Dynamic parameter optimization of evolutionary computation for on-line prediction of time series with changing dynamics

This paper introduces a dynamic evolving computation system (DECS) model, for adaptive on-line learning, and its application for dynamic time series prediction. DECS evolve through evolving clustering method and evolutionary computation for structure learning, Levenberg–Marquardt method for parameter learning, learning and accommodate new input data. DECS is created and updated during the operation of the system. At each time moment the output of DECS is calculated through a knowledge rule inference system based on m-most activated fuzzy rules which are dynamically chosen from a fuzzy rule set. An approach is proposed for a dynamic creation of a first order Takagi–Sugeno type fuzzy rule set for the DECS model. The fuzzy rules can be inserted into DECS before, or during its learning process, and the rules can also be extracted from DECS during, or after its learning process. It is demonstrated that DECS can effectively learn complex temporal sequences in an adaptive way and outperform some existing models.     

Numerical study on the feasibility of dynamic evolving neural-fuzzy inference system for approximation of compressive strength of dry-cast concrete

This paper assesses effectiveness of dynamic evolving neural-fuzzy inference system (DENFIS) models in predicting the compressive strength of dry-cast concretes, and compares their prediction performances with those of regression, neural network (NN) and ANFIS models. The results of this study emphasized capabilities of online first-order and offline high-order Takagi–Sugeno (TSK) type DENFIS models for prediction purposes, whereas offline first-order TSK-type DENFIS models did not produce reliable results. Comparison between the produced results of an elite high-order DENFIS model with those predicted by the selected NN, regression and ANFIS models showed effectiveness of DENFIS model than the regression model, while its performance was similar to or slightly better than the other artificial prediction tools.     

一种新型的基于遗传算法的进化模糊推理系统

介绍了遗传算法和进化模糊推理系统的融合方式及结构,应用一种新型的基于遗传算法的进化模糊推理系统动态自适应的在线学习和离线学习。使用进化聚类方法,模糊规则在系统执行过程中进行创建和更新,并且采用遗传算法优化进化聚类的结果,修改成员的隶属度函数,通过模糊推理系统计算系统的输出。     

Dynamic modelling of customer preferences for product design using DENFIS and opinion mining

Previous studies mainly employed customer surveys to collect survey data for understanding customer preferences on products and developing customer preference models. In reality, customer preferences on products could change over time. Thus, the time series data of customer preferences under different time periods should be collected for the modelling of customer preferences. However, it is difficult to obtain the time series data based on customer surveys because of long survey time and substantial resources involved. In recent years, a large number of online customer reviews of products can be found on various websites, from which the time series data of customer preferences can be extracted easily. Some previous studies have attempted to analyse customer preferences on products based on online customer reviews. However, two issues were not addressed in previous studies which are the fuzziness of the sentiment expressed by customers existing in online reviews and the modelling of customer preferences based on the time series data obtained from online reviews. In this paper, a new methodology for dynamic modelling of customer preferences based on online customer reviews is proposed to address the two issues which mainly involves opinion mining and dynamic evolving neural-fuzzy inference system (DENFIS). Opinion mining is adopted to analyze online reviews and perform sentiment analysis on the reviews under different time periods. With the mined time series data and the product attribute settings of reviewed products, a DENFIS approach is introduced to perform the dynamic modelling of customer preferences. A case study is used to illustrate the proposed methodology. The results of validation tests indicate that the proposed DENFIS approach outperforms various adaptive neuro-fuzzy inference system (ANFIS) approaches in the dynamic modelling of customer preferences in terms of the mean relative error and variance of errors. In addition, the proposed DENFIS approach can provide both crisp and fuzzy outputs that cannot be realized by using existing ANFIS and conventional DENFIS approaches.     

Stock Trading Using RSPOP: A Novel Rough Set-Based Neuro-Fuzzy Approach

This paper investigates the method of forecasting stock price difference on artificially generated price series data using neuro-fuzzy systems and neural networks. As trading profits is more important to an investor than statistical performance, this paper proposes a novel rough set-based neuro-fuzzy stock trading decision model called stock trading using rough set-based pseudo outer-product (RSPOP) which synergizes the price difference forecast method with a forecast bottleneck free trading decision model. The proposed stock trading with forecast model uses the pseudo outer-product based fuzzy neural network using the compositional rule of inference [POPFNN-CRI(S)] with fuzzy rules identified using the RSPOP algorithm as the underlying predictor model and simple moving average trading rules in the stock trading decision model. Experimental results using the proposed stock trading with RSPOP forecast model on real world stock market data are presented. Trading profits in terms of portfolio end values obtained are benchmarked against stock trading with dynamic evolving neural-fuzzy inference system (DENFIS) forecast model, the stock trading without forecast model and the stock trading with ideal forecast model. Experimental results showed that the proposed model identified rules with greater interpretability and yielded significantly higher profits than the stock trading with DENFIS forecast model and the stock trading without forecast model.     

基于三相连接的进化模糊神经网络及应用

介绍了一种新型的进化模糊神经网络,规则节点层融入了三相电路的连接方式,用于在线的监督学习或者无人监督学习。使用进化聚类方法,模糊规则在系统执行过程中进行创建和更新,并且采用遗传算法即时优化进化聚类的结果,通过T-S模型模糊推理系统计算输出。     

Evolving fuzzy neural networks for supervised/unsupervised onlineknowledge-based learning

This paper introduces evolving fuzzy neural networks (EFuNNs) as a means for the implementation of the evolving connectionist systems (ECOS) paradigm that is aimed at building online, adaptive intelligent systems that have both their structure and functionality evolving in time. EFuNNs evolve their structure and parameter values through incremental, hybrid supervised/unsupervised, online learning. They can accommodate new input data, including new features, new classes, etc., through local element tuning. New connections and new neurons are created during the operation of the system. EFuNNs can learn spatial-temporal sequences in an adaptive way through one pass learning and automatically adapt their parameter values as they operate. Fuzzy or crisp rules can be inserted and extracted at any time of the EFuNN operation. The characteristics of EFuNNs are illustrated on several case study data sets for time series prediction and spoken word classification. Their performance is compared with traditional connectionist methods and systems. The applicability of EFuNNs as general purpose online learning machines, what concerns systems that learn from large databases, life-long learning systems, and online adaptive systems in different areas of engineering are discussed.     

An evolving recurrent interval type-2 intuitionistic fuzzy neural network for online learning and time series prediction

The prediction of time series has both the theoretical value and practical significance in reality. However, since the high nonlinear and noises in the time series, it is still an open problem to tackle with the uncertainties and fuzziness in the forecasting process. In this article, an evolving recurrent interval type-2 intuitionistic fuzzy neural network (eRIT2IFNN) is proposed for time series prediction and regression problems. The eRIT2IFNN employs interval type-2 intuitionistic fuzzy sets to enhance the modeling of uncertainties by intuitionistic evaluation and noise tolerance of the system. In the eRIT2IFNN, the antecedent part of each fuzzy rule is defined using intuitionistic interval type-2 fuzzy sets, and the consequent realizes the Takagi–Sugeno–Kang type fuzzy inference mechanism. In order to utilize the prior knowledge including intuitionistic information, a local internal feedback is established by feeding the rule firing strength of each rule to itself eRIT2IFNN is fully adaptive to the evolving of sequence data by online learning of structure and parameters. A modified density-based clustering is implemented for the structure learning, where both densities and membership degrees are involved to determine the fuzzy rules. Performance of eRIT2IFNN is evaluated using a set of benchmark problems and compared with existing fuzzy inference systems. Moreover, the eRIT2IFNN is tested for identification of dynamics under both noise-free and noisy environments. Finally, a group of practical financial price-tracking problems including high-frequency data of financial future, commodity future and precious metal are used for the evaluation of the proposed inference system.     

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.      

A self-organizing fuzzy logic controller for dynamic systems usinga fuzzy auto-regressive moving average (FARMA) model

The paper proposes a complete design method for an online self-organizing fuzzy logic controller without using any plant model. By mimicking the human learning process, the control algorithm finds control rules of a system for which little knowledge has been known. In a conventional fuzzy logic control, knowledge on the system supplied by an expert is required in developing control rules, however, the proposed new fuzzy logic controller needs no expert in making control rules, Instead, rules are generated using the history of input-output pairs, and new inference and defuzzification methods are developed. The generated rules are stored in the fuzzy rule space and updated online by a self-organizing procedure. The validity of the proposed fuzzy logic control method has been demonstrated numerically in controlling an inverted pendulum     

Online identification of evolving Takagi–Sugeno–Kang fuzzy models for crane systems

This paper suggests new evolving Takagi–Sugeno–Kang (TSK) fuzzy models dedicated to crane systems. A set of evolving TSK fuzzy models with different numbers of inputs are derived by the novel relatively simple and transparent implementation of an online identification algorithm. An input selection algorithm to guide modeling is proposed on the basis of ranking the inputs according to their important factors after the first step of the online identification algorithm. The online identification algorithm offers rule bases and parameters which continuously evolve by adding new rules with more summarization power and by modifying existing rules and parameters. The potentials of new data points are used with this regard. The algorithm is applied in the framework of the pendulum–crane system laboratory equipment. The evolving TSK fuzzy models are tested against the experimental data and a comparison with other TSK fuzzy models and modeling approaches is carried out. The comparison points out that the proposed evolving TSK fuzzy models are simple and consistent with both training data and testing data and that these models outperform other TSK fuzzy models.     

一种快速模糊推理系统

提出一种新的模糊推理系统，其模糊知识库具有紧致模糊规则库，即规则集为仅存储规则后的完全规则集，推理过程中可以根据当前输入信号值直接寻址被激励的模糊规则，从而只是有选择地执行被激励的规则，其优点是可以提高模糊推理速度，减少规则库存储容量，针对模糊芯片的VLSI实现，提出了可以根据输入信号值直接寻址被激励规则的电路。     

FLEXFIS: A Robust Incremental Learning Approach for Evolving Takagi–Sugeno Fuzzy Models

In this paper, we introduce a new algorithm for incremental learning of a specific form of Takagi–Sugeno fuzzy systems proposed by Wang and Mendel in 1992. The new data-driven online learning approach includes not only the adaptation of linear parameters appearing in the rule consequents, but also the incremental learning of premise parameters appearing in the membership functions (fuzzy sets), together with a rule learning strategy in sample mode. A modified version of vector quantization is exploited for rule evolution and an incremental learning of the rules' premise parts. The modifications include an automatic generation of new clusters based on the nature, distribution, and quality of new data and an alternative strategy for selecting the winning cluster (rule) in each incremental learning step. Antecedent and consequent learning are connected in a stable manner, meaning that a convergence toward the optimal parameter set in the least-squares sense can be achieved. An evaluation and a comparison to conventional batch methods based on static and dynamic process models are presented for high-dimensional data recorded at engine test benches and at rolling mills. For the latter, the obtained data-driven fuzzy models are even compared with an analytical physical model. Furthermore, a comparison with other evolving fuzzy systems approaches is carried out based on nonlinear dynamic system identification tasks and a three-input nonlinear function approximation example.      

Influential rule search scheme (IRSS) - a new fuzzy pattern classifier

Automatic generation of fuzzy rule base and membership functions from an input-output data set, for reliable construction of an adaptive fuzzy inference system, has become an important area of research interest. We propose a new robust, fast acting adaptive fuzzy pattern classification scheme, named influential rule search scheme (IRSS). In IRSS, rules which are most influential in contributing to the error produced by the adaptive fuzzy system are identified at the end of each epoch and subsequently modified for satisfactory performance. This fuzzy rule base adjustment scheme is accompanied by an output membership function adaptation scheme for fine tuning the fuzzy system architecture. This iterative method has shown a relatively high speed of convergence. Performance of the proposed IRSS is compared with other existing pattern classification schemes by implementing it for Fisher's iris data problem and Wisconsin breast cancer data problems.     

Fast inference in SAM fuzzy systems using transition matrices

Fast inference using transition matrices (FITM) is a new fast algorithm for performing inferences in fuzzy systems. It is based on the assumption that fuzzy inputs can be expressed as a linear composition of the fuzzy sets used in the rule base. This representation let us interpret a fuzzy set as a vector, so we can just work with the coordinates of it instead of working with the whole set. The inference is made using transition matrices. The key of the method is the fact that a lot of operations can be precomputed offline to obtain the transition matrices, so actual inferences are reduced to a few online matrix additions and multiplications. The algorithm is designed for the standard additive model using the sum-product inference composition.     

Learning and tuning fuzzy logic controllers through reinforcements

A method for learning and tuning a fuzzy logic controller based on reinforcements from a dynamic system is presented. It is shown that: the generalized approximate-reasoning-based intelligent control (GARIC) architecture learns and tunes a fuzzy logic controller even when only weak reinforcement, such as a binary failure signal, is available; introduces a new conjunction operator in computing the rule strengths of fuzzy control rules; introduces a new localized mean of maximum (LMOM) method in combining the conclusions of several firing control rules; and learns to produce real-valued control actions. Learning is achieved by integrating fuzzy inference into a feedforward network, which can then adaptively improve performance by using gradient descent methods. The GARIC architecture is applied to a cart-pole balancing system and demonstrates significant improvements in terms of the speed of learning and robustness to changes in the dynamic system's parameters over previous schemes for cart-pole balancing.     

Adaptive fuzzy controller with sliding surface for vehicle suspension control

Since the hydraulic actuating suspension system has nonlinear and time-varying behavior, it is difficult to establish an accurate model for designing a model-based controller. Here, an adaptive fuzzy sliding mode controller is proposed to suppress the sprung mass position oscillation due to road surface variation. This intelligent control strategy combines an adaptive rule with fuzzy and sliding mode control algorithms. It has online learning ability to deal with the system time-varying and nonlinear uncertainty behaviors, and adjust the control rules parameters. Only eleven fuzzy rules are required for this active suspension system and these fuzzy control rules can be established and modified continuously by online learning. The experimental results show that this intelligent control algorithm effectively suppresses the oscillation amplitude of the sprung mass with respect to various road surface disturbances.     

FITSK: online local learning with generic fuzzy input Takagi-Sugeno-Kang fuzzy framework for nonlinear system estimation.

Existing Takagi-Sugeno-Kang (TSK) fuzzy models proposed in the literature attempt to optimize the global learning accuracy as well as to maintain the interpretability of the local models. Most of the proposed methods suffer from the use of offline learning algorithms to globally optimize this multi-criteria problem. Despite the ability to reach an optimal solution in terms of accuracy and interpretability, these offline methods are not suitably applicable to learning in adaptive or incremental systems. Furthermore, most of the learning methods in TSK-model are susceptible to the limitation of the curse-of-dimensionality. This paper attempts to study the criteria in the design of TSK-models. They are: 1) the interpretability of the local model; 2) the global accuracy; and 3) the system dimensionality issues. A generic framework is proposed to handle the different scenarios in this design problem. The framework is termed the generic fuzzy input Takagi-Sugeno-Kang fuzzy framework (FITSK). The FITSK framework is extensible to both the zero-order and the first-order FITSK models. A zero-order FITSK model is suitable for the learning of adaptive system, and the bias-variance of the system can be easily controlled through the degree of localization. On the other hand, a first-order FITSK model is able to achieve higher learning accuracy for nonlinear system estimation. A localized version of recursive least-squares algorithm is proposed for the parameter tuning of the first-order FITSK model. The local recursive least-squares is able to achieve a balance between interpretability and learning accuracy of a system, and possesses greater immunity to the curse-of-dimensionality. The learning algorithms for the FITSK models are online, and are readily applicable to adaptive system with fast convergence speed. Finally, a proposed guideline is discussed to handle the model selection of different FITSK models to tackle the multi-criteria design problem of applying the TSK-model. Extensive simulations were conducted using the proposed FITSK models and their learning algorithms; their performances are encouraging when benchmarked against other popular fuzzy systems.     

A neural fuzzy system with fuzzy supervised learning

A neural fuzzy system learning with fuzzy training data (fuzzy if-then rules) is proposed in this paper. This system is able to process and learn numerical information as well as linguistic information. At first, we propose a five-layered neural network for the connectionist realization of a fuzzy inference system. The connectionist structure can house fuzzy logic rules and membership functions for fuzzy inference. We use alpha-level sets of fuzzy numbers to represent linguistic information. The inputs, outputs, and weights of the proposed network can be fuzzy numbers of any shape. Furthermore, they can be hybrid of fuzzy numbers and numerical numbers through the use of fuzzy singletons. Based on interval arithmetics, a fuzzy supervised learning algorithm is developed for the proposed system. It extends the normal supervised learning techniques to the learning problems where only linguistic teaching signals are available. The fuzzy supervised learning scheme can train the proposed system with desired fuzzy input-output pairs which are fuzzy numbers instead of the normal numerical values. With fuzzy supervised learning, the proposed system can be used for rule base concentration to reduce the number of rules in a fuzzy rule base. Simulation results are presented to illustrate the performance and applicability of the proposed system.     

Evolving Takagi–Sugeno fuzzy model based on switching to neighboring models

In this paper, we propose a new online identification approach for evolving Takagi–Sugeno (TS) fuzzy models. Here, for a TS model, a certain number of models as neighboring models are defined and then the TS model switches to one of them at each stage of evolving. We define neighboring models for an in-progress (current) TS model as its fairly evolved versions, which are different with it just in two fuzzy rules. To generate neighboring models for the current model, we apply specially designed split and merge operations. By each split operation, a fuzzy rule is replaced with two rules; while by each merge operation, two fuzzy rules combine to one rule. Among neighboring models, the one with the minimum sum of squared errors – on certain time intervals – replaces the current model.To reduce the computational load of the proposed evolving TS model, straightforward relations between outputs of neighboring models and that of current model are established. Also, to reduce the number of rules, we define and use first-order TS fuzzy models whose generated local linear models can be localized in flexible fuzzy subspaces. To demonstrate the improved performance of the proposed identification approach, the efficiency of the evolving TS model is studied in prediction of monthly sunspot number and forecast of daily electrical power consumption. The prediction and modeling results are compared with that of some important existing evolving fuzzy systems.