Generating Z‐number based on OWA weights using maximum entropy

In the application of Z‐number, how to generate Z‐number is a significant and open issue. In this paper, we proposed a method of generating Z‐number based on the OWA weights using maximum entropy considering the attitude (preference) of the decision maker. Some numerical examples are used to illustrate the effectiveness of the proposed method. Results show that the attitude (preference) of the decision maker can give an optimal possibility distribution of the reliability for Z‐number using maximum entropy.     

Aggregating preference rankings using OWA operator weights

One important issue of aggregating preference rankings is to determine the weights of different ranking places. This paper proposes the use of ordered weighted averaging (OWA) operator weights to aggregate preference rankings, which allows the weights associated with different ranking places to be determined in terms of a decision maker (DM)’s optimism level characterized by an orness degree. By adjusting the DM’s optimism level, ties can be avoided and winner can be selected. Two numerical examples are examined using OWA operator weights to show their applications, simplicity and flexibility in aggregating preference rankings.     

On the extended set of weights of the OWA functions

ABSTRACT

The paper offers an extension and generalization of the definitions of the weighted arithmetic mean WAM, the ordered weighted averaging function OWA and the discrete Choquet integral using not only positive but also negative weights. Negative weights are important in various contexts, including statistics and robust aggregation, and they directly affect the monotonicity of the mentioned functions. The paper offers insights into the extended WAM, OWA and Choquet integral-based averaging functions with respect to their directional monotonicity, and establish the systems of linear inequalities which define the cone of monotonicity of these functions.     

Monotonic argument‐dependent OWA operators

The ordered weighted averaging (OWA) operator introduced by Yager is one of the most popular aggregation technique. In this paper, we develop two kinds of argument‐dependent OWA (DOWA) operators including the pessimistic‐dependent OWA (PE‐DOWA) operator and optimistic‐dependent OWA (OP‐DOWA) operator, that point out that the PE‐DOWA operator is decreasing and the OP‐DOWA operator is increasing, and investigate some properties of our proposed monotonic DOWA operators in detail. Furthermore, we introduce the concept of original function in which a gradient vector generates the weights of the PE‐DOWA and OP‐DOWA operators. Meanwhile, we propose two classes of original functions including summing‐type original function and multiplying‐type original function and investigate the sufficient monotonic conditions for the DOWA operators generated by the original functions. Finally, we discuss the characteristics and properties of our proposed DOWA operators in detail and use a numerical example to illustrate the flexibility of our proposed operators.     

结合OWA算子和模糊DEMATEL的风险评估方法

针对传统故障模式与影响分析(FMEA)方法在实际应用中的不足,提出一种基于有序加权平均(OWA)算子和决策试行与评价实验法(DEMATEL)的风险排序方法。FMEA专家对故障模式的3个风险因子给出模糊评价信息,应用OWA算子对评估信息进行集结,得到各故障原因对故障模式的影响强度。采用模糊DEMATEL法构建FMEA系统要素间的初始直接影响矩阵,经过运算可得综合影响矩阵,并计算各故障原因的原因度,据此进行产品或系统的失效风险评估。运用该方法对地铁车门系统的基础部件进行安全性分析,并将所得结果与传统RPN方法的结果做对比,验证了该方法的可行性和有效性。     

Dynamic weights allocation according to uncertain evaluation information

Weights allocation methods are critical in Multi-Criteria Decision Making. Given numerical importances for each involved criterion, direct normalizing those numerical importances to obtain weights for those criteria is plain, lack of flexibility, and thus cannot well model some more types of subjective preferences of different decision makers like Dominance Strength as defined in this study. We show that concave RIM quantifier Q based OWA weights allocation method can well handle and model such preference. However, in real decision making those numerical importances are very often embodied by uncertain information such as independent random variables with discrete or continuous distributions, statistic information and interval numbers. In any of those circumstances, simple RIM quantifier Q based OWA weights allocation cannot work. Therefore, in this study, we will propose some special dynamic weights allocation methods to gradually allocate weights and accumulate allocated parts to each criterion, and finally, obtain a total weights collection. When the uncertain numerical importances become equivalent to general real numbers, the method automatically degenerates into general RIM quantifier based OWA weights allocation. The innovative weight allocations have discrete and continuous versions: the former can be well programmed while the latter has neat and succinct mathematical expression. The method can also be widely used in many other applications like some economic problems including investment quota allocation for one’s favorite stocks, and the dynamic OWA aggregation for interval numbers.     

Reduction of artifacts in images from MR truncated data using singularity spectrum analysis

In this paper,the theory of signal singularity spectrum analysis (SSA) is proposed,Using SSA theory,a new method is presented to reduce truncation artifacts in magnetic resonance(MR) image due to truncated spectrum data.In the scheme,after detecting signal singulatrity locations using wavelet analysis in spectrum domain,SSA mathematic model is constructed,where weight coefficients are determined by known truncated spectrum data.Then,the remainder of the truncated spectrum can be obtained using SSA.Experiment and simulation results show that the SSA method will produce fewer artifacts in MR image from truncated spectrum than existing methods.     

Semiconductor yield models using contagious distributions and their limiting forms

In order to set up a semiconductor yield model, one should consider defect density variations not only among chips but also within a chip. In this paper, we propose semiconductor yield models based on the contagious distributions reflecting the variations. These models incorporate the probability that a defect becomes fatal. We also consider various limiting forms of a proposed contagious distribution by taking extreme values of the related parameters. A simplified form of the proposed yield formula based on the limiting distribution is derived and its performance is compared with others using computer simulation. The proposed three yield models are shown in a simulation study to outperform alternative models based on the existing ideas.     

Probabilistic wind speed forecasting using Bayesian model averaging with truncated normal components

Bayesian model averaging (BMA) is a statistical method for post-processing forecast ensembles of atmospheric variables, obtained from multiple runs of numerical weather prediction models, in order to create calibrated predictive probability density functions (PDFs). The BMA predictive PDF of the future weather quantity is the mixture of the individual PDFs corresponding to the ensemble members and the weights and model parameters are estimated using forecast ensembles and validating observations from a given training period. A BMA model for calibrating wind speed forecasts is introduced using truncated normal distributions as conditional PDFs and the method is applied to the ALADIN-HUNEPS ensemble of the Hungarian Meteorological Service and to the University of Washington Mesoscale Ensemble. Three parameter estimation methods are proposed and each of the corresponding models outperforms the traditional gamma BMA model both in calibration and in accuracy of predictions.     

Learning the stress function pattern of ordered weighted average aggregation using DBSCAN clustering

Ordered weighted average (OWA) operator provides a parameterized class of mean type operators between the minimum and the maximum. It is an important tool that can reflect the strategy of a decision maker for decision-making problems. In this study, the idea of obtaining the stress function from OWA weights has been put forward to generalize and characterize OWA weights. The main idea in this paper is mainly constructed on the basis that, generally, stress functions can be constructed using a mixture of constant and linear components. So, we can consider the stress function as a piecewise linear function. For obtaining stress functions as piecewise linear functions, we present a clustering-based approach for OWA weight generalization. This generalization is made using the DBSCAN algorithm as the learning method of a stress function associated with known OWA weights. In the learning process, the whole data set is divided into clusters, and then linear functions are obtained via a least squares estimator.     

互连线延迟的瑞利度量

从统计概率的角度出发,提出一种采用瑞利分布的延迟度量——互连线延迟的瑞利度量(RLD)．该算法仅需要采用前两个瞬态,计算简单,而且准确性较好,特别是对于远端节点的延迟与SPICE十分接近．     

Saddlepoint approximation based structural reliability analysis with non-normal random variables

The saddlepoint approximation (SA) can directly estimate the probability distribution of linear performance function in non-normal variables space. Based on the property of SA, three SA based methods are developed for the structural system reliability analysis. The first method is SA based reliability bounds theory (RBT), in which SA is employed to estimate failure probability and equivalent normal reliability index for each failure mode firstly, and then RBT is employed to obtain the upper and the lower bo...     

电力系统边际发电成本的概率分布函数估计方法

应用系统边际发电单元的概念，利用随机生产模拟方法，提出一种计算电力系统边际发电成本概率分布函数的有效方法，它不仅能考虑发电机组强迫停运和负荷预测的不确定性，且易于计入燃料价格的不确定性，该方法物理概念清晰，易于理解和实现，可用于电力市场的定价研究，用ＩＥＥＥ－ＲＴＳ的数据测试结果表明了该方法的合理性和有效性。     

随机分布控制系统的自适应迭代学习控制

介绍输出概率密度函数(PDF)常规的迭代学习控制(ILC)的收敛条件,并利用此条件设计相应的迭代学习律.主要讨论如何解决输出PDF迭代学习控制(ILC)中的过迭代,收敛速度等问题.以离散输出概率密度函教(PDF)控制模型为基础,介绍了直接迭代学习控制算法收敛的必要条件,提出自适应的迭代学习参数调节方法和避免过迭代的迭代结束条件,这些措施能够保证输出PDF的迭代控制收敛且具有较快的收敛速度.仿真结果表明,输出PDF的自适应迭代学习控制具有较快的收敛速度,而学习终止条件能很好地避免过迭代.     

On-Line Shape recognition with incremental training using binary synaptic weights algorithm

Recognition of hand drawn shapes is beneficial in drawing packages and automated sketch entry in handheld computers. In this paper, we propose a new approach to on-line geometric shape recognition with incremental training function, which utilizes a heuristic function to reduce noise and a neural network for classification and on-line training. Instead of recognizing segments of a drawing and then performing syntactical analysis to match with a predefined shape, which is weak in terms of generalization and dealing with noise, we examine the shape as a whole. The main concept of the recognition method is derived from the fact that internal angles are very important in the perceived shape of outlines. Our application's aim is to recognize elliptic, rectangular, and triangular shapes in a way similar to human cognition of these shapes. Human beings recognize such basic shapes regardless of the variations in size, noise on the shape border, rotation and in the case of triangles, regardless of the type of the triangle. The key concept is that the neural network learns the relationships between the internal angles of a shape and its classification, therefore only a few training samples which represent the class of the shape are sufficient. Fast meremental training, which is performed on-line, is accomplished by the use of the Binary Synaptic Weights algorithm, a one pass, feedforward neural network training algorithm. Incremental training offers the advantage of adjusting the recognition capability of the system to the user's drawings. the results are very successful, such that the neural network correctly classified shapes that did not have any resemblance to the shapes in the initial training set.     

Probability Density Estimation Using Adaptive Activation Function Neurons

In this paper we deal with the problem of approximating the probability density function of a signal by means of adaptive activation function neurons. We compare the proposed approach to the one based on a mixture of kernels and show through computer simulations that comparable results may be obtained with limited expense in computational efforts.     

Shaping probability density functions using a switching linear controller

Linear controllers for dynamic systems have been used in a stochastic context to decrease the variance of certain key variables. An extension is to use nonlinear controllers for shaping the entire probability density function (PDF). Typically, polynomial controllers are preferred due to their flexibility and also because their continuity makes them mathematically attractive. However, due to restrictions on stability, these controllers tend to be quasi-linear around the desired operating point. So, in this paper, a switching linear controller is presented as an alternative for PDF shaping. It is shown that, despite the discontinuity, an analytical solution of the PDF can be obtained using the Fokker-Planck-Kolmogorov equation. Also, for a simple case, even the Gram-Charlier coefficients can be computed analytically. Thus, it is demonstrated that the PDF shaping problem with a switching controller does not cause any further complications than using polynomial controllers. It is then shown in simulation that switching controllers are more robust and could create more skewness due to their discontinuity.     

随机分布系统状态记忆保性能控制的研究

对于连续随机分布控制中的保守性问题,采用平方根B样条逼近建立系统静态模型（输出概率密度函数模型）,利用系统输入和输出概率密度函数权值之间的动态关系建立动态模型,提出状态记忆反馈保性能控制算法,并利用凸优化技术优化算法,通过计算机仿真验证,该算法能够实现系统输出概率密度函数追踪目标概率密度函数,并满足规定的性能指标。     

Detecting abnormal situations using the Kullback–Leibler divergence

This article develops statistics based on the Kullback–Leibler (KL) divergence to monitor large-scale technical systems. These statistics detect anomalous system behavior by comparing estimated density functions for the current process behavior with reference density functions. For Gaussian distributed process variables, the paper proves that the difference in density functions, measured by the KL divergence, is a more sensitive measure than existing work involving multivariate statistics. To cater for a wide range of potential application areas, the paper develops monitoring concepts for linear static systems, that can produce Gaussian as well as non-Gaussian distributed process variables. Using recorded data from a glass melter, the article demonstrates the increased sensitivity of the KL-based statistics by comparing them to competitive ones.     

Technological information extraction of free form surfaces using neural networks

The aim of this paper is to show how to predict the accurate machining technology for the particular free form NURBS or B-spline surface. Since that kind of a surface is very hard to describe in an analytical manner, the topological and geometrical information about the surface was acquired with the help of self-organized neural networks (NNs) and first- or second-order statistic parameters. It is proved that the most significant parameter in this process is the curvature, especially when rapid changes of curvature on a free form surface occurred. As the Gaussian distribution of surface curvatures and slope gradient data were presumed, the mean and variance was used for one-dimensional data presentation, and the Hebbian output data vector was used to assess probability, density function and distribution of the presented data. For collecting the maximum amount of surface information, the principal component analysis method inside the Hebbian NN was used.