On application of input data partitioning to Bayesian weighted averaging of biomedical signals

Averaging in the time domain may be used for noise attenuation in case of biomedical signals with a quasi‐cyclical character. Traditional arithmetic averaging technique assumes the constancy of the noise power cycle‐wise, however, most types of noise are not stationary and the variability of noise power is observed. It constitutes a motivation for using methods of weighted averaging, in particular Bayesian weighted averaging. This paper presents the computational study of Bayesian weighted averaging with traditional (sharp) and fuzzy partition of the input data in the presence of non‐stationary noise. There is presented the known empirical Bayesian weighted averaging method (EBWA), with the parameter p describing the probabilistic model, and its modification NBWA which eliminates the parameter. Both methods can be extended by partitioning of the input data. The performance of presented methods is experimentally evaluated for an analytical signal as well as a real ECG signal and compared with traditional arithmetic averaging method. However, the methods can be applied to any signal with a quasi‐cyclical character. The aim of the paper is to show the influence of the type of partition as well as the number of parts on the quality of the averaged signal.     

Density-clusters ordered weighted averaging operator based on generalized trapezoidal fuzzy numbers

To the problem of multi-attribute decision making with fuzzy numbers, this paper proposes a new type of operator called the density-clusters ordered weighted averaging (OWA) operator based on generalized trapezoidal fuzzy (GTF) numbers. This operator is abbreviated as the GTF-DOWA operator. A primary characteristic of the GTF-DOWA operator is that it considers the implicit structure of the GTF numbers to be aggregated by grouping the numbers to various local clusters. We discuss the grouping methods of the GTF numbers using the centroids of the numbers. The cluster weights are determined by the combined consideration of the decision maker's attitude and the scale of each local cluster. In addition, we discuss the primary properties of the GTF-DOWA operator. Finally, a numerical example regarding the selection of optimal alternative is provided. The aggregations of the GTF-DOWA operator are compared with those of the weighted arithmetic averaging (WAA) operator and the OWA operator based on GTF numbers to illustrate the validity of the GTF-DOWA operator.     

Multi-sensor information fusion white noise filter weighted by scalars based on Kalman predictor

A unified multi-sensor optimal information fusion criterion weighted by scalars is presented in the linear minimum variance sense. The criterion considers the correlation among local estimation errors, only requires the computation of scalar weights, and avoids the computation of matrix weights so that the computational burden can obviously be reduced. Based on this fusion criterion and Kalman predictor, an optimal information fusion filter for the input white noise, which can be applied to seismic data processing in oil exploration, is given for discrete time-varying linear stochastic control systems measured by multiple sensors with correlated noises. It has a two-layer fusion structure. The first fusion layer has a netted parallel structure to determine the first-step prediction error cross-covariance for the state and the filtering error cross-covariance for the input white noise between any two sensors at each time step. The second fusion layer is the fusion center to determine the optimal scalar weights and obtain the optimal fusion filter for the input white noise. Two simulation examples for Bernoulli-Gaussian white noise filter show the effectiveness.     

Point Cloud Denoising via Moving RPCA

We present an algorithm for the restoration of noisy point cloud data, termed Moving Robust Principal Components Analysis (MRPCA). We model the point cloud as a collection of overlapping two‐dimensional subspaces, and propose a model that encourages collaboration between overlapping neighbourhoods. Similar to state‐of‐the‐art sparse modelling‐based image denoising, the estimated point positions are computed by local averaging. In addition, the proposed approach models grossly corrupted observations explicitly, does not require oriented normals, and takes into account both local and global structure. Sharp features are preserved via a weighted ?₁ minimization, where the weights measure the similarity between normal vectors in a local neighbourhood. The proposed algorithm is compared against existing point cloud denoising methods, obtaining competitive results.     

基于二元联系数集结算子的多准则群决策方法

定义了二元联系数的加性运算法则, 给出了几种新的算术集结算子, 即二元联系数加权算术平均(BCNWAA)算子、二元联系数有序加权平均(BCNOWA) 算子和二元联系数混合集结(BCNHA) 算子, 提出了一种基于二元联系数的准则权重信息不完全确定的群决策方法. 该方法利用BCNWAA算子和BCNHA算子对二元联系数准则值进行集结; 利用二元联系数准则值的方差和准则权重的随机性, 通过构建优化模型确定最优准则权重. 最后, 通过实例分析表明了该方法的可行性和有效性.

     

Single machine scheduling problems with uncertain parameters and the OWA criterion

In this paper a class of single machine scheduling problems is discussed. It is assumed that job parameters, such as processing times, due dates, or weights are uncertain and their values are specified in the form of a discrete scenario set. The ordered weighted averaging (OWA) aggregation operator is used to choose an optimal schedule. The OWA operator generalizes traditional criteria used in decision making under uncertainty, such as the maximum, average, median, or Hurwicz criterion. It also allows us to extend the robust approach to scheduling by taking into account various attitudes of decision makers towards a risk. In this paper, a general framework for solving single machine scheduling problems with the OWA criterion is proposed and some positive and negative computational results for two basic single machine scheduling problems are provided.     

Robust weighted fusion Kalman estimators for multisensor systems with multiplicative noises and uncertain‐covariances linearly correlated white noises

This paper addresses the design of robust weighted fusion Kalman estimators for a class of uncertain multisensor systems with linearly correlated white noises. The uncertainties of the systems include the same multiplicative noises perturbations both on the systems state and measurement output and the uncertain noise variances. The measurement noises and process noise are linearly correlated. By introducing two fictitious noises, the system under consideration is converted into one with only uncertain noise variances. According to the minimax robust estimation principle, based on the worst‐case systems with the conservative upper bounds of the noise variances, the four robust weighted fusion time‐varying Kalman estimators are presented in a unified framework, which include three robust weighted state fusion estimators with matrix weights, diagonal matrix weights, scalar weights, and a modified robust covariance intersection fusion estimator. The robustness of the designed fusion estimators is proved by using the Lyapunov equation approach such that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. The accuracy relations among the robust local and fused time‐varying Kalman estimators are proved. The corresponding robust local and fused steady‐state Kalman estimators are also presented, a simulation example with application to signal processing to show the effectiveness and correctness of the proposed results. Copyright © 2016 John Wiley & Sons, Ltd.     

Generalized ordered weighted logarithm aggregation operators and their applications to group decision making

We present the generalized ordered weighted logarithm averaging (GOWLA) operator based on an optimal deviation model. It is a new aggregation operator that generalizes the ordered weighted geometric averaging (OWGA) operator. This operator adds to the OWGA operator an additional parameter. controlling the power to which the arguments are raised. We further generalize the GOWLA operator and obtain the generalized ordered weighted hybrid logarithm averaging (GOWHLA) operator. We next introduce a nonlinear objective programming model for determining GOWHLA weights and an approach to group decision making based on the GOWHLA operator. Finally, we present a numerical example to illustrate the new approach in human resource management problem. © 2010 Wiley Periodicals, Inc.     

pSnakes: A new radial active contour model and its application in the segmentation of the left ventricle from echocardiographic images

Active contours are image segmentation methods that minimize the total energy of the contour to be segmented. Among the active contour methods, the radial methods have lower computational complexity and can be applied in real time. This work aims to present a new radial active contour technique, called pSnakes, using the 1D Hilbert transform as external energy. The pSnakes method is based on the fact that the beams in ultrasound equipment diverge from a single point of the probe, thus enabling the use of polar coordinates in the segmentation. The control points or nodes of the active contour are obtained in pairs and are called twin nodes. The internal energies as well as the external one, Hilbertian energy, are redefined. The results showed that pSnakes can be used in image segmentation of short-axis echocardiogram images and that they were effective in image segmentation of the left ventricle. The echo-cardiologist's golden standard showed that the pSnakes was the best method when compared with other methods. The main contributions of this work are the use of pSnakes and Hilbertian energy, as the external energy, in image segmentation. The Hilbertian energy is calculated by the 1D Hilbert transform. Compared with traditional methods, the pSnakes method is more suitable for ultrasound images because it is not affected by variations in image contrast, such as noise. The experimental results obtained by the left ventricle segmentation of echocardiographic images demonstrated the advantages of the proposed model. The results presented in this paper are justified due to an improved performance of the Hilbert energy in the presence of speckle noise.     

On two weighted signal averaging methods and their application to the surface detection of cardiac micropotentials

In this paper, the variance normalized averaging (VNA) and the optimal weighted averaging (OWA) are derived and their application to the surface detection of cardiac micropotentials is discussed. Theoretical analysis and computer simulation showed that VNA and OWA are superior to the conventional signal averaging (CSA) in reducing random noise with changing variance and the larger the change of noise variance the better the improvements of VNA and OWA relative to CSA. Clinical application of VNA and OWA using a proposed noise variance estimation technique indicated that residual noise on the PR and ST segments can be further reduced in most of the cases. This manifests that the new techniques have a potential advantage for improving the effectiveness of signal averaging as a fundamental method for surface detection of cardiac micropotentials.     

Measuring global prosperity using data envelopment analysis and OWA operator

Prosperity is one of the key economic indicators of a nation's success. The measure of a country's true prosperity is best achieved by considering a set of criteria and identifying the optimal weights associated with each criterion. This study introduces a novel method for measuring global prosperity by employing a combination of variables that characterize economic wealth and social wellbeing using data envelopment analysis (DEA) and ordered weighted averaging (OWA) operator. It extends the existing global prosperity assessment approach proposed by the Legatum Institute, an international organization that produces a global prosperity index every year. The current Legatum Prosperity Index is obtained by averaging a set of distinct variables, but it fails to identify the optimal variable weights for each country. This is a significant drawback that we address in this study. Using DEA, each country can freely assign optimal weights that are most favorable to achieving maximum prosperity. It provides a flexible and competitive environment in which all countries can present their strengths, thereby creating a level playing field. This study also uses multilevel DEA efficiency frontiers for classifying countries into different groups based on their levels of prosperity score. Additionally, we apply the OWA operator to distinguish further between the countries within each cluster.     

基于加权超图和IOWA算子的图像椒盐噪声滤除算法

针对图像椒盐噪声,提出基于加权超图和诱导有序加权平均(IOWA)算子的椒盐噪声滤除算法.首先,用加权超图对图像进行表示,根据椒盐噪声为极值的特点,定义超图边的权值,该权值能够反映边内中心节点对应像素为噪声点的可能性,进而利用超图边的权值进行噪声检测;其次,构建IOWA算子对噪声点进行复原,并采用噪声检测与复原交替进行的方式完成图像的椒盐噪声滤除.仿真实验结果表明,所提出的算法不但可有效复原椒盐噪声,而且能保持原图像的轮廓等细节信息.     

Elliptical distribution-based weight-determining method for ordered weighted averaging operators

The ordered weighted averaging (OWA) operators play a crucial role in aggregating multiple criteria evaluations into an overall assessment supporting the decision makers’ choice. One key point steps is to determine the associated weights. In this paper, we first briefly review some main methods for determining the weights by using distribution functions. Then we propose a new approach for determining OWA weights by using the regular increasing monotone quantifier. Motivated by the idea of normal distribution-based method to determine the OWA weights, we develop a method based on elliptical distributions for determining the OWA weights, and some of its desirable properties have been investigated.     

Automatic interpolation methods for mapping piezometric surfaces

The purpose of analysis of spatial data should determine the approach to be adopted. If estimation is concerned with detailed local interpretation rather than some form of global averaging, then kriging would seem to be an inappropriate method. This is especially so for the interpolation of precise observations which consequently are better estimated by deterministic methods. Five such efficient direct automatic interpolation methods are discussed and applied to the contour mapping of a piezometric surface.     

New approach to information fusion steady-state Kalman filtering

By the modern time series analysis method, based on the autoregressive moving average (ARMA) innovation model, a unified and general information fusion steady-state Kalman filtering approach is presented for the general multisensor systems with different local dynamic models and correlated noises. It can handle the filtering, smoothing, and prediction fusion problems for state or signal. The optimal fusion rule weighted by matrices is re-derived as a weighted least squares (WLS) fuser, and is reviewed. An optimal fusion rule weighted by diagonal matrices is presented, which is equivalent to the optimal fusion rule weighted by scalars for components, and it realizes a decoupled fusion. The new algorithms of the steady-state Kalman estimator gains are presented. In order to compute the optimal weights, the formulas of computing the cross-covariances among local estimation errors by Lyapunov equations are presented. The exponential convergence of the iterative solution of Lyapunov equation is proved. It is proved that the optimal fusion estimators under three weighted fusion rules are locally optimal, but are globally suboptimal. The proposed steady-state Kalman fusers can reduce the on-line computational burden, and are suitable for real-time applications. A simulation example for the 3-sensor steady-state Kalman tracking fusion estimators shows their effectiveness and correctness, and gives the accuracy comparison of the fusion rules.     

A fuzzy group decision making model with trapezoidal fuzzy preference relations based on compatibility measure and COWGA operator

This paper proposes a fuzzy group decision-making model based on a logarithm compatibility measure with multiplicative trapezoidal fuzzy preference relations (MTFPRs) based on a continuous ordered weighted geometric averaging (COWGA) operator. New concepts are presented to measure deviation between MTFPR and its expected fuzzy preference relation. Then, an iterative algorithm is developed to help individual MTFPR reach acceptable compatibility. To determine the weights of decision makers, an optimal model is constructed using group logarithm compatibility index COWGA operator. Finally, we illustrate an example to show how it works and compare it with the existing methods. The main advantages of the proposed approach are the following: (1) The COWGA operator makes decision making more flexible; (2) an iterative and convergent algorithm is proposed to improve the compatibility of MTFPR; (3) decision makers’ weights in group decision making are determined by an optimal model based on a logarithm compatibility measure.     

Least‐squared ordered weighted averaging operator weights

The ordered weighted averaging (OWA) operator by Yager (IEEE Trans Syst Man Cybern 1988; 18; 183–190) has received much more attention since its appearance. One key point in the OWA operator is to determine its associated weights. Among numerous methods that have appeared in the literature, we notice the maximum entropy OWA (MEOWA) weights that are determined by taking into account two appealing measures characterizing the OWA weights. Instead of maximizing the entropy in the formulation for determining the MEOWA weights, a new method in the paper tries to obtain the OWA weights that are evenly spread out around equal weights as much as possible while strictly satisfying the orness value provided in the program. This consideration leads to the least‐squared OWA (LSOWA) weighting method in which the program is to obtain the weights that minimize the sum of deviations from the equal weights since entropy is maximized when all the weights are equal. Above all, the LSOWA method allocates the positive and negative portions to the equal weights that are identical but opposite in sign from the middle point in the number of criteria. Furthermore, interval LSOWA weights can be constructed when a decision maker specifies his or her orness value in uncertain numerical bounds and we present a method, with those uncertain interval LSOWA weights, for prioritizing alternatives that are evaluated by multiple criteria. © 2008 Wiley Periodicals, Inc.     

Two new models for determining OWA operator weights

The determination of ordered weighted averaging (OWA) operator weights is a very crucial issue of applying the OWA operator for decision making. This paper proposes two new models for determining the OWA operator weights. The weights determined by the new models do not follow a regular distribution and therefore make more sense than those obtained by other methods.