Mamdani模糊系统I/O关系的表示及隶属函数优化

探讨一类高效率Mamdani模糊系统隶属函数优化方法.首先通过严密的理论分析将MISO(多输入单输出)_Mamdani模糊系统的输入/输出函数表示成系统隶属函数的局部线性表达式;论证了这个表达式中系统隶属函数项的系数仅由该点所对应的2p个隶属函数值,按大小排成的序列决定.以此为基础,提出了根据输入/输出样本集误差对系统隶属函数进行优化的新方法.该方法近似地将隶属函数优化问题转换成一组线性规划问题进行求解.本文提供的仿真结果也进一步证实了该方法的有效性.     

一种新的自适应模糊系统

提出应用B-Spline函数为隶属函数的自适应模糊系统，该系统将B-Spline和ANFIS两有机地结合在一起，取长补短，达到简捷的隶属函数自寻优。研究结果表明，该方法运算速度快、系统的逼近误差小、精度高、简单易行，非常适合于隶属函数的在线优化。     

一种基于聚类的超闭球模糊神经网络

针对一类不确定非线性多输入多输出复杂系统,根据系统的输入输出数据对,提出一种基于聚类的超闭球模糊神经网络系统．该系统通过改进的模糊聚类方法（FCM）确定模糊规则数,采用高维隶属度函数取代常规的单维隶属度函数,并对隶属度函数中心值和隶属度函数参数采用一步通过算法,所提方法可降低系统的模糊规则数,简化网络计算．此外,当系统的输入输出发生变化时,可实现模糊规则库的在线修改．仿真实例验证了所提方法的有效性．     

基于混合聚类算法的模糊函数系统辨识方法

针对传统模糊系统存在的结构难以确定和参数辨识复杂的问题,提出了一种基于混合聚类算法的模糊函数系统辨识算法.与一般的模糊函数系统相比,混合聚类算法结合模糊C均值和模糊C回归模型聚类算法的样本距离.在模型预测部分,采用高斯函数计算每个输入变量的隶属度,利用输入变量隶属度的模糊化算子得到输入向量的隶属度.应用于Box-Jenkins煤气炉数据、一个双入单出的非线性系统和Mackey-Glass混沌时间序列数据的试验结果表明,本文算法具有很好的辨识效果,从而验证了本文算法的有效性与实用性.     

一种基于模糊规则的神经网络结构及其学习算法研究

文章提出了一种基于模糊规则的神经网络结构,并用形式化语言进行描述。基于模糊规则的神经网络由输入层、规则层和输出层三层网络结构组成,以隶属度函数（语义值）作为网络权值,输入值沿权值的传播即进行隶属度计算。在充分分析三角形函数特征的基础上,应用启发式方法,导出了FRBNN网络的学习算法。最后应用FRBNN评价船舶碰撞危险度,表明FRBNN兼备神经网络和模糊推理系统的优点。     

基于目标多特征的mass函数确定方法

针对D-S证据理论在目标识别中mass函数难以获取的问题,提出一种基于目标多特征的mass函数确定方法,该方法首先利用模糊理论中的隶属函数确定目标的特征隶属度矩阵,然后根据特征隶属度矩阵计算mass函数确定过程中各特征的可信度,最后把各特征的隶属度值和可信度转化成mass函数。仿真结果表明,该方法获取的mass函数具有很好的可靠性和抗干扰性。     

基于模糊证据理论算法在火灾检测中的应用

在复杂多变的火灾检测环境中,针对传统火灾检测方式准确率不高,适应性较差的问题。将模糊集合和D-S证据推理有机结合,提出一种新的用于火灾检测的多传感器数据融合的方法。该方法首先利用火焰、烟雾和温度传感器感知火灾状态,然后根据给出模糊隶属函数计算各个传感器的模糊隶属度。为了增强系统的抗干扰性,引入了计算传感器可信度的方法,并根据每次测量隶属度和可信度转化为基本概率分配函数(mass函数),最后利用证据理论对一个周期内多次测量的信息进行融合。结果表明,该方法提高了火灾检测判别的准确率,克服单个传感器带来的不稳定性和不确定性,增强了火灾检测系统的鲁棒性。     

自适应神经网络模糊推理系统最优参数的研究

模糊规则的提取和隶属度函数的学习是模糊系统设计中重要而困难的问题。自适应神经网络模糊推理系统（ANFIS）能基于数据建模，无须专家经验，自动产生模糊规则和调整隶属度函数。在建立一个初始系统进行训练时，其隶属度函数的类型、隶属度函数的数日以及训练次数都是待定的，这三个参数的选择直接影响系统训练后的效果，它们的确定方法有待研究。该文应用自适应神经网络模糊推理系统的方法对一个典型系统进行建模仿真，并阐述这三个参数的寻优方法。     

基于模糊模式识别的场景图像分类方法

为解决装甲车车载图像跟踪系统中对场景进行分类的问题．提出了一种根据模糊模式识别原理对场景图像进行分类的方法。首先通过建立场景图像的特征向量来对场景进行描述，并根据所选特征参数设计了矢量隶属函数，然后通过计算隶属函数的值来对场景图像进行分类。实验证明，场景分类的结果对跟踪系统中目标提取方法的选取，有较好的指导作用。     

T-S模糊系统的二次稳定

应用LMI(线性矩阵不等式)方法,研究了T-S模糊系统二次稳定性及控制器设计问题.首先,通过考虑模糊系统隶属函数的性质,将原系统进行变换,给出了T-S模糊系统二次稳定的新条件,并提出了基于LMI的控制器设计方法.与现有结果相比,该方法不仅考虑了各子系统间的关系,还考虑到隶属函数的性质,计算量和保守性较小.仿真算例验证了其有效性.     

模糊神经网络变幅液压系统故障诊断

针对变幅液压系统复杂性、不确定性、模糊性的特点,提出基于故障树的模糊神经网络作为变幅液压系统故障诊断的方法。该方法利用故障树知识提取变幅液压系统故障诊断的输入变量和输出变量,引入模糊逻辑的概念,采用模糊隶属函数来描述这些故障的程度,利用Levenberg-Marquardt优化算法对神经网络进行训练,系统推理速度快,容错能力强,并通过实例分析验证了变幅液压系统模糊神经网络故障诊断的有效性。     

Direct adaptive fuzzy control with membership function tuning

In this paper, a direct self‐structured adaptive fuzzy control is introduced for the class of nonlinear systems with unknown dynamic models. Control is accomplished by an adaptive fuzzy system with a fixed number of rules and adaptive membership functions. The reference signal and state errors are used to tune the membership functions and update them instantaneously. The Lyapunov synthesis method is also used to guarantee the stability of the closed loop system. The proposed control scheme is applied to an inverted pendulum and a magnetic levitation system, and its effectiveness is shown via simulation. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

基于遗传算法的模糊控制器的优化设计——采用模糊数据挖掘技术

论文为模糊系统建模提出了一种新颖的方法——由输入输出数据集合设计基于遗传算法的模糊控制器,该方法采用模糊数据挖掘技术,从大量的输入输出数据集合中自动地提取模糊规则模型,确定模糊分割点及各变量的隶属度函数;并利用实数编码的遗传算法RGA对隶属度函数参数进行全面优化。最后通过实例及仿真验证了该方法的有效性。     

A Genetic Approach for Simultaneous Design of Membership Functions and Fuzzy Control Rules

Based on the genetic algorithm (GA), an approach is proposed for simultaneous design of membership functions and fuzzy control rules since these two components are interdependent in designing a fuzzy logic controller (FLC). With triangular membership functions, the left and right widths of these functions, the locations of their peaks, and the fuzzy control rules corresponding to every possible combination of input linguistic variables are chosen as parameters to be optimized. By using a proportional scaling method, these parameters are then transformed into real-coded chromosomes, over which the offspring are generated by rank-based reproduction, convex crossover, and nonuniform mutation. Meanwhile, the concept of enlarged sampling space is used to expedite the convergence of the evolutionary process. To show the feasibility and validity of the proposed method, a cart-centering example will be given. The simulation results will show that the designed FLC can drive the cart system from any given initial state to the desired final state even when the cart mass varies within a wide range.     

PROPOSAL OF AN INTERPOLATIVE FUZZY INFERENCE METHOD

In this paper, we propose an interpolative fuzzy inference method, in which the fuzzy relation is represented by the membership functions of the antecedent and consequent parts. The strong point of this method is that the membership function of an inferred conclusion has a simple shape and thus its meaning can be interpreted easily. Firstly, the proposed method is explained, and then it is applied to fuzzy modeling of distributed data. From the modeling result, it was found that the method performed as a possibility distribution model. The proposed method is expected to be effective on a human supervised system, in which a human being takes any action according to the interpretation of a fuzzy inferred conclusion.     

Fine Tuning Of Membership Functions For Fuzzy Neural Systems

This paper presents a new method for fine‐tuning the Gaussian membership functions of a fuzzy neural network ( FNN ) to improve approximation accuracy. This method results in special shape membership functions without the convex property. We first recall that any continuous function can be represented by a linear combination of Gaussian functions with any standard deviation. Therefore, the Gaussian membership function in the second layer of the FNN can be replaced by several small Gaussian functions; the weighting vectors of this new network (called FNN₅ ) can then be updated using the backpropagation algorithm. The proposed method can adapt proper membership functions for any nonlinear input/output mapping to achieve highly accurate approximation. Convergence analysis shows that the weighting vectors of the FNN₅ eventually converge to the optimal values. Simulation results indicate that (a) this approach improves approximation accuracy, and (b) that the number of rules can be reduced for any given level of accuracy. For the purpose of illustrating the proposed method, the FNN₅ is also applied to tune PI controllers such that gain and phase margins of the closed‐loop system achieve the desired specifications.     

On the influence of using fuzzy extensions in linguistic fuzzy rule-based regression systems

Fuzzy Rule-Based Systems, FRBSs, are powerful tools to address regression problems. They can model the relationship between inputs and outputs by linguistic concepts. However, those FRBSs which are based on the conventional Type-1 fuzzy sets may not be able to handle some difficulties of real-world applications. In such situations, using novel representations of fuzzy sets seems like a good idea. Different extensions of fuzzy sets usually help to provide more precise models in the real-world problems. In this study, the influence of using fuzzy extensions in improving the efficiency of linguistic fuzzy rule-based regression models is investigated. For this purpose, a conventional Type-1 Mamdani FRBS is adapted to the three extensions of fuzzy sets, namely Interval Type-2, Intuitionistic, and Interval Type-2 Intuitionistic fuzzy sets. A two-pass method is proposed to define membership (non-membership) functions of these fuzzy sets; this method is based on the 3-tuples representation of the standard Type-1 membership functions. Wang and Mendel’s rule learning method is adapted to extract fuzzy rules from regression data. In order to tune the membership functions up to different extents, three evolutionary extensions are also presented for each type of the proposed FRBSs. Individual, internal, and external comparisons of the proposed FRBSs were done using 22 real-world regression datasets and statistical tests. Experimental results confirm that all the three proposed FRBSs outperform the classical Type-1 framework; furthermore, the Interval Type-2 Intuitionistic FRBS is the superior system so that an appropriate tuning of its parameters makes it the most accurate model.     

Fuzzy system reliability evaluation using time-dependent intuitionistic fuzzy set

In general, fuzzy sets are used to analyse the system reliability. In this article, the concept of fuzzy set is extended by the idea of intuitionistic fuzzy set (IFS) and a new general procedure is proposed to construct the membership and non-membership functions of the fuzzy reliability using time-dependent IFS. Here, failure rate function of the system is represented by a triangular intuitionistic fuzzy number (IFN). Also, using proposed approach, membership and non-membership functions of fuzzy reliability of series and parallel systems are constructed, where the failure rate of each component is taken as a time-dependent triangular IFN. The major advantage of using IFS over fuzzy sets is that IFS separate the positive and negative evidences for membership of an element in the set. Numerical examples are given to illustrate the proposed approach.     

Granular type-2 membership functions: A new approach to formation of footprint of uncertainty in type-2 fuzzy sets

In this study, a new approach for the formation of type-2 membership functions is introduced. The footprint of uncertainty is formed by using rectangular type-2 fuzzy granules and the resulting membership function is named as granular type-2 membership function. This new approach provides more degrees of freedom and design flexibility in type-2 fuzzy logic systems. Uncertainties on the grades of membership functions can be represented independently for any region in the universe of discourse and free of any functional form. So, the designer could produce nonlinear, discontinuous or hybrid membership functions in granular formation and therefore could model any desired discontinuity and nonlinearity. The effectiveness of the proposed granular type-2 membership functions is firstly demonstrated by simulations done on noise corrupted Mackey–Glass time series prediction. Secondly, flexible design feature of granular type-2 membership functions is illustrated by modeling a nonlinear system having dead zone with uncertain system parameters. The simulation results show that type-2 fuzzy logic systems formed by granular type-2 membership functions have more modeling capabilities than the systems using conventional type-2 membership functions and they are more robust to system parameter changes and noisy inputs.