二进神经网络学习算法研究

把二进神经网络对布尔函数映射的学习归结为神经元对学习样本集合的表达。通过对神经元表达能力的分析研究,引入加权距离汉明球的概念,既提高了学习效率也简化了布尔函数实现结构。同时把汉明球及立方体集合覆盖思想等统一在加权汉明距离球覆盖的框架下,另外,还得到旨在提高输出层神经元表达能力的新结果,最后举例说明了此学习策略的可行性与特点,经学习得到的二进神经网络的权系数及阈值皆为整数,易于硬件实现。     

基于云综合方法的三支群决策模型

在三支决策问题中，领域专家群决策是一种确定损失函数的最直接方法。相较于体现单一不确定性的语言变量模型和模糊集模型，云模型描述的专家评价更能够反映认知过程中复杂的不确定性形式，并能通过云综合的方法获得综合评价函数。但当前的云综合方法仅对数字特征进行简单的线性组合，缺乏对概念语义差异上的描述，难以获得令人信服的结果。因此首先证明了在云模型的距离空间中赋权距离和是一个凸函数，并将综合云模型定义为此函数的最小值点。然后，将该定义推广到多个云模型的场景下，提出了一种新的云综合方法——基于密度中心的云综合方法。群决策过程中，该方法在保证综合评价与基础评价之间的相似度最高的同时获得最精确的综合评价，为损失函数的确定提供了一种新的语义解释。实验结果表明，在与简单线性组合和合理粒度方法对比中，该方法所确定的损失函数使得三支决策中的误分类率最低。     

A method for fuzzy group decision making based on induced aggregation operators and Euclidean distance

In this paper, we present the fuzzy‐induced Euclidean ordered weighted averaging distance (FIEOWAD) operator. It is an extension of the ordered weighted averaging (OWA) operator that uses the main characteristics of the induced OWA (IOWA), the Euclidean distance and uncertain information represented by fuzzy numbers. The main advantage of this operator is that it is able to consider complex attitudinal characters of the decision maker by using order‐inducing variables in the aggregation of the Euclidean distance. Moreover, it is able to deal with uncertain environments where the information is very imprecise and can be assessed with fuzzy numbers. We study some of its main properties and particular cases such as the fuzzy maximum distance, fuzzy minimum distance, fuzzy‐normalized Euclidean distance (FNED), fuzzy‐weighted Euclidean distance (FWED), and fuzzy Euclidean ordered weighted averaging distance (FEOWAD) operator. Finally, we present an application of the operator to a group decision‐making problem concerning the selection of strategies.     

加权犹豫三角模糊距离度量及其在群决策中的应用

对于犹豫三角模糊元中不同的元素作为隶属度的重要性不同,提出加权犹豫三角模糊元和加权犹豫三角模糊集的概念,研究了决策值为加权犹豫三角模糊元的群决策问题。首先,给出了加权犹豫三角模糊距离公式;其次,基于计算方便且不改变三角模糊数作为隶属度的重要性,提出一种对加权犹豫三角模糊元添加元素的方法;最后,提出加权犹豫三角模糊距离度量的群决策方法,并应用于加权犹豫三角模糊环境下的群决策。数值实例表明,加权犹豫三角模糊距离度量在群决策中具有合理性和可行性。     

基于单值中智集的投资决策方案优选模型

为了优化投资决策方案优选模型,提出一个基于单值中智环境下的多属性决策问题的新方法。首先给出一个基于单值中智集的广义距离公式,然后通过语言变量确定了决策专家和属性指标的权重,接着构建了加权的综合决策矩阵,进一步得到各备选方案与正负理想方案的距离,利用相对贴近度系数对各备选方案就进行综合排序,得到最优决策方案。最后通过一个投资决策的实例,验证了该模型的有效性和实用性。     

Pythagorean模糊对称交叉熵及加权投影的多属性决策

在Pythagorean模糊多属性决策问题中,以欧式距离等距离测度为基础计算各备选方案与正、负理想解的距离,可能产生与正理想解距离更近的待选方案却与负理想解的距离也更近,导致所得方案排序结果并不能真实反映各备选方案的优劣程度.为有效克服决策结果的逆序问题,提出满足对称性、有界性的Pythagorean模糊对称交叉熵,进...     

用区间直觉模糊集方法对属性权重未知的群求解其多属性决策

本文首先提出群区间直觉模糊有序加权几何(groupinterval-valuedintuitionistic fuzzy orderedweighted geometric,GIVIFOWG)算子和群区间直觉模糊有序加权平均(group interval-valued intuitionistic fuzzy ordered weighted averaging,GIVIFOWA)算子.利用GIVIFOWG算子或GIVIFOWA算子聚集群的决策矩阵以获得方案在属性上的综合区间直觉模糊决策矩阵(collectiveinterval-valuedintuitionistic fuzzy decision-matrix,CIVIFDM).然后定义了一个考虑犹豫度的区间直觉模糊熵(interval-valuedintuitionistic fuzzyentropy,IVIFE);通过熵衡量每个属性所含的信息来求解属性权重.最后,提出基于可能度的接近理想解的区间排序法(interval technique for order preference by similarity to an ideal solution,ITOPSIS)和区间得分函数法.在ITOPSIS法中,依据区间距离公式计算候选方案和理想方案的属性加权区间距离,进而采用ITOPSIS准则对各方案进行排序;在区间得分函数法中,算出CIVIFDM中各方案的得分值以及精确值,然后利用区间得分准则对各方案进行排序.实验结果验证了决策方法的有效性和可行性.     

Linguistic continuous ordered weighted distance measure and its application to multiple attributes group decision making

This paper develops a new method for group decision making and introduces a linguistic continuous ordered weighted distance (LCOWD) measure. It is a new distance measure that combines the linguistic continuous ordered weighted averaging (LCOWA) operator with the ordered weighted distance (OWD) measure considering the risk attitude of decision maker. Moreover, it also can relieve the influence of extremely large or extremely small deviations on the aggregation results by assigning them smaller weights. These advantages make it suitable to deal with the situations where the input arguments are represented with uncertain linguistic information. Some of the main properties of the LCOWD measure and different particular cases are studied. The applicability of the new approach is also analyzed focusing on a group decision making problem.     

基于多核Fisher判别分析的人脸特征提取

核Fisher判别分析法是一种有效的非线性判别分析法。传统的核Fisher判别分析仅选用单个核函数,在人脸特征提取方面仍显不足。鉴于此,提出多核Fisher判别分析法,即通过将多个单核Fisher判别得到的投影进行加权组合得到加权投影,以加权投影为依据进行特征提取和分类。实验表明,在进行人脸特征提取和分类时,多核Fisher判别分析法优于单核Fisher判别分析法。     

Adam revisited: a weighted past gradients perspective

Adaptive learning rate methods have been successfully applied in many fields, especially in training deep neural networks. Recent results have shown that adaptive methods with exponential increasing weights on squared past gradients (i.e., ADAM, RMSPROP) may fail to converge to the optimal solution. Though many algorithms, such as AMSGRAD and ADAMNC, have been proposed to fix the non-convergence issues, achieving a data-dependent regret bound similar to or better than ADAGRAD is still a challenge to these methods. In this paper, we propose a novel adaptive method weighted adaptive algorithm (WADA) to tackle the non-convergence issues. Unlike AMSGRAD and ADAMNC, we consider using a milder growing weighting strategy on squared past gradient, in which weights grow linearly. Based on this idea, we propose weighted adaptive gradient method framework (WAGMF) and implement WADA algorithm on this framework. Moreover, we prove that WADA can achieve a weighted data-dependent regret bound, which could be better than the original regret bound of ADAGRAD when the gradients decrease rapidly. This bound may partially explain the good performance of ADAM in practice. Finally, extensive experiments demonstrate the effectiveness of WADA and its variants in comparison with several variants of ADAM on training convex problems and deep neural networks.     

Fuzzy linguistic induced OWA Minkowski distance operator and its application in group decision making

The Minkowski distance is a distance measure that generalizes a wide range of other distances such as the Euclidean and the Hamming distance. In this paper, we develop a new decision making model using induced ordered weighted averaging operators and the Minkowski distance of the fuzzy linguistic variables. Then, the authors introduce a new aggregation operator called the fuzzy linguistic induced ordered weighted averaging Minkowski distance (FLIOWAMD) operator by defining a fuzzy linguistic variable distance. It is an induced generalized aggregation operator that utilizes induced OWA operator, Minkowski distance measures and uncertain information represented as fuzzy linguistic variables. Some of its main properties and particular cases are studied. And a further generalization that uses quasi-arithmetic means also is presented. A method based on the FLIOWAMD operator for decision making is presented. At last, we end the paper with a numerical example of the new method.     

Locally Weighted Learning

This paper surveys locally weighted learning, a form of lazy learning and memory-based learning, and focuses on locally weighted linear regression. The survey discusses distance functions, smoothing parameters, weighting functions, local model structures, regularization of the estimates and bias, assessing predictions, handling noisy data and outliers, improving the quality of predictions by tuning fit parameters, interference between old and new data, implementing locally weighted learning efficiently, and applications of locally weighted learning. A companion paper surveys how locally weighted learning can be used in robot learning and control.     

A Method for Decision Making Based on Generalized Aggregation Operators

A new method for decision making based on generalized aggregation operators is presented. We use a concept that it is known in the literature as the index of maximum and minimum level (IMAM). This index uses distance measures and other techniques that are very useful for decision making. In this paper, it is suggested a generalization by using generalized and quasi‐arithmetic means. As a result, it is obtained the generalized and quasi‐arithmetic weighted IMAM (GWIMAM and quasi‐WIMAM) and the generalized ordered weighted averaging IMAM (GOWAIMAM) and the quasi‐OWAIMAM operator. The main advantage is that it provides a parameterized family of aggregation operators that includes a wide range of special cases such as the generalized IMAM and the OWAIMAM. Thus, the decision maker may take decisions according to his degree of optimism and considering ideals in the decision process. We also develop an application of the new approach in a decision‐making problem regarding product selection.     

A new multiple criteria decision making method based on intuitionistic fuzzy information

The risk attitude of a decision maker is considered in the decision process. Inspired by mean-variance type utility functions in the financial risk management, a new class of decision functions are defined based on the weighted score function and the weighted accuracy function in the intuitionistic fuzzy setting. By choosing a suitable parameter value, the decision maker’s risk attitude can be flexibly reflected by our decision function. The new method can be applied for both the exactly known and partly known criteria weight situations. For the latter case, it is only necessary to solve one linear programming problem. The developed models and algorithms are then extended to multiple criteria decision making problems with the interval-valued intuitionistic fuzzy information. Numerical examples are provided to illustrate the practicality, flexibility and efficiency of our new algorithms.     

A neuron model with trainable activation function (TAF) and its MFNN supervised learning

This paper addresses a new kind of neuron model, which has trainable activation function (TAF) in addition to only trainable weights in the conventional M-P model. The final neuron activation function can be derived from a primitive neuron activation function by training. The BP like learning al-gorithm has been presented for MFNN constructed by neurons of TAP model. Several simulation ex-amples are given to show the network capacity and performance advantages of the new MFNN in com-parison with that of conventional sigmoid MFNN.     

A class of discrete time recurrent neural networks with multivalued neurons

This paper discusses a class of discrete time recurrent neural networks with multivalued neurons (MVN), which have complex-valued weights and an activation function defined as a function of the argument of a weighted sum. Complementing state-of-the-art of such networks, our research focuses on the convergence analysis of the networks in synchronous update mode. Two related theorems are presented and simulation results are used to illustrate the theory.     

Generalized Radial Basis Function Networks Trained with Instance Based Learning for Data Mining of Symbolic Data

The application of the Radial Basis Function neural networks in domains involving prediction and classification of symbolic data requires a reconsideration and a careful definition of the concept of distance between patterns. This distance in addition to providing information about the proximity of patterns should also obey some mathematical criteria in order to be applicable. Traditional distances are inadequate to access the differences between symbolic patterns. This work proposes the utilization of a statistically extracted distance measure for Generalized Radial Basis Function (GRBF) networks. The main properties of these networks are retained in the new metric space. Especially, their regularization potential can be realized with this type of distance. However, the examples of the training set for applications involving symbolic patterns are not all of the same importance and reliability. Therefore, the construction of effective decision boundaries should consider the numerous exceptions to the general motifs of classification that are frequently encountered in data mining applications. The paper supports that heuristic Instance Based Learning (IBL) training approaches can uncover information within the uneven structure of the training set. This information is exploited for the estimation of an adequate subset of the training patterns serving as RBF centers and for the estimation of effective parameter settings for those centers. The IBL learning steps are applicable to both the traditional and the statistical distance metric spaces and improve significantly the performance in both cases. The obtained results with this two-level learning method are significantly better than the traditional nearest neighbour schemes in many data mining problems.     

An Accurate Method for Determining Hesitant Fuzzy Aggregation Operator Weights and Its Application to Project Investment

As a generalization of fuzzy sets, hesitant fuzzy set is a very useful technique to represent decision makers’ hesitancy in decision making. Various hesitant fuzzy weighted operators have been developed to aggregate hesitant fuzzy information, but it seems that there is no investigation on the weighted approach of obtaining their weights, which is decisive for the calculation and comparison of hesitant fuzzy elements (HFEs) in multicriteria group decision making. In this paper, we propose an accurate weighted method (AWM) of monotonicity and proportionality, based on nothing but the score function and the new deviation function. Because of the above properties, AWM may be an accurate and objective technique to calculate the weights of HFEs and aggregation operator. Then, based on this weighted approach, we develop two new hesitant fuzzy ordered weighted aggregation operators, that is, hesitant fuzzy ordered accurate weighted averaging and hesitant fuzzy ordered accurate weighted geometric operators, and study their relationships and properties. In the end, an illustrative project investment problem is used to demonstrate how to apply the proposed weighted approach and to observe the computational consequences resulting from new aggregation operators. This work contributes significantly to improve the hesitant fuzzy theory, and proposes two new hesitant fuzzy aggregation operators.     

基于呼叫详细记录数据的城市功能区识别

不同城市功能区区域之间具有外在物理差异和内在功能差异,且随时间和人类活动不断发生演变。针对卫星遥感等传统监测方法存在运行周期长、成本高,不能表征内在功能差异等问题,利用通信运营商提供的用户生活数据——呼叫详细记录（CDR）,进行城市功能区识别研究。首先,以人工标注的方法对基站小区进行功能区分类,得到住宅区、办公区、商业区、高校区、景点区五类训练样本;然后,提取各功能区内用户群体的通话行为和移动行为特征,进行差异性对比分析;最后,利用高斯混合模型（GMM）设计出多特征加权判决的功能区识别算法,并用训练集对该算法进行仿真。实验结果表明,CDR数据可以对城市功能区之间的内在差异进行表征,功能区性质与用户的通话行为和移动行为存在对应关系;判决权重为0.6时,该算法在现有数据集下的功能区召回率达到了最大,为51.08%。结合误差分析表明CDR数据在城市功能区识别应用上具有可行性。     

基于三角Pythagorean模糊集的多准则决策方法

Pythagorean模糊集在直觉模糊集的基础上扩大了适用范围,三角模糊数在决策过程中可以保留决策者较多的不确定信息.鉴于此,首先提出三角Pythagorean模糊集的定义及其欧氏距离表示;然后定义三角Pythagorean模糊加权平均(TPFWA)算子、广义三角Pythagorean模糊加权平均(GTPFWA)算子、三角Pythagorean模糊加权几何(TPFWG)算子和广义三角Pythagorean模糊加权几何(GTPFWG)算子,并对算子所满足的幂等性、有界性和单调性予以证明;最后通过一个医药代表选择的多准则决策问题和灵敏度分析验证所提出算子的合理性和有效性.