基于中心型TSK模糊模型的分层模糊系统

模糊系统随着输入维数的增加,其中模糊规则和辨识参数的数量将按指数级增长,针对这一问题,采用分层模糊系统是一种很好的解决方法,但分层模糊系统中各层的辨识变量没有明确的物理含义,无法进行合理的模糊化设计和解释。基于一种分层模糊系统,引用中心性TSK模糊系统思想,从而构造了一种新型的模糊系统。这种新型模糊系统保留了分层模糊系统的结构优势,极大地减少了模糊系统的模糊规则数量和辨识参数数量,又能对用到的内部参数进行很好的解释。并通过实例仿真表明基于中心型TSK模糊模型的分层模糊系统具有较好的逼近性能和更简单的结构。     

一种基于扩张原理的模糊模型 及其辨识方法1)

提出一种新的基于LR型模糊数及其运算的模糊模型结构——扩展的TSK模型(ETSK模型).借助于LR型模糊数隶属函数图形的面积和重心横坐标这两个“数字特征”,导出了ETSK模型的输入输出解析表达式,并证明了ETSK模型与变权TSK模型的等价关系,同时给出一种对ETSK模型规则后件的参数辨识方法.仿真辨识实验结果表明,ETSK模型的辨识效果和预报精度更优.     

一种基于扩张原理的模糊模型及其辨识方法

提出一种新的基于LR型模糊数及其运算的模糊模型结构--扩展的TSK模型 (ETSK模型).借助于LR型模糊数隶属函数图形的面积和重心横坐标这两个"数字特征", 导出了ETSK模型的输入输出解析表达式,并证明了ETSK模型与变权TSK模型的等价关 系,同时给出一种对ETSK模型规则后件的参数辨识方法.仿真辨识实验结果表明,ETSK模 型的辨识效果和预报精度更优.     

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.     

自组织区间二型模糊神经网络及其自适应学习算法

针对复杂不确定非线性系统的辨识问题,提出一种基于聚类的自组织区间二型模糊神经网络学习算法.首先采用具有两个不同加权参数的FCM算法对输入数据进行划分来获取规则前件的不确定均值,同时结合聚类有效性标准确定模糊规则数目,从而自动完成神经网络的结构辨识和规则前件参数辨识;随后给出了基于梯度下降法和Lyapunov函数稳定收敛定理的规则后件权向量学习速率的自适应学习算法.通过非线性系统辨识实例,验证了该算法与其他方法相比具有更快的收敛速度和更高的逼近精度;并且利用该算法建立了某市电力短期负荷预测模型,结果表明该模型具有较高的预测精度,泛化性能更佳.     

一种新的基于神经模糊推理网络的复杂系统模糊辨识方法

针对基于输入输出数据的复杂系统的模糊辨识问题,提出了一种新的神经模糊推理网络及相应的学习算法．学习算法被应用于系统的结构辨识与参数辨识．在结构辨识阶段,介绍了一种新的直接从输入输出数据中抽取和优化模糊规则的学习算法;在参数辨识阶段,提出和推导了一种非监督学习和监督学习相结合的混合式学习算法,实现模糊隶属函数的初步调整和优化．仿真结果表明,本文的方法可以同时满足对辨识精度、收敛速度、可读性和规则数的要求．     

一种基于模糊分类的模糊神经网络辨识方法

针对非线性辨识问题,基于改进的T-S模型,提出一种自适应模糊神经网络模型(AFNN)。首先,基于模糊竞争学习算法确定系统的模糊空间和模糊规则数,并得出每个样本对每条规则的适用程度。其次,利用卡尔曼滤波算法在线辨识AFNN的后件参数。AFNN具有结构简洁,逼近能力强,能够显著提高辨识精度,并且辨识的模糊模型简单有效。最后,将该AFNN用于非线性系统的模糊辨识,仿真结果验证了该方法的有效性。     

基于训练空间重构的多模块TSK模糊系统

利用重构训练样本空间的手段,提出一种多训练模块Takagi-Sugeno-Kang （TSK）模糊分类器H-TSK-FS.它具有良好的分类性能和较高的可解释性,可以解决现有层次模糊分类器中间层输出和模糊规则难以解释的难题.为了实现良好的分类性能,H-TSK-FS由多个优化零阶TSK模糊分类器组成.这些零阶TSK模糊分类器内部采用一种巧妙的训练方式.原始训练样本、上一层训练样本中的部分样本点以及所有已训练层中最逼近真实值的部分决策信息均被投影到当前层训练模块中,并构成其输入空间.通过这种训练方式,前层的训练结果对后层的训练起到引导和控制作用.这种随机选取样本点、在一定范围内随机选取训练特征的手段可以打开原始输入空间的流形结构,保证较好或相当的分类性能.另外,该研究主要针对少量样本点且训练特征数不是很大的数据集.在设计每个训练模块时采用极限学习机获取模糊规则后件参数.对于每个中间训练层,采用短规则表达知识.每条模糊规则则通过约束方式确定不固定的输入特征以及高斯隶属函数,目的是保证所选输入特征具有高可解释性.真实数据集和应用案例实验结果表明,H-TSK-FS具有良好的分类性能和高可解释性.     

双层模糊系统融合中心约束型最小包含球

与传统的TSK模糊系统相比,改进的双层TSK模糊系统CTSK(Central TSK Fuzzy System)有如下优点:良好的可解释性、更好的鲁棒性、较强的逼近能力。但对于大样本或超大样本数据集,其时间复杂度和空间复杂度的开销都极大地限制了它的实用性。针对此不足,通过模糊系统融合中心约束型最小包含球(CCMEB)理论提出了CCMEB-CTSK(CCMEB-based CTSK)算法。该算法在继承CTSK优点的同时,又较好地实现了处理大样本和超大样本数据集的有效性和快速性。仿真实验研究分析了采用不同模糊规则数的CCMEB-CTSK的性能指标和运行时间的比较,以及训练样本不加噪声和加入噪声情况下CCMEB-CTSK泛化能力和鲁棒性能的测试。     

A Recurrent Self-Evolving Interval Type-2 Fuzzy Neural Network for Dynamic System Processing

This paper proposes a recurrent self-evolving interval type-2 fuzzy neural network (RSEIT2FNN) for dynamic system processing. An RSEIT2FNN incorporates type-2 fuzzy sets in a recurrent neural fuzzy system in order to increase the noise resistance of a system. The antecedent parts in each recurrent fuzzy rule in the RSEIT2FNN are interval type-2 fuzzy sets, and the consequent part is of the Takagi-Sugeno-Kang (TSK) type with interval weights. The antecedent part of RSEIT2FNN forms a local internal feedback loop by feeding the rule firing strength of each rule back to itself. The TSK-type consequent part is a linear model of exogenous inputs. The RSEIT2FNN initially contains no rules; all rules are learned online via structure and parameter learning. The structure learning uses online type-2 fuzzy clustering. For the parameter learning, the consequent part parameters are tuned by a rule-ordered Kalman filter algorithm to improve learning performance. The antecedent type-2 fuzzy sets and internal feedback loop weights are learned by a gradient descent algorithm. The RSEIT2FNN is applied to simulations of dynamic system identifications and chaotic signal prediction under both noise-free and noisy conditions. Comparisons with type-1 recurrent fuzzy neural networks validate the performance of the RSEIT2FNN.     

A Self-Evolving Interval Type-2 Fuzzy Neural Network With Online Structure and Parameter Learning

This paper proposes a self-evolving interval type-2 fuzzy neural network (SEIT2FNN) with online structure and parameter learning. The antecedent parts in each fuzzy rule of the SEIT2FNN are interval type-2 fuzzy sets and the fuzzy rules are of the Takagi–Sugeno–Kang (TSK) type. The initial rule base in the SEIT2FNN is empty, and the online clustering method is proposed to generate fuzzy rules that flexibly partition the input space. To avoid generating highly overlapping fuzzy sets in each input variable, an efficient fuzzy set reduction method is also proposed. This method independently determines whether a corresponding fuzzy set should be generated in each input variable when a new fuzzy rule is generated. For parameter learning, the consequent part parameters are tuned by the rule-ordered Kalman filter algorithm for high-accuracy learning performance. Detailed learning equations on applying the rule-ordered Kalman filter algorithm to the SEIT2FNN consequent part learning, with rules being generated online, are derived. The antecedent part parameters are learned by gradient descent algorithms. The SEIT2FNN is applied to simulations on nonlinear plant modeling, adaptive noise cancellation, and chaotic signal prediction. Comparisons with other type-1 and type-2 fuzzy systems in these examples verify the performance of the SEIT2FNN.      

Bayesian zero-order TSK fuzzy system modeling

Different from the existing TSK fuzzy system modeling methods, a novel zero-order TSK fuzzy modeling method called Bayesian zero-order TSK fuzzy system (B-ZTSK-FS) is proposed from the perspective of Bayesian inference in this paper. The proposed method B-ZTSK-FS constructs zero-order TSK fuzzy system by using the maximum a posteriori (MAP) framework to maximize the corresponding posteriori probability. First, a joint likelihood model about zero-order TSK fuzzy system is defined to derive a new objective function which can assure that both antecedents and consequents of fuzzy rules rather than only their antecedents of the most existing TSK fuzzy systems become interpretable. The defined likelihood model is composed of three aspects: clustering on the training set for antecedents of fuzzy rules, the least squares (LS) error for consequent parameters of fuzzy rules, and a Dirichlet prior distribution for fuzzy cluster memberships which is considered to not only automatically match the “sum-to-one” constraints on fuzzy cluster memberships, but also make the proposed method B-ZTSK-FS scalable for large-scale datasets by appropriately setting the Dirichlet index. This likelihood model indeed indicates that antecedent and consequent parameters of fuzzy rules can be linguistically interpreted and simultaneously optimized by the proposed method B-ZTSK-FS which is based on the MAP framework with the iterative sampling algorithm, which in fact implies that fuzziness and probability can co-jointly work for TSK fuzzy system modeling in a collaborative rather than repulsive way. Finally, experimental results on 28 synthetic and real-world datasets are reported to demonstrate the effectiveness of the proposed method B-ZTSK-FS in the sense of approximation accuracy, interpretability and scalability.     

A two-stage evolutionary process for designing TSK fuzzy rule-basedsystems

Nowadays, fuzzy rule-based systems are successfully applied to many different real-world problems. Unfortunately, relatively few well-structured methodologies exist for designing and, in many cases, human experts are not able to express the knowledge needed to solve the problem in the form of fuzzy rules. Takagi-Sugeno-Kang (TSK) fuzzy rule-based systems were enunciated in order to solve this design problem because they are usually identified using numerical data. In this paper we present a two-stage evolutionary process for designing TSK fuzzy rule-based systems from examples combining a generation stage based on a (mu, lambda)-evolution strategy, in which the fuzzy rules with different consequents compete among themselves to form part of a preliminary knowledge base, and a refinement stage in which both the antecedent and consequent parts of the fuzzy rules in this previous knowledge base are adapted by a hybrid evolutionary process composed of a genetic algorithm and an evolution strategy to obtain the final Knowledge base whose rules cooperate in the best possible way. Some aspects make this process different from others proposed until now: the design problem is addressed in two different stages, the use of an angular coding of the consequent parameters that allows us to search across the whole space of possible solutions, and the use of the available knowledge about the system under identification to generate the initial populations of the Evolutionary Algorithms that causes the search process to obtain good solutions more quickly. The performance of the method proposed is shown by solving two different problems: the fuzzy modeling of some three-dimensional surfaces and the computing of the maintenance costs of electrical medium line in Spanish towns. Results obtained are compared with other kind of techniques, evolutionary learning processes to design TSK and Mamdani-type fuzzy rule-based systems in the first case, and classical regression and neural modeling in the second.     

A probabilistic fuzzy approach to modeling nonlinear systems

Recently, the study of incorporating probability theory and fuzzy logic has received much interest. To endow the traditional fuzzy rule-based systems (FRBs) with probabilistic features to handle randomness, this paper presents a probabilistic fuzzy neural network (ProFNN) by introducing the probability of input linguistic terms and providing linguistic meaning into the connectionist architecture. ProFNN integrates the probabilistic information of fuzzy rules into the antecedent parts and quantifies the impacts of the rules on the consequent parts using mutual subsethood, which work in conjunction with volume defuzzification in a gradient descent learning frame work. Despite the increase in the number of parameters, ProFNN provides a promising solution to deal with randomness and fuzziness in a single frame. To evaluate the performance and applicability of the proposed approach, ProFNN is carried out on various benchmarking problems and compared with other existing models with a performance better than most of them.     

A type-2 neural fuzzy system learned through type-1 fuzzy rules and its FPGA-based hardware implementation

This paper first proposes a type-2 neural fuzzy system (NFS) learned through its type-1 counterpart (T2NFS-T1) and then implements the built IT2NFS-T1 in a field-programmable gate array (FPGA) chip. The antecedent part of each fuzzy rule in the T2NFS-T1 uses interval type-2 fuzzy sets, while the consequent part uses a Takagi-Sugeno-Kang (TSK) type with interval combination weights. The T2NFS-T1 uses a simplified type-reduction operation to reduce system training time and hardware implementation cost. Given a training data set, a TSK type-1 NFS is first learned through structure and parameter learning. The built type-1 fuzzy logic system (FLS) is then extended to a type-2 FLS, where highly overlapped type-1 fuzzy sets are merged into interval type-2 fuzzy sets to reduce the total number of fuzzy sets. Finally, the rule consequent and antecedent parameters in the T2NFS-T1 are tuned using a hybrid of the gradient descent and rule-ordered recursive least square (RLS) algorithms. Simulation results and comparisons with various type-1 and type-2 FLSs verify the effectiveness and efficiency of the T2NFS-T1 for system modeling and prediction problems. A new hardware circuit using both parallel-processing and pipeline techniques is proposed to implement the learned T2NFS-T1 in an FPGA chip. The T2NFS-T1 chip reduces the hardware implementation cost in comparison to other type-2 fuzzy chips.     

基于模糊子空间聚类的0 阶岭回归TSK 模糊系统

经典数据驱动型TSK模糊系统在利用高维数据训练模型时,由于规则前件采用的特征过多,导致规则的解释性和简洁性下降.对此,根据模糊子空间聚类算法的子空间特性,为TSK模型添加特征抽取机制,并进一步利用岭回归实现后件的学习,提出一种基于模糊子空间聚类的0阶岭回归TSK模型构建方法.该方法不仅能为规则抽取出重要子空间特征,而且可为不同规则抽取不同的特征.在模拟和真实数据集上的实验结果验证了所提出方法的优势.     

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.     

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.     

Data-driven fuzzy modeling for Takagi-Sugeno-Kang fuzzy system

This paper presents a systematic approach to design first order Tagaki-Sugeno-Kang (TSK) fuzzy systems. This approach attempts to obtain the fuzzy rules without any assumption about the structure of the data. The structure identification and parameter optimization steps in this approach are carried out automatically, and are capable of finding the optimal number of the rules with an acceptable accuracy. Starting with an initial structure, the system first tries to improve the structure and, then, as soon as an improved structure is found, it fine tunes its rules’ parameters. Then, it goes back to improve the structure again to find a better structure and re-fine tune the rules’ parameters. This loop continues until a satisfactory solution (TSK model) is found. The proposed approach has successfully been applied to well-known benchmark datasets and real-world problems. The obtained results are compared with those obtained with other methods from the literature. Experimental studies demonstrate that the predicted properties have a good agreement with the measured data by using the elicited fuzzy model with a small number of rules. Finally, as a case study, the proposed approach is applied to the desulfurization process of a real steel industry. Comparing the proposed approach with some other fuzzy systems and neural networks, it is shown that the developed TSK fuzzy system exhibits better results with higher accuracy and smaller size of architecture.