的系统仿真可信度评估方法。首先验证各专家给出的判断矩阵的一致性,并确定判断矩阵每行的可信度,再计算各判断矩阵的可信度,给出判断矩阵中各要素的相对权重,最后得到仿真可信度的定量指标。应用结果表明,该方法能更好地集中了各专家的智慧,克服人为主观判断、偏好给决策带来的影响,因而更符合客观规律,为仿真可信度的定量评估提供了有效的技术途径。

Abstract：

Group AHP （Group Analytic Hierarchy Process） is a method of Group Decision executed by many experts who have different knowledge and experience. The method of simulation credibility evaluation based on Group AHP was proposed. In this method,the consistency of every judgment matrix built by experts was verified firstly. And every row＇s credibility of judgment matrix was given. Then reliability of every judgment matrix was calculated and the weight was constructed. Finally,quantitative credibility of simulation system was calculated. Group AHP collects intelligences of experts and reduces subjective effects and biases. The application result shows that the method is reasonable and feasible.     

CONVERGENCE PROPERTIES OF DFP METHOD WITH MODIFIED QUASI-NEWTON EQUATIONS

1 IntroductionWe know that in order to obtain a superlinearly convergent method it is necessary to approximate the Newton step asymptotically (see [ll). How can we do this without actually evaluatingthe Hessian matrix by ally approximate to the Hessian matrix at every iteration? The answerwas discovered by Davidonl2] and was subsequently developed and popularized by Fletcher andPowell[3l. It consists of starting with any approximation to the Hessian matrir, and at eachiteration, updating th…     

Receding horizon H∞ control for discrete-time Markovian jump linear systems

Receding horizon H∞ control scheme which can deal with both the H∞ disturbance attenuation and mean square stability is proposed for a class of discrete-time Markovian jump linear systems when minimizing a given quadratic performance criteria. First, a control law is established for jump systems based on pontryagin’s minimum principle and it can be constructed through numerical solution of iterative equations. The aim of this control strategy is to obtain an optimal control which can minimize the cost function under the worst disturbance at every sampling time. Due to the difficulty of the assurance of stability, then the above mentioned approach is improved by determining terminal weighting matrix which satisfies cost monotonicity condition. The control move which is calculated by using this type of terminal weighting matrix as boundary condition naturally guarantees the mean square stability of the closed-loop system. A sufficient condition for the existence of the terminal weighting matrix is presented in linear matrix inequality (LMI) form which can be solved efficiently by available software toolbox. Finally, a numerical example is given to illustrate the feasibility and effectiveness of the proposed method.     

Approximation methods of mixed l_1/H_2 optimization problems for MIMO discrete-time systems

The mixed l1/H2 optimization problem for MIMO (multiple input-multiple output) discrete-time systems is considered. This problem is formulated as minimizing the l1-norm of a closed-loop transfer matrix while maintaining the H2-norm of another closed-loop transfer matrix at prescribed level. The continuity property of the optimal value in respect to changes in the H2-norm constraint is studied. The existence of the optimal solutions of mixed l1/H2 problem is proved. Because the solution of the mixed l1/H2 problem is based on the scaled-Q method, it avoids the zero interpolation difficulties. The convergent upper and lower bounds can be obtained by solving a sequence of finite dimensional nonlinear programming for which many efficient numerical optimization algorithms exist.     

ISAR target recognition based on non-negative sparse coding

Aiming at technical difficulties in feature extraction for the inverse synthetic aperture radar (ISAR) target recognition, this paper imports the concept of visual perception and presents a novel method, which is based on the combination of non-negative sparse coding (NNSC) and linear discrimination optimization, to recognize targets in ISAR images. This method implements NNSC on the matrix constituted by the intensities of pixels in ISAR images for training, to obtain non-negative sparse bases which characterize sparse distribution of strong scattering centers. Then this paper chooses sparse bases via optimization criteria and calculates the corresponding non-negative sparse codes of both training and test images as the feature vectors, which are input into k neighbors classifier to realize recognition finally. The feasibility and robustness of the proposed method are proved by comparing with the template matching, principle component analysis (PCA) and non-negative matrix factorization (NMF) via simulations.     

THE TRANSITION PROBABILITY MATRIX OF A MARKOV CHAIN MODEL IN AN ATM NETWORK

In this paper we consider a Markov chain model in an ATM network, which has been studied by Dag and Stavrakakis. On the basis of the iterative formulas obtained by Dag and Stavrakakis, we obtain the explicit analytical expression of the transition probability matrix. It is very simple to calculate the transition probabilities of the Markov chain by these expressions. In addition, we obtain some results about the structure of the transition probability matrix, which are helpful in numerical calculation and theoretical analysis.     

Higher-order principal component pursuit via tensor approximation and convex optimization

Recovering the low-rank structure of data matrix from sparse errors arises in the principal component pursuit （PCP）. This paper exploits the higher-order generalization of matrix recovery, named higher-order principal component pursuit （HOPCP）, since it is critical in multi-way data analysis. Unlike the convexification （nuclear norm） for matrix rank function, the tensorial nuclear norm is stil an open problem. While existing preliminary works on the tensor completion field provide a viable way to indicate the low complexity estimate of tensor, therefore, the paper focuses on the low multi-linear rank tensor and adopt its convex relaxation to formulate the convex optimization model of HOPCP. The paper further propose two algorithms for HOPCP based on alternative minimization scheme： the augmented Lagrangian alternating direction method （ALADM） and its truncated higher-order singular value decomposition （ALADM-THOSVD） version. The former can obtain a high accuracy solution while the latter is more efficient to handle the computationally intractable problems. Experimental results on both synthetic data and real magnetic resonance imaging data show the applicability of our algorithms in high-dimensional tensor data processing.     

Stability of GM(1,1) power model on vector transformation

The morbidity problem of the GM(1,1) power model in parameter identification is discussed by using multiple and rotation transformation of vectors. Firstly we consider the morbidity problem of the special matrix and prove that the condition number of the coefficient matrix is determined by the ratio of lengths and the included angle of the column vector, which could be adjusted by multiple and rotation transformation to turn the matrix to a well-conditioned one. Then partition the corresponding matrix of the GM(1,1) power model in accordance with the column vector and regulate the matrix to a well-conditioned one by multiple and rotation transformation of vectors, which completely solve the instability problem of the GM(1,1) power model. Numerical results show that vector transformation is a new method in studying the stability problem of the GM(1,1) power model.     

基于矩阵分析的线性分组码盲识别

针对现有的矩阵分析法对线性分组码进行盲识别时,容错性能较差的问题,提出了一种改进的方法。首先利用截获的码字数据建立分析矩阵并进行高斯消元,然后计算各列列重的归一化值,按照判决门限找出分析矩阵中的线性相〖JP2〗关列,并以此建立统计量,最后通过统计量极大值的分布规律完成码长的识别。识别出码长后,通过移位处理及随机交换分析矩阵的行进行多次平均,实现高误码率下码字起点的识别。仿真结果表明,该方法与传统矩阵分析法相比,计算量基本相当,但容错性能有很大提升,能在较高误码率下有效实现线性分组码的盲识别。     

基于JADE与特征提取的正交/非正交空时分组码盲识别

针对非协作多输入多输出通信系统中正交空时分组码(orthogonal space-time block codes, OSTBC)与非正交空时分组码(non-orthogonal space-time block code, NOSTBC)的盲识别问题,提出结合特征值矩阵联合近似对角化(joint approximate diagonalization of eigenvalue matrix, JADE)与特征提取的盲识别方法。首先将接收信号转换为盲源分离问题中的线性瞬时混合模型,然后利用JADE算法估计出该模型的虚拟信道矩阵,根据该信道矩阵的相关矩阵为数量矩阵的特点,从相关矩阵中提取特征参数,利用此特征参数识别OSTBC与NOSTBC。仿真结果表明,在较低信噪比以及不同的调制模式下,所提方法均可有效识别出OSTBC与NOSTBC。     

基于A-DBSCAN的欠定盲源分离算法

为提升欠定盲源分离问题中混合矩阵的估计精度,在噪声环境下基于密度的空间聚类(density-based spatial clustering of applications with noise, DBSCAN)算法的基础上,提出一种自适应确定输入参数的DBSCAN算法(adaptive DBSCAN, A-DBSCAN)用于混合矩阵估计。针对DBSCAN算法邻域半径(Eps)及邻域点数(MinPts)依赖人为设定的问题,首先利用曲线拟合方法得出Eps,然后通过分析聚类输出类别数与噪声点数关系确定MinPts,并将其与混合矩阵估计模型相结合,最后通过最短路径算法实现源信号恢复。实验结果表明,提出的算法在估计混合矩阵和恢复源信号时,相关性能与对比算法相较均有明显提升。     

基于A-DBSCAN的欠定盲源分离算法

为提升欠定盲源分离问题中混合矩阵的估计精度,在噪声环境下基于密度的空间聚类(density-based spatial clustering of applications with noise, DBSCAN)算法的基础上,提出一种自适应确定输入参数的DBSCAN算法(adaptive DBSCAN, A-DBSCAN)用于混合矩阵估计。针对DBSCAN算法邻域半径(Eps)及邻域点数(MinPts)依赖人为设定的问题,首先利用曲线拟合方法得出Eps,然后通过分析聚类输出类别数与噪声点数关系确定MinPts,并将其与混合矩阵估计模型相结合,最后通过最短路径算法实现源信号恢复。实验结果表明,提出的算法在估计混合矩阵和恢复源信号时,相关性能与对比算法相较均有明显提升。     

基于累积张量分解的雷达信号欠定盲分离算法

针对时域和频域不充分稀疏条件下的雷达信号欠定盲分离问题,提出了基于信号不同时延的累积量与三阶张量分解估计混合矩阵的方法,并通过修正子空间投影算法完成对雷达源信号的恢复。首先将混合信号的四阶累积量表示成三阶张量,利用三阶张量分解获得混合矩阵估计值;通过求解雷达源信号任意时频点处对应的估计矩阵的列矢量,得到该时频点处最优超定矩阵的伪逆并恢复源信号。该算法可以解决复杂电磁环境下时频域同时混叠的雷达信号盲分离问题,仿真结果表明与现有算法相比提高了盲分离中混合矩阵估计性能和源信号恢复性能。     

盲信号压缩重构——模型与方法

通过分析欠定盲信号分离模型和压缩感知模型本质内涵和内在联系,建立了基于压缩感知的欠定盲信号重构问题的数学模型,该模型对于欠定盲信号分离的实现提供了一个新的解决途径。基于该模型的压缩重构方法通过两步来实现：分别利用源信号稀疏域性质实现对盲估计欠定混合矩阵的估计;利用压缩感知的重构稀疏源信号的方法,实现对欠定稀疏盲信号的分离和重构。提出的算法根据实际应用场合,具有一定扩展能力。最后通过模拟实验验证了提出模型和相应算法的有效性。     

基于相似度的直扩信号盲解扩方法

针对传统方法对直扩(direct sequence spread spectrum, DS-SS)信号进行盲解扩时,需要在估计出扩频序列后,才能完成信号盲解扩的问题,提出了一种基于相似度的DS SS信号盲解扩方法。该方法首先在扩频码的码片速率和周期已知的条件下,以单倍扩频码周期的窗长对接收信号进行数据分段,然后对任意两段数据求相似度函数值,构造相似度函数值的特征信息矩阵,最后通过对构造的特征信息矩阵进行特征值分解就可以实现对信息序列及扩频码序列的盲估计。理论推导和仿真实验结果表明,该方法具有精度高、稳定性好,在信噪比容限值为-22 dB的条件下也能够有效的盲估计DS-SS信号的信息序列及扩频码序列。     

基于特征值检测的多天线盲频谱感知算法的研究(英文)

在多天线感知场景中噪声不确定和信号相关现象可能同时存在,经典的基于能量检测(ED)感知性能将急剧恶化。利用多天线接收信号存在的相关特性,提出一种基于取样协方差矩阵(SCM)特征值的盲频谱感知方法。新方法无需噪声方差、主信号和无线信道的信息参与感知过程。与经典的能量检测方法相比,由于无需噪声方差参与感知节点的判决过程,新方法的感知性能对噪声不确定性具有良好的鲁棒性。利用多元统计理论和随机矩阵理论(RMT)获得了相应的理论判决门限。仿真结果表明新算法比基于ED的感知算法具有更好的误警性能和更可靠的检测性能。     

基于阵列接收模型的宽带盲源分离算法

针对传统盲分离算法对宽带信号不适用的问题,提出了一种基于阵列接收模型的宽带盲源分离算法。该算法以子带分解的方法实现了瞬时复值盲分离方法在宽带情形下的扩展。针对扩展过程中可能出现的子带间次序模糊及子带内幅度模糊的问题,利用阵列接收情况下分离矩阵与混合矩阵的特点,提出了一种基于波达方向(direction of arrival, DOA)估计的次序调整及幅度去模糊方法。仿真结果表明,该算法不仅能有效地分离宽带信号,而且可准确地恢复出信号幅度。     

基于离散正则模型的时变信道盲辨识算法

以CDMA时变信道离散正则模型为基础,提出了基于改进的矩阵外积分解的时变信道盲辨识算法。算法对传统的矩阵外积分解算法进行修正,使其适应离散正则模型两级盲辨识,并引入了精确的时延阶数估计,克服了现有算法需要预先知道信道时延实际阶数的局限,使其在仅知道信道阶数上界的条件下完成盲辨识。仿真结果表明了该算法的有效性。