Hybrid learning for interval type-2 fuzzy logic systems based on orthogonal least-squares and back-propagation methods

This paper presents a novel learning methodology based on a hybrid algorithm for interval type-2 fuzzy logic systems. Since only the back-propagation method has been proposed in the literature for the tuning of both the antecedent and the consequent parameters of type-2 fuzzy logic systems, a hybrid learning algorithm has been developed. The hybrid method uses a recursive orthogonal least-squares method for tuning the consequent parameters and the back-propagation method for tuning the antecedent parameters. Systems were tested for three types of inputs: (a) interval singleton, (b) interval type-1 non-singleton, and (c) interval type-2 non-singleton. Experiments were carried out on the application of hybrid interval type-2 fuzzy logic systems for prediction of the scale breaker entry temperature in a real hot strip mill for three different types of coil. The results proved the feasibility of the systems developed here for scale breaker entry temperature prediction. Comparison with type-1 fuzzy logic systems shows that hybrid learning interval type-2 fuzzy logic systems provide improved performance under the conditions tested.     

Asymmetric subsethood-product fuzzy neural inference system (ASuPFuNIS)

This work presents an asymmetric subsethood-product fuzzy neural inference system (ASuPFuNIS) that directly extends the SuPFuNIS model by permitting signal and weight fuzzy sets to be modeled by asymmetric Gaussian membership functions. The asymmetric subsethood-product network admits both numeric as well as linguistic inputs. Input nodes, which act as tunable feature fuzzifiers, fuzzify numeric inputs with asymmetric Gaussian fuzzy sets; and linguistic inputs are presented as is. The antecedent and consequent labels of standard fuzzy if-then rules are represented as asymmetric Gaussian fuzzy connection weights of the network. The model uses mutual subsethood based activation spread and a product aggregation operator that works in conjunction with volume defuzzification in a gradient descent learning framework. Despite the increase in the number of free parameters, the proposed model performs better than SuPFuNIS, on various benchmarking problems, both in terms of the performance accuracy and architectural economy and compares excellently with other various existing models with a performance better than most of them.     

复杂系统的递阶模糊辨识

针对Takagi_Sugeno模糊模型 (T_S模型 )严重的维数灾问题, 借鉴GMDH算法, 提出了一种新的复杂系统递阶模糊辨识方法. 本文首先详细描述了由两输入变量的特殊T_S模型所组成的递阶模糊模型 ;然后提出了具体的辨识该递阶模糊模型的方法. 该方法的特点是 :a)在结构辨识阶段, 用FCM模糊聚类方法评价系统中每个输入变量的重要性, 以便构造合理的递阶模糊模型 ;b)预先合理地确定了所要辨识的参数的初始值, 用扩展卡尔曼滤波方法可很快地得到这些参数. 最后, 给出的仿真实例说明了本文辨识方法的有     

Adaptive fuzzy identification and predictive control for industrial processes

This paper proposes a method for adaptive identification and control for industrial applications. The learning of a T–S fuzzy model is performed from input/output data to approximate unknown nonlinear processes by a hierarchical genetic algorithm (HGA). The HGA approach is composed by five hierarchical levels where the following parameters of the T–S fuzzy system are learned: input variables and their respective time delays, antecedent fuzzy sets, consequent parameters, and fuzzy rules. In order to reduce the computational cost and increase the algorithm’s performance an initialization method is applied on HGA. To deal with nonlinear plants and time-varying processes, the T–S fuzzy model is adapted online to maintain the quality of the identification/control. The identification methodology is proposed for two application problems: (1) the design of data-driven soft sensors, and (2) the learning of a model for the Generalized predictive control (GPC) algorithm. The integration of the proposed adaptive identification method with the GPC results in an effective adaptive predictive fuzzy control methodology. To validate and demonstrate the performance and effectiveness of the proposed methodologies, they are applied on identification of a model for the estimation of the flour concentration in the effluent of a real-world wastewater treatment system; and on control of a simulated continuous stirred tank reactor (CSTR) and on a real experimental setup composed of two coupled DC motors. The results are presented, showing that the developed evolving T–S fuzzy model can identify the nonlinear systems satisfactorily and it can be used successfully as a prediction model of the process for the GPC controller.     

Hierarchical wavelet packet fuzzy inference system for pattern classification and system identification

This study presents a hierarchical Takagi–Sugeno–Kang type fuzzy system called hierarchical wavelet packet fuzzy inference system. In the proposed method, wavelet packet transform is applied on the input data to produce approximation and detail sub-bands of the input data and the output is used as the input vector of the proposed network. This network uses a hierarchical structure same as wavelet packet decomposition tree, in which adaptive network-based fuzzy inference system is used as sub-model. Also, gradient descent algorithm is chosen for training the parameters of antecedent and conclusion parts of the sub-models. In order to evaluate the capability of the proposed method, its applications in pattern classification, system identification and time-series prediction have been studied. The results show that the proposed method performs better than the other conventional models.     

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.     

有混合数据输入的自适应模糊神经推理系统

现有数据建模方法大多依赖于定量的数值信息,而对于数值与分类混合输入的数据建模问题往往根据分类变量组合建立多个子模型,当有多个分类变量输入时易出现子模型数据分布不均匀、训练耗时长等问题.针对上述问题,提出一种具有混合数据输入的自适应模糊神经推理系统模型,在自适应模糊推理系统的基础上,引入激励强度转移矩阵和结论影响矩阵,采用基于高氏距离的减法聚类辨识模型结构,通过混合学习算法训练模型参数,使数值与分类混合数据对模糊规则的前后件参数同时产生作用,共同影响模型输出.仿真实验分析了分类数据对模型规则后件的作用以及结构辨识算法对模糊规则数的影响,与其他几种混合数据建模方法对比表明本文所提出的模型具有较高的预测精度和计算效率.     

Constraint-Based Fuzzy Models for an Environment with Heterogeneous Information-Granules

A novel framework for fuzzy modeling and model-based control design is described. Based on the theory of fuzzy constraint processing, the fuzzy model can be viewed as a generalized Takagi-Sugeno （TS） fuzzy model with fuzzy functional consequences. It uses multivariate antecedent membership functions obtained by granular-prototype fuzzy clustering methods and consequent fuzzy equations obtained by fuzzy regression techniques. Constrained optimization is used to estimate the consequent parameters, where the constraints are based on control-relevant a priori knowledge about the modeled process. The fuzzy-constraint-based approach provides the following features. 1） The knowledge base of a constraint-based fuzzy model can incorporate information with various types of fuzzy predicates. Consequently, it is easy to provide a fusion of different types of knowledge. The knowledge can be from data-driven approaches and/or from controlrelevant physical models. 2） A corresponding inference mechanism for the proposed model can deal with heterogeneous information granules. 3） Both numerical and linguistic inputs can be accepted for predicting new outputs. The proposed techniques are demonstrated by means of two examples： a nonlinear function-fitting problem and the well-known Box-Jenkins gas furnace process. The first example shows that the proposed model uses fewer fuzzy predicates achieving similar results with the traditional rule-based approach, while the second shows the performance can be significantly improved when the control-relevant constraints are considered.     

多层递阶融合模糊特征映射的模糊C均值聚类算法

针对复杂非线性数据的无监督学习问题,提出一种新型的映射方式来有效提高算法对复杂非线性数据的学习能力。以TSK模糊系统的规则前件学习为基础,提出一种新型的模糊特征映射新方法。接着,针对映射之后的数据维度过大问题,引入多层递阶融合的概念,进一步提出基于多层递阶融合的模糊特征映射新方法,从而有效避免了因单层模糊特征映射之后特征维数过高而导致的数据混乱和冗余的问题。最后与模糊C均值算法相结合,提出基于多层递阶融合模糊特征映射的模糊C均值聚类算法。实验研究表明,文中算法相比于经典模糊聚类方法,有着更加优越、稳定的性能。     

Gradient‐based back‐propagation dynamical iterative learning scheme for the neuro‐fuzzy inference system

In this paper, a gradient‐based back propagation dynamical iterative learning algorithm is proposed for structure optimization and parameter tuning of the neuro‐fuzzy system. Premise and consequent parameters of the neuro‐fuzzy model are initialized randomly and then tuned by the proposed iterative algorithm. The learning algorithm is based on the first order partial derivative of the output with respect to the structure parameters. The first order derivative of the model output with respect to the structure parameters determines the sensitivity of the model to structure parameters. The sensitivity values are then used to set the tuning factors and parameters updating step sizes. Therefore, an adaptive dynamical iterative scheme is achieved which adapts the learning procedure to the current state of the performance during the optimization process. Larger tuning step sizes make the convergence speed higher and vice versa. In this regard, this parameter is treated according to the calculated sensitivity of the model to the parameter. The proposed learning algorithm is compared with the least square back propagation method, genetic algorithm and chaotic genetic algorithm in the neuro‐fuzzy model structure optimization. Smaller mean square error and shorter learning time are sought in this paper, and the performance of the proposed learning algorithm is versified regarding these criteria.     

Evolutionary design of Sugeno-type fuzzy systems for modelling humanoid robots

An evolutionary design of Sugeno-type fuzzy systems for modelling humanoid robots is presented in this article, and issues related to the determination of the antecedent and consequent structures of the fuzzy model are addressed. In the design of the fuzzy model, determination of the type, the number of membership functions assigned to the input variables, the types of consequent equations for the fuzzy rules, the optimal number of input variables, and the dominant input variables among the input candidates are carried out using evolutionary algorithms. Using these algorithms, proper structures are evolved for the antecedent and the consequent of the Sugeno-type fuzzy model. Simulations are performed to show the effectiveness of the developed method when applied to a humanoid robot system with strong nonlinearities that have 10 input candidates.     

一种模糊逻辑系统的快速学习算法

本文提出了一种模糊逻辑系统的快速学习算法．算法要求预先确定各输入变量上模 糊集合的数目及分布;模糊规则前件可以是任意形状的模糊集合,后件则必须采用单值模糊 集合;模糊推理采用乘积推理;解模糊方法采用Tsukamoto方法．算法由输入－输出数据对 提取模糊规则．模糊规则的后件采用最小二乘方法一次计算得出．本算法对目标对象的逼近 精度取决于输入参数上模糊集合的数目,数目越多,精度越高．算法所需计算量小．     

基于增广输入变量的T-S 模糊模型建模

针对现有T-S 模糊模型建模精度与计算效率之间的矛盾, 提出一种利用增广输入变量进行T-S 模糊模型建模的方法. 对输入变量进行多项式增广处理后, 以核模糊?? 均值聚类算法配合聚类评价指标自适应获得最佳聚类数及相应的模糊划分, 并通过递推最小二乘计算得出T-S 模糊模型的后件参数. 提出可利用后件参数反推断前件结构的方法来快速有效地确定前件结构. 最后通过仿真验证了上述方法的有效性.

     

A fuzzy neural network based on fuzzy hierarchy error approach

This paper presents a novel fuzzy neural network which consists of an antecedent network and a consequent network. The antecedent network matches the premises of the fuzzy rules and the consequent network implements the consequences of the rules. In the network learning and training phase, a concise and effective algorithm based on the fuzzy hierarchy error approach is proposed to update the parameters of the network. This algorithm is simple to implement and it does not require as many calculations as some other classic neural network learning algorithms. A model reference adaptive control structure incorporating the proposed fuzzy neural network is studied. Simulation results of a cart-pole balancing system demonstrate the effectiveness of the proposed method     

基于特征选择和协同模糊聚类的模糊建模研究

为了提高模糊模型辨识效率,提出了一种新的模糊模型建摸方法,该方法由两步组成：（1）采用基于特征相似性的特征选择方法,去除原始数据的冗余;（2）利用协同模糊聚类与G-K相结合的算法初始化模糊模型,使其前件和后件参数得到优化。采用该算法对有效的特征进行协同模糊聚类,模型参数得到改善,提高了模糊模型辨识的效率。模糊建模的实验结果表明了该方法的有效性。     

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.     

结构辨识和参数优化协同学习的概率TSK模糊系统

传统Takagi-Sugeno-Kang (TSK)模糊系统的结构辨识和参数优化往往分阶段进行, 同时模糊规则数需要预先设定, 因此TSK模糊系统的逼近性能和解释性往往不理想.针对此问题, 提出了一种结构辨识和参数优化协同学习的概率TSK模糊系统(Probabilistic TSK fuzzy system, PTSK).首先, PTSK使用概率模型表示模糊回归系统, 将结构辨识和参数优化作为一个整体来考虑.其次, PTSK不借助于专家经验, 使用粒子滤波方法对规则数和前后件参数协同学习, 得到系统全部参数的最优解.实验结果表明, PTSK具有良好的逼近性能, 同时能获得较少的模糊规则数.     

Efficient stock price prediction using a Self Evolving Recurrent Neuro-Fuzzy Inference System optimized through a Modified Differential Harmony Search Technique

This paper proposes a new Self Evolving Recurrent Neuro-Fuzzy Inference System (SERNFIS) for efficient prediction of highly fluctuating and irregular financial time series data like stock market indices over varying time frames. The network is modeled including the first order Takagi Sugeno Kang (TSK) type fuzzy if then rules with two types of feedback loops. The recurrent structure in the proposed model comes from locally feeding the firing strength of the fuzzy rule back to itself and by including a few time delay components at the output layer. The novelty of the model is based on the fact that the internal temporal feedback loops and time delayed output feedback loops are used for further enhancing the prediction capability of traditional neuro-fuzzy system in handling more dynamic financial time series data. Another recurrent functional link artificial neural network (RCEFLANN) model is also presented for a comparative study. In the second part of the paper a modified differential harmony search (MDHS) technique is proposed for estimating the parameters of the model including the antecedent, consequent and feedback loop parameters. Experimental results obtained by implementing the model on two different stock market indices demonstrate the effectiveness of the proposed model compared to existing models for stock price prediction.     

Gaussian kernel-based fuzzy inference systems for high dimensional regression

We propose a novel architecture for a higher order fuzzy inference system (FIS) and develop a learning algorithm to build the FIS. The consequent part of the proposed FIS is expressed as a nonlinear combination of the input variables, which can be obtained by introducing an implicit mapping from the input space to a high dimensional feature space. The proposed learning algorithm consists of two phases. In the first phase, the antecedent fuzzy sets are estimated by the kernel-based fuzzy c-means clustering. In the second phase, the consequent parameters are identified by support vector machine whose kernel function is constructed by fuzzy membership functions and the Gaussian kernel. The performance of the proposed model is verified through several numerical examples generally used in fuzzy modeling. Comparative analysis shows that, compared with the zero-order fuzzy model, first-order fuzzy model, and polynomial fuzzy model, the proposed model exhibits higher accuracy, better generalization performance, and satisfactory robustness.     

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.