A fuzzy system modeling algorithm for data analysis and approximate reasoning

In this paper a new fuzzy system modeling (FSM) algorithm is introduced as a data analysis and approximate reasoning tool. The performance of the proposed algorithm is tested in two different data sets and compared with some well-known algorithms from the literature. In the comparison two benchmark data sets from the literature, namely the automobile mpg (miles per gallon) prediction and Box and Jenkins gas-furnace data are used. The comparisons demonstrated that the proposed algorithm can be successfully applied in system modeling.     

A new version of Kovarik’s approximate orthogonalization algorithm without matrix inversion

In 1970 Kovarik proposed approximate orthogonalization algorithms. One of them (algorithm B) has quadratic convergence but requires at each iteration the inversion of a matrix of similar dimension to the initial one. An attempt to overcome this difficulty was made by replacing the inverse with a finite Neumann series expansion involving the original matrix and its adjoint. Unfortunately, this new algorithm loses the quadratic convergence and requires a large number of terms in the Neumann series which results in a dramatic increase in the computational effort per iteration. In this paper we propose a much simpler algorithm which, by using only the first two terms in a different series expansion, gives us the desired result with linear convergence. Systematic numerical experiments for collocation and Toeplitz matrices are also described.     

Stability connection between sampled-data fuzzy control systems with quantization and their approximate discrete-time model

This paper concerns the stability of a sampled-data Takagi-Sugeno (T-S) fuzzy control system with quantization, when a controller design is based on an approximate discrete-time model of the plant without quantization. The motivations come from the facts that digital devices for interfacing a plant with a controller quantize signals and an exact discrete-time model of the T-S fuzzy system is generally not amenable to synthesis process. We show that the concerned system is Lagrange stabilizable by the controller asymptotically stabilizing the approximate discrete-time model. A constructive design algorithm for the developed stability analysis is proposed in terms of linear matrix inequalities.     

基于计算型模糊推理算法的模糊控制器设计

针对传统模糊推理算法在推理过程中容易忽略部分推理信息,模糊规则一旦确定就难以调整的缺点,提出一种基于数值计算的模糊推理算法。算法采用数值计算的方法对推理过程进行了改进,这种改进能够充分考虑所有输入的影响,又能根据输入的变化,对模糊规则进行适当的调整。基于该算法的模糊控制器能够大大提高控制性能和精度,减小稳态误差。通过对直流电动机的仿真控制效果表明,该控制器比传统模糊控制器的控制性能好,精度高,抗干扰能力强。     

基于模糊近似推理的Vague集双向近似推理方法

给出由有限论域上的Vague集导出的分拆真模糊向量和分拆非假模糊向量的定义。进而得到Vague集近似推理的真近似推理模型和非假近似推理模型。最后得到Vague集正向近似推理结论和逆向近似推理结论。实例表明这种Vague集双向近似推理方法是可行的。     

A parametrized model of seasonal temperature changes in lakes

A one-dimensional model of the heat regime in a reservoir is described, based on a parametric representation of the vertical temperature structure in the form of an homogeneous mixed layer and an underlying thermocline. The self-similar expressions of the type suggested by Kitaigorodski and Miropolski (1970) and refined by Mälkki and Tamsaly (1985) are used for the latter. The thickness of the mixed layer is determined in the following way: at a very small heat flux into water — in accordance with the classical Rossby-Montgomery formula; at large values of stabilizing heating — in accordance with the formula derived by Zilitinkevich (1972); in the case of convection — with the help of the Driedonks and Tennekes equation (1984). The model is intended for calculation of the temporal evolution of temperature and the bulk characteristics of turbulent mixing (thickness of the upper homogeneous layer, friction velocity, convective velocity scale) in any natural lake or man-made reservoir under the following conditions:

• 1.(a) the horizontal extent of a reservoir is not so great as to generate significant climatic differences between various parts of the water area and at the same time it is not so small as to negate the assumption of horizontally homogeneous wind-induced mixing;
• 2.(b) the lake depth does not exceed a hundred metres (in which case Eqaations (5) and (17) for the temperature profile at z >h are not applicable);
• 3.(c) currents due to inflowing and outflowing rivers and streams are not large enough to affect significantly the turbulence regime;
• 4.(d) the major part of the basin has a more or less horizontal bottom.

The results of the model verification and the example of its prognostic applications are presented.     

基于预测模型的传感器网络近似数据采集算法

基于模型的数据采集技术可以有效抑制不必要的数据传输,节省能量开销,已经在传感器网络中得到广泛应用。对传统基于模型的数据采集进行了改进,提出基于卡尔曼滤波器的近似数据采样算法ADCA。ADCA可以在一定误差范围内有效获取数据。空间相近的节点被组织成簇,簇头和成员分别建立卡尔曼滤波模型,并保存对方的镜像模型。簇头节点可以为成员节点产生近似的数据,所以用户查询可以通过簇头来回答。实验表明ADCA具有较好的性能。     

Bayesian inversion of imaging spectrometer data using a fuzzy geological outcrop model

In geological remote sensing, in particular when studying the Earth with use of high spectral resolution sensors (so-called imaging spectrometers), ‘mineral maps' are the outcome of the image processing. Such mineral maps portray the spatial arrangement of classes of surface mineralogy derived from a comparison between known mineral signatures from spectral libraries and unknown (imaged in the hyperspectral domain) pixel spectra. With this information, geologists can build up a geological model of an area. Here, the reverse approach is advocated by introducing the geological model (where geology is converted to physical measurements by introducing spectra) at the start of the hyperspectral processing chain. This model is refined in an iterative way by comparing its mismatch with the observed reflectance measurements. Hence, a (geophysical) inversion of the hyperspectral dataset to a geological model is done. In a previous article explaining the physics and mathematics of the Bayesian inversion techniques, a ‘rigid geological model’ was used. Although the model takes on the advantage of including spatial arrangement and contextual information, hard field evidence is not included. Here an extension to this model is presented in the form of a ‘fuzzy outcrop geological model’. It is shown that the fuzzy outcrop model, which uses known outcrops and inferred outcrop patterns, outperforms the rigid geological model.     

A fuzzy clustering algorithm enhancing local model interpretability

In this work, simple modifications on the cost index of particular local-model fuzzy clustering algorithms are proposed in order to improve the readability of the resulting models. The final goal is simultaneously providing local linear models (reasonably close to the plant’s Jacobian) and clustering in the input space so that desirable characteristics (regarding final model accuracy, and convexity and smoothness of the cluster membership functions) are improved with respect to other proposals in literature. Some examples illustrate the proposed approach.     

基于模糊SVM模型的入侵检测分类算法

为解决入侵检测分类遇到的训练样本数量少、分类准确率低的问题,提出基于模糊支持向量机的多级分类机制。该分类机制训练模糊SVM模型将数据粗分为正常与攻击大类,采用DBSCAN算法产生细分模型进行攻击子集的自动聚类,将有关数据细分得到攻击的具体细类。在机制设计中,优化了隶属度函数的计算、设计了数据标准化与归一化等过程,并训练了高效分类器。实验表明,针对网络入侵检测数据中常见的孤立点干扰、噪声多,并且负样本占比多的网络业务数据集,新算法在保持分类准确率高的前提下,分类过程的计算时间较短。     

可变直觉模糊多粒度粗糙集模型及其近似分布约简算法

为了在多粒度粗糙集模型中对目标概念达到更好的近似逼近效果,首先将直觉模糊粗糙集与多粒度粗糙集结合,提出直觉模糊多粒度粗糙集模型。由于该模型的目标近似存在过于宽松的缺陷,因此通过引入参数的方式对所提模型进行改进,提出一种可变直觉模糊多粒度粗糙集模型,并证明了该模型的有效性,同时基于该模型提出了相应的近似分布约简算法。在仿真实验结果中,所提出的下近似分布约简结果比已提出的模糊多粒度决策理论粗糙集约简和多粒度双量化决策理论粗糙集多了2~4个属性,所提出的上近似分布约简算法比这些算法少了1~5个属性,同时约简结果的近似精度拥有了更为合理且优越的表现。因此,理论和实验结果均验证了所提的可变直觉模糊多粒度粗糙集模型在近似逼近和数据降维方面均具有更高的优越性。     

Application of fuzzy Naive Bayes and a real-valued genetic algorithm in identification of fuzzy model

We present a method to identify a fuzzy model from data by using the fuzzy Naive Bayes and a real-valued genetic algorithm. The identification of a fuzzy model is comprised of the extraction of “if–then” rules that is followed by the estimation of their parameters. The involved parameters include those which determine the membership function of fuzzy sets and the certainty factors of fuzzy if–then rules. In our method, as long as the fuzzy partition in the input–output space is given, the certainty factor of each rule is computed with the fuzzy conditional probability of the consequent conditioned on the antecedent by using the fuzzy Naive Bayes, which is a generalization of Naive Bayes. The fuzzy model involves the rules characterized by the highest values of certainty factors. The certainty factor of each rule is the fuzzy conditional probability, and it reflects the inner relationship between the antecedent and the consequent. In order to improve the accuracy of the fuzzy model, the real-valued genetic algorithm is incorporated into our identification process. This process concerns the optimization of the membership functions occurring in the rules. We just involve the parameters of membership function of the fuzzy sets into the real-valued genetic algorithm, since the certainty factor of each rule can be computed automatically. The performance of the model is shown for the backing-truck problem and the prediction of Mackey–Glass time series.     

直觉模糊近似推理中的可信度传播

针对直觉模糊近似推理中的可信度传播,提出计算结论可信度的相关算法。首先介绍了可信度因子的概念,分析了规则中的可信度因子传播对结论可信度的影响。然后针对直觉模糊近似推理的三种基本模式（取式、拒式、假言式）,给出了计算结论可信度值的相关公式,最后通过实例验证了算法的正确性。     

Averaging linguistic truth values in fuzzy approximate reasoning

The properties of a new rule for fuzzy conditional inference are presented and discussed. The rule is based on the extended mean operator defined on fuzzy numbers. The related propositions have the form “X is A is τ,” where τ is an element of the term set of the linguistic variable truth. The results obtained via the rule match with Fukami's and with the critical analysis carried out by Mizumoto and Zimmermann about the generalized modus ponens. © 1998 John Wiley & Sons, Inc.     

基于加权相似性测度的直觉模糊近似推理

在可信度传播的基础上,提出一种加权相似性测度的直觉模糊近似推理方法.运用实例分析现有典型方法的不足,针对带有可信度因子的直觉模糊近似推理的3种形式,综合研究了直觉模糊集隶属度、非隶属度和犹豫度对相似性测度的影响,给出一种考虑权重的相似性测度方法,并将其运用到直觉模糊近似推理中.通过实例以及与同类推理算法比较,结果表明了该推理算法的合理性和可行性.     

一种改进的多边形近似算法

多边形近似是曲线矢量数据压缩技术中的一种,其实质是多边形信息压缩问题,目的在于减少多边形曲线数据的冗余信息,释放所占用的空间,达到高效、快速地显示图形。通过分析基于显著点删除的多边形近似算法的特性,发现基于显著点删除算法由于没有考虑多边形与多边形之间的联系以及多边形中特殊点的问题,以至于在处理具有孤立点等情况时的多边形近似效果不理想。为了更好地解决上述缺陷,提出了一种改进的多边形近似算法。通过分析现有算法,发现在处理特殊孤立点、边界处裂缝、多点处于同一直线时处理效果不理想,针对这些问题,通过孤立点单独处理、边界点建立索引以及根据多边形形状忽略处于同一直线上的多点方法,对算法进行改进。同时利用数据集对改进算法性能进行分析,实验结果表明,改进的算法在多边形近似处理效率和效果上更加明显。     

遗传算法在模糊模型参数辨识中的应用

介绍了T-S模糊模型的建模过程,在现有T-S模糊模型参数辨识方法的基础上,提出了一种先应用最小二乘法对结论参数进行粗略辨识,以确定参数的大致范围之后,再应用遗传算法对前提参数和结论参数同时优化的参数辨识方法,通过MATLAB对本算法进行了仿真,并对非线性函数进行了逼近实验,所取得的结果令人满意。     

基于目标函数的模糊模型一体化建模

基于模糊集合的模糊模型, 利用模糊推理规则描述复杂、病态、非线性系统是一种有效方法. 本文提出了利用目标函数确定非线性系统的结构和参数的方法. 首先, 通过Gustafson-Kessel(GK)模糊聚类确定模型结构. 然后, 通过目标函数与参数估计一起进行递推计算, 进而实现对模糊模型结构简化, 删除冗余规则. 结构确定过程中采用了UD矩阵分解方法, 大大降低了计算量. 仿真结果证明了提出方法的有效性.     

扩展T-S模糊模型的PSO神经网络优化算法

针对机械设备具有模糊性和非线性的特点,提出了一种利用扩展T-S模糊模型的,自适应PSO算法和BP神经网络相结合的新型智能结构优化算法。通过自适应的高斯函数来更改基本T-S模糊模型中的隶属度函数,进而使用扩展的T-S模糊模型来调整PSO算法的参数。以BP 神经网络隐含层神经元数目为设计变量,提取训练后的均方误差作为评价函数,用改进后的粒子群算法进行寻优。把优化后的网络模型应用于轮盘结构优化中,实验表明,该方法在保证轮盘性能的同时,对其结构进行了重新优化,是一种可行的结构优化方法。     

On fuzzy modeling using fuzzy neural networks with theback-propagation algorithm

A fuzzy modeling method using fuzzy neural networks with the backpropagation algorithm is presented. The method can identify the fuzzy model of a nonlinear system automatically. The feasibility of the method is examined using simple numerical data.