针对大样本集的融合模糊系统

为了解决处理大样本和超大样本数据集消耗大量时间和准确性问题,本文将中心约束型最小包含球(CCMEB)理论融合对TSK模糊系统(Takagi-Sugeno-Kang Fuzzy System)重新审视和改进而成的双层TSK模糊系统CTSK（Centralized TSK Fuzzy System）模糊系统。两种系统取长补短结合成新的适合处理大样本数据的算法系统。仿真实验研究分析了不同的模糊规则对新算法的影响以及所提出的算法与另外三种国际上较为先进的处理大数据算法的性能比较。结果表明所提出的算法对处理大样本数据的有效性和快速性。     

中心化模糊系统CTSK的分析及应用

从一个新角度重新探讨TSK模糊系统建模问题,引入并分析推导一种新的TSK模糊系统——CTSK。与传统TSK模糊系统相比,CTSK模糊系统具有良好的可解释性、更好的鲁棒性和较强的逼近能力。仿真实验结果有效地验证了上述优点,在用CTSK模糊系统进行地下水质的评价时取得了较好的效果。     

贝叶斯L2型TSK模糊系统

针对传统Takagi-Sugeno-Kan(TSK)模糊系统处理大规模数据时间代价较高的问题,提出一种基于概率模型框架的L2型TSK模糊系统建模策略,建立具有处理大规模数据能力的贝叶斯L2型TSK模糊系统(B-TSK-FS).具体地,基于L2型TSK模糊系统的输出误差概率化表示,对系统前后件参数联合学习,提高系统的泛化能力.另外,引入狄利克雷先验分布函数,对模糊隶属度稀疏化表示,实现样本的压缩,降低运算时间.在模拟和真实数据集上的实验结果验证了所提出模糊系统的优势.     

基于模糊划分和支持向量机的TSK模糊系统

为了提高模糊系统处理高维问题的推广能力与鲁棒性能,提出将模糊聚类和支持向量机算法结合起来构造TSK模糊系统的算法.首先运用模糊聚类算法对输入空间进行划分,确定模糊规则前件的隶属函数.然后用支持向量机算法确定模糊规则的后件参数.该支持向量机的核函数是由模糊规则前件的隶属函数构造的,并且是Mercer核.在3个数据集的实验结果表明,与TSK模糊系统的传统算法和支持向量机相比较,本文算法具有更好的推广能力和鲁棒性.     

并行集成具有高可解释的TSK模糊分类器

针对分层Takagi-Sugeno-Kang(TSK)模糊分类器可解释性差,以及当增加或删除一个TSK模糊子分类器时Boosting模糊分类器需要重新训练所有TSK模糊子分类器等问题,提出一种并行集成具有高可解释的TSK模糊分类器EP-Q-TSK.该集成模糊分类器每个TSK模糊子分类器可以使用最小学习机(LLM)被并行地快速构建.作为一种新的集成学习方式,该分类器利用每个TSK模糊子分类器的增量输出来扩展原始验证数据空间,然后采用经典的模糊聚类算法FCM获取一系列代表性中心点,最后利用KNN对测试数据进行分类.在标准UCI数据集上,分别从分类性能和可解释性两方面验证了EP-Q-TSK的有效性.     

基于一型模糊规则自主构建二型TSK神经模糊系统方法设计

本文提出了一种使用一型模糊规则生成区间二型TSK(Takagi-Sugeno-Kang)神经模糊系统的新方法.该方法以训练数据集与使用自组织方法由该训练集训练生成的一型模糊系统为驱动,通过新型模糊系统前件类型转换算法与规则参数自适应学习算法的训练,在不高于原一型系统模糊集合总数前提下,自主构建区间二型TSK神经模糊系统.此外,针对两种典型的多输入单输出和多输入多输出系统,在3种不同强度的系统扰动场景下进行了对比仿真实验.实验结果表明,在含有不同扰动状态系统的建模与辨识中本方法较于对比方法具有更加优异的性能.     

基于最小包含球的异质空间大数据集快速相似度学习算法

针对跨空间数据相似度学习问题提出的跨空间相似度学习(CSAL) 算法表现出了良好的性能, 并已成功地应用于各类推荐系统中. 但构建一个完善的推荐系统, 其待处理的数据量常呈现大样本特征, 而CSAL 算法并不具备大样本快速处理能力. 针对此不足, 提出了跨空间相似度学习-最小包含球(CSAL-MEB) 方法和跨空间相似度学习-核向量机(CSAL-CVM) 快速方法. CSAL-CVM 方法既具有渐近线性时间复杂度和空间复杂度的优点, 同时又继承了CSAL 的良好性能. 相关实验亦验证了所提出方法的有效性.

     

基于一型规则自主构建二型TSK神经模糊系统方法设计

本文提出了一种使用一型模糊规则生成区间二型TSK(Takagi-Sugeno-Kang)神经模糊系统的新方法. 该方 法以训练数据集与使用自组织方法由该训练集训练生成的一型模糊系统为驱动,通过新型模糊系统前件类型转换 算法与规则参数自适应学习算法的训练,在不高于原一型系统模糊集合总数前提下,自主构建区间二型TSK神经模 糊系统.此外, 针对两种典型的多输入单输出和多输入多输出系统, 在3种不同强度的系统扰动场景下进行了对比仿 真实验. 实验结果表明, 在含有不同扰动状态系统的建模与辨识中本方法较于对比方法具有更加优异的性能.     

构建适用于深度学习的海浪样本数据集的并行算法实现及性能优化

采用深度学习算法来实现海浪等级的划分,数据来源于洋山港视频监测及同步海浪测量。针对近岸海浪识别系统中,构建海浪样本数据集中图像处理部分计算量超大的问题,设计一种海浪样本数据集图像处理的并行化运算方案。构建海浪样本数据集时,主要将视频进行关键帧提取,经过加权均值滤波去噪,生成与海浪等级对应标签,实现了海浪样本数据集的构建。在多核计算机上采用Open MP对海浪样本数据集图像处理过程进行并行算法仿真,同时完善相关代码的性能优化。实验结果表明,设计的并行算法比串行算法大大地提高运算速度和多核利用率,当优化后线程K=8时,加速比可以达到24.29。该算法具有扩展性好、性能高、使用简单方便、价格低廉的优点,具有良好的实用价值。     

融合稀疏自表示和残差驱动的自适应模糊C均值聚类

提出一种融合稀疏自表示和残差驱动的自适应模糊C均值聚类算法(R²AFCM).该算法的优点主要体现在以下两个方面:1)利用稀疏自表示技术求解样本数据的字典矩阵,并将其表征的全局信息考虑到目标函数中,充分考虑数据分布特点,改进传统模糊C均值聚类算法重点关注局部信息的不足; 2)在目标函数中引入加权残差估计正则化项,与自适应模糊聚类算法的正则化项相结合,约束模型训练,有效降低混合噪声对分割结果的影响.在磁共振成像、VOC 2012数据集以及自然图像上进行对比实验,结果表明,所提出的聚类算法在添加了20%椒盐噪声和均值为0.4、方差为0.01的高斯噪声,以及50%椒盐噪声和均值为0、方差为0.1的混合噪声下与其他算法相比,具有更高的分割精度和更强的鲁棒性.     

Robust TSK fuzzy modeling for function approximation with outliers

The Takagi-Sugeno-Kang (TSK) type of fuzzy models has attracted a great attention of the fuzzy modeling community due to their good performance in various applications. Most approaches for modeling TSK fuzzy rules define their fuzzy subspaces based on the idea of training data being close enough instead of having similar functions. Besides, training data sets algorithms often contain outliers, which seriously affect least-square error minimization clustering and learning algorithms. A robust TSK fuzzy modeling approach is presented. In the approach, a clustering algorithm termed as robust fuzzy regression agglomeration (RFRA) is proposed to define fuzzy subspaces in a fuzzy regression manner with robust capability against outliers. To obtain a more precision model, a robust fine-tuning algorithm is then employed. Various examples are used to verify the effectiveness of the proposed approach. From the simulation results, the proposed robust TSK fuzzy modeling indeed showed superior performance over other approaches     

一种线性化模糊内模自适应控制算法

针对非线性对象，提出一种线性化模糊内模自适应控制算法。该算法以一组模糊规则作为非线性对象内部模型，一条模糊规则表示一个局部线性系统；根据对象输入与输出测量值，利用TSK建模方法在线辨识局部模糊内部模型；同时依据辨识模型设计局部H2最优模糊控制规则，所有规则构成H2最优模糊控制器。仿真实验显示：该算法适用于非线性对象的控制，具有较好的鲁棒性和抗干扰能力。     

Transformation between type-2 TSK fuzzy systems and an uncertain Gaussian mixture model

In this paper, an interval extension of the Gaussian mixture model called uncertain Gaussian mixture model (UGMM) is proposed and its transformation into the additive type-2 TSK fuzzy systems is presented. The conditions under which a UGMM becomes a corresponding type-2 TSK fuzzy system are derived theoretically. Furthermore, the mathematical equivalence between the conditional mean of a UGMM and the defuzzified output of a type-2 TSK fuzzy system is proved. Our results provide a new perspective for type-2 TSK fuzzy systems, i.e., interpreting them from a probabilistic viewpoint. Thus, instead of directly estimating the parameters of the fuzzy rules in a type-2 TSK fuzzy system, we can first estimate the parameters of the corresponding UGMM using any popular density estimation algorithm like the expectation maximization (EM) algorithm. Our experimental results clearly indicate that a type-2 fuzzy system trained in such a new way has higher approximation accuracy and stronger robustness than current type-2 fuzzy systems.     

适合大规模数据集且基于LLM的0阶TSK模糊分类器

针对传统分类器的泛化性能差、可解释性及学习效率低等问题, 提出0阶TSK-FC模糊分类器.为了将该分类器 应用到大规模数据的分类中, 提出增量式0阶TSK-IFC模糊分类器, 采用增量式模糊聚类算 法(IFCM($c+p$))训练模糊规则参数并通过适当的矩阵变换提升参数学习效率.仿真实验表明, 与FCPM-IRLS模糊分类器、径向基函数神经网 络相比, 所提出的模糊分类器在不同规模数据集中均能保持很好的性能, 且TSK-IFC模糊分类器在大规模数据分类中尤为突出.     

Takagi-Sugeno-Kang fuzzy system fusion: A survey at hierarchical,wide and stacked levels

With excellent global approximation performance and interpretability, Takagi-Sugeno-Kang (TSK) fuzzy systems have enjoyed a wide range of applications in various fields, such as smart control, medical, and finance. However, in handling high-dimensional complex data, the performance and interpretability of a single TSK fuzzy system are easily degraded by rule explosion due to the curse of dimensionality. Ensemble learning comes into play to deal with the problem by the fusion of multiple TSK fuzzy systems using appropriate ensemble learning strategies, which has shown to be effective in eliminating the issue of the curse of dimensionality curse problem and reducing the number of fuzzy rules, thereby maintaining the interpretability of fuzzy systems. To this end, this paper gives a comprehensive survey of TSK fuzzy system fusion to provide insights into further research development. First, we briefly review the fundamental concepts related to TSK fuzzy systems, including fuzzy rule structures, training methods, and interpretability, and discuss the three different development directions of TSK fuzzy systems. Next, along the direction of TSK fuzzy system fusion, we investigate in detail the current ensemble strategies for fusion at hierarchical, wide and stacked levels, and discuss their differences, merits and weaknesses from the aspects of time complexity, interpretability (model complexity) and classification performance. We then present some applications of TSK fuzzy systems in real-world scenarios. Finally, the challenges and future directions of TSK fuzzy system fusion are discussed to foster prospective research.     

Improving the interpretability of TSK fuzzy models by combiningglobal learning and local learning

The fuzzy inference system proposed by Takagi, Sugeno, and Kang, known as the TSK model in fuzzy system literature, provides a powerful tool for modeling complex nonlinear systems. Unlike conventional modeling where a single model is used to describe the global behavior of a system, TSK modeling is essentially a multimodel approach in which simple submodels (typically linear models) are combined to describe the global behavior of the system. Most existing learning algorithms for identifying the TSK model are based on minimizing the square of the residual between the overall outputs of the real system and the identified model. Although these algorithms can generate a TSK model with good global performance (i.e., the model is capable of approximating the given system with arbitrary accuracy, provided that sufficient rules are used and sufficient training data are available), they cannot guarantee the resulting model to have a good local performance. Often, the submodels in the TSK model may exhibit an erratic local behavior, which is difficult to interpret. Since one of the important motivations of using the TSK model (also other fuzzy models) is to gain insights into the model, it is important to investigate the interpretability issue of the TSK model. We propose a new learning algorithm that integrates global learning and local learning in a single algorithmic framework. This algorithm uses the idea of local weighed regression and local approximation in nonparametric statistics, but remains the component of global fitting in the existing learning algorithms. The algorithm is capable of adjusting its parameters based on the user's preference, generating models with good tradeoff in terms of global fitting and local interpretation. We illustrate the performance of the proposed algorithm using a motorcycle crash modeling example     

A Highly Accurate Model-Free Motion Control System with a Mamdani Fuzzy Feedback Controller combined with a TSK Fuzzy Feed-forward Controller

In this paper, a new intelligent robot motion control architecture – a highly accurate model-free fuzzy motion control- is proposed in order to achieve improved robot motion accuracy and dynamic performance. Its architecture combines a Mamdani fuzzy proportional (P) and a conventional integral (I) plus derivative (D) controller for the feedback part of the system, and a Takagi-Sugeno-Kang fuzzy controller for the feed-forward, nonlinear part. The fuzzy P + ID controller improves the performance of the nonlinear system, and the TSK fuzzy controller uses a TSK fuzzy inference system based on extended subtractive- clustering method which integrates information on joint angular displacement, velocity and acceleration for torque identification. The advantage of this kind of model-free control is that it uses the information directly from the input/output of the nonlinear system, without any complex robot model computation, in order to decrease the control system’s sensitivity to any dynamical uncertainty. Furthermore, parametric search for clustering parameters in extended subtractive clustering secures the high accuracy of the system identification. Consequently, this proposed model-free fuzzy motion control benefits from the advantages of two kinds of fuzzy system. It not only incorporates flexible design, good performance and simple conception but also ensures precise motion control and great robustness. Comparisons with other intelligent models and results from numerical studies on a 4-bar planar parallel mechanism show the effectiveness and competitiveness of the proposed control.     

Nature-inspired optimal tuning of input membership functions of Takagi-Sugeno-Kang fuzzy models for Anti-lock Braking Systems

This paper suggests a synergy of fuzzy logic and nature-inspired optimization in terms of the nature-inspired optimal tuning of the input membership functions of a class of Takagi-Sugeno-Kang (TSK) fuzzy models dedicated to Anti-lock Braking Systems (ABSs). A set of TSK fuzzy models is proposed by a novel fuzzy modeling approach for ABSs. The fuzzy modeling approach starts with the derivation of a set of local state-space models of the nonlinear ABS process by the linearization of the first-principle process model at ten operating points. The TSK fuzzy model structure and the initial TSK fuzzy models are obtained by the modal equivalence principle in terms of placing the local state-space models in the rule consequents of the TSK fuzzy models. An operating point selection algorithm to guide modeling is proposed, formulated on the basis of ranking the operating points according to their importance factors, and inserted in the third step of the fuzzy modeling approach. The optimization problems are defined such that to minimize the objective functions expressed as the average of squared modeling errors over the time horizon, and the variables of these functions are a part of the parameters of the input membership functions. Two representative nature-inspired algorithms, namely a Simulated Annealing (SA) algorithm and a Particle Swarm Optimization (PSO) algorithm, are implemented to solve the optimization problems and to obtain optimal TSK fuzzy models. The validation and the comparison of SA and PSO and of the new TSK fuzzy models are carried out for an ABS laboratory equipment. The real-time experimental results highlight that the optimized TSK fuzzy models are simple and consistent with both training data and validation data and that these models outperform the initial TSK fuzzy models.     

Artificial Neural Networks are Zero-Order TSK Fuzzy Systems

In this paper, the functional equivalence between the action of a multilayered feed-forward artificial neural network (NN) and the performance of a system based on zero-order TSK fuzzy rules is proven. The resulting zero-order TSK fuzzy systems have the two following features: (A) the product t-norm is used to add IF-part fuzzy propositions of the obtained rules and (B) their inputs are the same as the initial neural networkNN ones. This fact makes us gain an understanding of the ANN-embedded knowledge. Besides, it allows us to simplify the architecture of a network through the reduction of fuzzy propositions in its equivalent zero-order TSK system. These advantages are the result of applying fuzzy system area properties on the neural networkNN area. They are illustrated with several examples.