Fuzzy impulsive control of chaotic systems based on TS fuzzy model

Combining Takagi–Sugeno (TS) fuzzy model and impulsive control, a new approach to control chaotic systems, namely fuzzy impulsive control, is proposed in this paper. The rigorous stability analysis of the proposed method is given. The effectiveness of the approach is tested on Chua’s circuit, Chen’s system and Rössler’s system.     

Fuzzy modelling of a moving grate biomass furnace for simulation and control purposes

Takagi–Sugeno (TS) fuzzy models are developed for a moving grate biomass furnace for the purpose of simulating and predicting the main process output variables, which are heat output, oxygen concentration of flue gas, and temperature of flue gas. Numerous approaches to modelling biomass furnaces have been proposed in the literature. Usually their objective is to simulate the furnace as accurately as possible. Hence, very complex model architectures are utilized which are not suited for applications like model predictive control. TS fuzzy models are able to approximate the global non-linear behaviour of a moving grate biomass furnace by interpolating between local linear, time-invariant models. The fuzzy partitions of the individual TS fuzzy models are constructed by an axis-orthogonal, incremental partitioning scheme. Validation results with measured process data demonstrate the excellent performance of the developed fuzzy models.     

Online identification of Takagi–Sugeno fuzzy models based on self-adaptive hierarchical particle swarm optimization algorithm

This paper presents an approach for online learning of Takagi–Sugeno (T-S) fuzzy models. A novel learning algorithm based on a Hierarchical Particle Swarm Optimization (HPSO) is introduced to automatically extract all fuzzy logic system (FLS)’s parameters of a T–S fuzzy model. During online operation, both the consequent parameters of the T–S fuzzy model and the PSO inertia weight are continually updated when new data becomes available. By applying this concept to the learning algorithm, a new type T–S fuzzy modeling approach is constructed where the proposed HPSO algorithm includes an adaptive procedure and becomes a self-adaptive HPSO (S-AHPSO) algorithm usable in real-time processes. To improve the computational time of the proposed HPSO, particles positions are initialized by using an efficient unsupervised fuzzy clustering algorithm (UFCA). The UFCA combines the K-nearest neighbour and fuzzy C-means methods into a fuzzy modeling method for partitioning of the input–output data and identifying the antecedent parameters of the fuzzy system, enhancing the HPSO’s tuning. The approach is applied to identify the dynamical behavior of the dissolved oxygen concentration in an activated sludge reactor within a wastewater treatment plant. The results show that the proposed approach can identify nonlinear systems satisfactorily, and reveal superior performance of the proposed methods when compared with other state of the art methods. Moreover, the methodologies proposed in this paper can be involved in wider applications in a number of fields such as model predictive control, direct controller design, unsupervised clustering, motion detection, and robotics.     

Solving generalized fuzzy data envelopment analysis model: a parametric approach

Data envelopment analysis (DEA) is a non-parametric technique to assess the performance of a set of homogeneous decision making units (DMUs) with common crisp inputs and outputs. Regarding the problems that are modelled out of the real world, the data cannot constantly be precise and sometimes they are vague or fluctuating. So in the modelling of such data, one of the best approaches is using the fuzzy numbers. Substituting the fuzzy numbers for the crisp numbers in DEA, the traditional DEA problem transforms into a fuzzy data envelopment analysis (FDEA) problem. Different methods have been suggested to compute the efficiency of DMUs in FDEA models so far but the most of them have limitations such as complexity in calculation, non-contribution of decision maker in decision making process, utilizable for a specific model of FDEA and using specific group of fuzzy numbers. In the present paper, to overcome the mentioned limitations, a new approach is proposed. In this approach, the generalized FDEA problem is transformed into a parametric programming, in which, parameter selection depends on the decision maker’s ideas. Two numerical examples are used to illustrate the approach and to compare it with some other approaches.     

Sampled‐data reliable stabilization of T‐S fuzzy systems and its application

In this article, based on sampled‐data approach, a new robust state feedback reliable controller design for a class of Takagi–Sugeno fuzzy systems is presented. Different from the existing fault models for reliable controller, a novel generalized actuator fault model is proposed. In particular, the implemented fault model consists of both linear and nonlinear components. Consequently, by employing input‐delay approach, the sampled‐data system is equivalently transformed into a continuous‐time system with a variable time delay. The main objective is to design a suitable reliable sampled‐data state feedback controller guaranteeing the asymptotic stability of the resulting closed‐loop fuzzy system. For this purpose, using Lyapunov stability theory together with Wirtinger‐based double integral inequality, some new delay‐dependent stabilization conditions in terms of linear matrix inequalities are established to determine the underlying system's stability and to achieve the desired control performance. Finally, to show the advantages and effectiveness of the developed control method, numerical simulations are carried out on two practical models. © 2016 Wiley Periodicals, Inc. Complexity 21: 518–529, 2016     

Handling forecasting problems using fuzzy time series

In [6–9], Song et al. proposed fuzzy time-series models to deal with forecasting problems. In [10], Sullivan and Woodall reviewed the first-order time-invariant fuzzy time series model and the first-order time-variant model proposed by Song and Chissom [6–8], where the models are compared with each other and with a time-invariant Markov model using linguistic labels with probability distributions. In this paper, we propose a new method to forecast university enrollments, where the historical enrollments of the University of Alabama shown in [7,8] are used to illustrate the forecasting process. The average forecasting errors and the time complexity of these methods are compared. The proposed method is more efficient than the ones presented in [7, 8, 10] due to the fact that the proposed method simplifies the arithmetic operation process. Furthermore, the average forecasting error of the proposed method is smaller than the ones presented in [2, 7, 8].     

一种遗传模糊神经网络数据挖掘算法

数据挖掘是近年来信息处理领域出现的新的研究方向。本文探讨了扩展型TS模糊神经网络和遗传算法在数据挖掘中的应用,并提出了一种把模糊神经网络与遗传算法相结合的数据挖掘方法。在该方法中由遗传算法自适应地构造和优化TS模型,TS模型完成预测,这种预测是建立在遗传算法的聚类结果之上的。二者的结合,提高数据挖掘的应用效果。文章最后给出该方法的应用实例。     

Intelligent data analysis and model interpretation with spectral analysis fuzzy symbolic modeling

This paper proposes fuzzy symbolic modeling as a framework for intelligent data analysis and model interpretation in classification and regression problems. The fuzzy symbolic modeling approach is based on the eigenstructure analysis of the data similarity matrix to define the number of fuzzy rules in the model. Each fuzzy rule is associated with a symbol and is defined by a Gaussian membership function. The prototypes for the rules are computed by a clustering algorithm, and the model output parameters are computed as the solutions of a bounded quadratic optimization problem. In classification problems, the rules’ parameters are interpreted as the rules’ confidence. In regression problems, the rules’ parameters are used to derive rules’ confidences for classes that represent ranges of output variable values. The resulting model is evaluated based on a set of benchmark datasets for classification and regression problems. Nonparametric statistical tests were performed on the benchmark results, showing that the proposed approach produces compact fuzzy models with accuracy comparable to models produced by the standard modeling approaches. The resulting model is also exploited from the interpretability point of view, showing how the rule weights provide additional information to help in data and model understanding, such that it can be used as a decision support tool for the prediction of new data.     

基于GMDH的LSSVM预测模型及其实证

自从Suykens提出新型统计理论学习方法-最小二乘支持向量机(LSSVM)以来,这种方法引起了广泛的关注,它在预测方面的良好性能得到了广泛应用.应用自组织数据挖掘(GMDH)方法改进LSSVM,提升了预测精度.首先利用GMDH方法选择有效的输入变量,再将这些变量作为LSSVM模型的输入,进行时间序列的预测,从而建立LSSVM和GMDH组合的混合模型GLSSVM.并通过汇率时间序列对本文模型进行了实证.结果表明,混合模型预测精度得到了明显的提高.     

Dynamics of fuzzy impulsive bidirectional associative memory neural networks with time-varying delays

Complex nonlinear systems can be represented to a set of linear sub-models by using fuzzy sets and fuzzy reasoning via ordinary Takagi-Sugeno (TS) fuzzy models. In this paper, the exponential stability of TS fuzzy bidirectional associative memory (BAM) neural networks with impulsive effect and time-varying delays is investigated. The model of fuzzy impulsive BAM neural networks with time-varying delays established as a modified TS fuzzy model is new in which the consequent parts are composed of a set of impulsive BAM neural networks with time-varying delays. Further the exponential stability for fuzzy impulsive BAM neural networks is presented by utilizing the Lyapunov-Krasovskii functional and the linear matrix inequality (LMI) technique without tuning any parameters. In addition, an example is provided to illustrate the applicability of the result using LMI control toolbox in MATLAB.     

A method for solving fuzzy goal programming problems based on MINMAX approach

Narasimhan incorporated fuzzy set theory within goal programming formulation in 1980. Since then numerous research has been carried out in this field. One of the well-known models for solving fuzzy goal programming problems was proposed by Hannan in 1981. In this paper the conventional MINMAX approach in goal programming is applied to solve fuzzy goal programming problems. It is proved that the proposed model is an extension to Hannan model that deals with unbalanced triangular linear membership functions. In addition, it is shown that the new model is equivalent to a model proposed in 1991 by Yang et al. Moreover, a weighted model of the new approach is introduced and is compared with Kim and Whang’s model presented in 1998. A numerical example is given to demonstrate the validity and strengths of the new models.     

基于观测器的模糊Delta算子系统的控制器设计

对于非线性模糊系统控制器和观测器的分析和设计,提出一种统一方法。利用Delta域离散T—S模糊模型对非线性系统建模,并基于李雅普诺夫稳定性理论给出模糊状态反馈控制器和观测器的设计策略,将所得结果归结为求解一组线性矩阵不等式。同时结论表明:分离性原理对Delta算子T—S模糊系统仍然成立。所得结果可将现有关于连续和离散T—S模糊系统的相关结论统一于Delta算子框架内。     

Stock market forecasting by using a hybrid model of exponential fuzzy time series

The initial aim of this study is to propose a hybrid method based on exponential fuzzy time series and learning automata based optimization for stock market forecasting. For doing so, a two-phase approach is introduced. In the first phase, the optimal lengths of intervals are obtained by applying a conventional fuzzy time series together with learning automata swarm intelligence algorithm to tune the length of intervals properly. Subsequently, the obtained optimal lengths are applied to generate a new fuzzy time series, proposed in this study, named exponential fuzzy time series. In this final phase, due to the nature of exponential fuzzy time series, another round of optimization is required to estimate certain method parameters. Finally, this model is used for future forecasts. In order to validate the proposed hybrid method, forty-six case studies from five stock index databases are employed and the findings are compared with well-known fuzzy time series models and classic methods for time series. The proposed model has outperformed its counterparts in terms of accuracy.     

Estimation of parameters in latent class models using fuzzy clustering algorithms

A mixture approach to clustering is an important technique in cluster analysis. A mixture of multivariate multinomial distributions is usually used to analyze categorical data with latent class model. The parameter estimation is an important step for a mixture distribution. Described here are four approaches to estimating the parameters of a mixture of multivariate multinomial distributions. The first approach is an extended maximum likelihood (ML) method. The second approach is based on the well-known expectation maximization (EM) algorithm. The third approach is the classification maximum likelihood (CML) algorithm. In this paper, we propose a new approach using the so-called fuzzy class model and then create the fuzzy classification maximum likelihood (FCML) approach for categorical data. The accuracy, robustness and effectiveness of these four types of algorithms for estimating the parameters of multivariate binomial mixtures are compared using real empirical data and samples drawn from the multivariate binomial mixtures of two classes. The results show that the proposed FCML algorithm presents better accuracy, robustness and effectiveness. Overall, the FCML algorithm has the superiority over the ML, EM and CML algorithms. Thus, we recommend FCML as another good tool for estimating the parameters of mixture multivariate multinomial models.     

正权重组合预测模型及其在经济中的应用

介绍了组合预测的方法,并利用最优组合和递归方差倒数方法对组合预测方法进行改进;提出通过GMDH方法首先对影响经济预测模型的各变量进行筛选然后再建立回归模型、神经网络模型等单项预测模型的思想;最后结合GMDH方法建立的时间序列模型,建立正权重组合预测模型．     

A robust data envelopment analysis model with different scenarios

Input and output data, under uncertainty, must be taken into account as an essential part of data envelopment analysis (DEA) models in practice. Many researchers have dealt with this kind of problem using fuzzy approaches, DEA models with interval data or probabilistic models. This paper presents an approach to scenario-based robust optimization for conventional DEA models. To consider the uncertainty in DEA models, different scenarios are formulated with a specified probability for input and output data instead of using point estimates. The robust DEA model proposed is aimed at ranking decision-making units (DMUs) based on their sensitivity analysis within the given set of scenarios, considering both feasibility and optimality factors in the objective function. The model is based on the technique proposed by Mulvey et al. (1995) for solving stochastic optimization problems. The effect of DMUs on the product possibility set is calculated using the Monte Carlo method in order to extract weights for feasibility and optimality factors in the goal programming model. The approach proposed is illustrated and verified by a case study of an engineering company.     

一种基于新的区间二型梯形模糊相似测度的多属性群决策方法

本文首先基于区间二型梯形模糊数的周长、面积、负指数距离提出了一种新的区间二型梯形模糊相似测度,讨论了其性质。其次,基于该相似测度公式分别构建了区间二型梯形模糊专家权重和属性权重确定模型,然后通过集结区间二型梯形模糊决策信息与权重信息,给出了一种基于该相似测度的群决策方法。最后,通过投资方案选择实例说明了该方法的合理性和有效性。     

基于2-可加模糊测度的NPD项目复杂性评价

针对NPD项目复杂性各因素间具有的关联性以及传统评价方法的局限性,提出一种基于关联多属性的2-可加模糊测度方法来对NPD项目复杂性进行评价。在界定项目复杂性内涵的基础上,从产品复杂性、环境复杂性、组织复杂性和技术复杂性四个方面构建了NPD项目复杂性评价指标体系。从模糊测度、默比乌斯变换和交互作用系数间的转化关系出发,基于最大Marichal熵原则,提出了一种确定2-可加模糊测度值的新方法。利用Choquet积分作为集结算子,自下而上计算各候选方案的综合评价值。最后,通过具体算例说明了该方法的可行性和有效性。     

基于自组织理论的GMDH神经网络算法及应用

本文在自组织控制论的基础上提出了成组数据处理的神经网络算法— GMDH算法 ,通过寻找最优复杂性 ,实现变量的自动筛选并得到明确的模型结构 .文章还给出了 GMDH网络用于分析和预测四川省电力需求状况的一个实例