Enhanced Fuzzy System Models With Improved Fuzzy Clustering Algorithm

Although traditional fuzzy models have proven to have high capacity of approximating the real-world systems, they have some challenges, such as computational complexity, optimization problems, subjectivity, etc. In order to solve some of these problems, this paper proposes a new fuzzy system modeling approach based on improved fuzzy functions to model systems with continuous output variable. The new modeling approach introduces three features: i) an improved fuzzy clustering (IFC) algorithm, ii) a new structure identification algorithm, and iii) a nonparametric inference engine. The IFC algorithm yields simultaneous estimates of parameters of c-regression models, together with fuzzy c-partitioning of the data, to calculate improved membership values with a new membership function. The structure identification of the new approach utilizes IFC, instead of standard fuzzy c-means clustering algorithm, to fuzzy partition the data, and it uses improved membership values as additional input variables along with the original scalar input variables for two different choices of regression methods: least squares estimation or support vector regression, to determine ldquofuzzy functionsrdquo for each cluster. With novel IFC, one could learn the system behavior more accurately compared to other FSM models. The nonparametric inference engine is a new approach, which uses the alike -nearest neighbor method for reasoning. Empirical comparisons indicate that the proposed approach yields comparable or better accuracy than fuzzy or neuro-fuzzy models based on fuzzy rules bases, as well as other soft computing methods.     

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。     

基于VISIT算法设计模糊分类器的进化方法

介绍了在没有数据分布先验知识的情况下,用进化方法直接从训练数据中建立紧致模糊分类系统的方法。使用VISIT算法获取每个个体模糊系统,再用遗传算法从中搜索最优的模糊系统。规则和隶属函数是在进化过程中自动建立和优化的。为了同时有效地评价系统的精度和紧致性,用一个模糊专家系统作适应度函数。在2个基准分类问题上的实验结果表明了新方法的有效性。     

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.     

Resolving semantic inconsistencies in elibrary.ru based on fuzzy inference

An approach to solving semantic inconsistency problems in critical information systems based on the generation of the fuzzy rules database and further application of the Mamdani fuzzy inference scheme is proposed. The approach is considered with the electronic library elibrary.ru taken as an example. The composition of the compared fields and form of membership functions for input linguistic variables are validated. Examples of resolving inconsistencies for making a decision on the possibility of attributing a specific publication or reference to it to a particular category (new or already available publication) are presented.     

基于直觉模糊推理的威胁评估改进算法

针对实战系统中的威胁评估问题,提出一种基于直觉模糊推理的改进算法。设计系统状态变量的三角型隶属度和非隶属度函数,给出详细的计算步骤,将包含可信度的推理规则植入评估系统,当系统有输入时,即可进行威胁评估值的直觉模糊推理计算。实战数据仿真结果证明了该算法的有效性。     

Multistage fuzzy inference formulated as linguistic-truth-valuepropagation and its learning algorithm based on back-propagating errorinformation

Multistage fuzzy inference, where in the consequence in an inference stage is passed to the next stage as a fact, is studied and formulated as a type of linguistic-truth-value propagation, based on a concept of linguistic similarities between conditional propositions in successive stages. The formulation is useful in studying the characteristics of multistage fuzzy inference and reveals its structural relationship to multilayer perceptrons. The learning algorithm for multistage fuzzy inference is then derived, using backpropagating error information. The algorithm provides a means of automatically training the multistage fuzzy inference network, using input-output exemplar patterns. Intermediate membership functions based on simulation results, which are generated automatically in the intermediate stage, are proposed. The intermediate stage fuzzy-classifies the input space using intermediate membership functions. In this way, intermediate membership functions provide information regarding regional characteristics in exemplar patterns     

Evolutionary design of a fuzzy classifier from data

Genetic algorithms show powerful capabilities for automatically designing fuzzy systems from data, but many proposed methods must be subjected to some minimal structure assumptions, such as rule base size. In this paper, we also address the design of fuzzy systems from data. A new evolutionary approach is proposed for deriving a compact fuzzy classification system directly from data without any a priori knowledge or assumptions on the distribution of the data. At the beginning of the algorithm, the fuzzy classifier is empty with no rules in the rule base and no membership functions assigned to fuzzy variables. Then, rules and membership functions are automatically created and optimized in an evolutionary process. To accomplish this, parameters of the variable input spread inference training (VISIT) algorithm are used to code fuzzy systems on the training data set. Therefore, we can derive each individual fuzzy system via the VISIT algorithm, and then search the best one via genetic operations. To evaluate the fuzzy classifier, a fuzzy expert system acts as the fitness function. This fuzzy expert system can effectively evaluate the accuracy and compactness at the same time. In the application section, we consider four benchmark classification problems: the iris data, wine data, Wisconsin breast cancer data, and Pima Indian diabetes data. Comparisons of our method with others in the literature show the effectiveness of the proposed method.     

模糊神经网络在非线性短期负荷预测中的应用

为提高负荷预测精度,提出了一种新的4层模糊神经网络短期负荷预测模型.该模型将模糊逻辑和神经网络的长处融合在一起,使模糊推理和解模糊均通过神经网络来实现.选取的隶属函数使神经网络权值有一定的知识表示意义,并通过模糊化层将输入特征量转化为模糊量.在模糊推理层提出了两种不同的算法来完成模糊推理,然后从中确定出模糊取小算法预测效果更好.最后在输出层通过适当的解模糊得到确切的预测输出值.仿真结果表明了该方法的有效性.     

Fuzzy functions with support vector machines

A new fuzzy system modeling (FSM) approach that identifies the fuzzy functions using support vector machines (SVM) is proposed. This new approach is structurally different from the fuzzy rule base approaches and fuzzy regression methods. It is a new alternate version of the earlier FSM with fuzzy functions approaches. SVM is applied to determine the support vectors for each fuzzy cluster obtained by fuzzy c-means (FCM) clustering algorithm. Original input variables, the membership values obtained from the FCM together with their transformations form a new augmented set of input variables. The performance of the proposed system modeling approach is compared to previous fuzzy functions approaches, standard SVM, LSE methods using an artificial sparse dataset and a real-life non-sparse dataset. The results indicate that the proposed fuzzy functions with support vector machines approach is a feasible and stable method for regression problems and results in higher performances than the classical statistical methods.     

The simplest fuzzy PID controllers: mathematical models and stability analysis

This paper reveals mathematical models for the simplest fuzzy PID controllers which employ two fuzzy sets for each of the three input variables and four fuzzy sets for the output variable. Mathematical models are derived via left and right trapezoidal membership functions for each input, singleton or triangular membership functions for output, algebraic product triangular norm, different combinations of triangular co-norms and inference methods, and center of sums (COS) defuzzification method. Properties of these structures are studied to examine their suitability for control application. For the structure which is suitable for control, bounded-input bounded-output (BIBO) stability proof is presented. An approach to design fuzzy PID controllers is given. Finally, some numerical examples along with their simulation results are included to demonstrate the effectiveness of the simplest fuzzy PID controllers.     

A structure identification method of submodels for hierarchical fuzzy modeling using the multiple objective genetic algorithm

Fuzzy models describe nonlinear input‐output relationships with linguistic fuzzy rules. A hierarchical fuzzy modeling is promising for identification of fuzzy models of target systems that have many input variables. In the identification, (1) determination of a hierarchical structure of submodels, (2) selection of input variables of each submodel, (3) division of input and output space, (4) tuning of membership functions, and (5) determination of fuzzy inference method are carried out. This article presents a hierarchical fuzzy modeling method with an uneven division method of input space of each submodel. For selecting input variables of submodels, the multiple objective genetic algorithm (MOGA) is utilized. MOGA finds multiple models with different input variables and different numbers of fuzzy rules as compromising solutions. A human designer can choose desirable ones from these candidates. The proposed method is applied to acquisition of fuzzy rules from cyclists' pedaling data. In spite of a small number of data, the obtained model was able to give detailed suggestions to each cyclist. © 2002 Wiley Periodicals, Inc.     

Environmental comprehensive assessment of agricultural systems at the farm level using fuzzy logic: A case study in cane farms in Iran

Development of a fuzzy inference model is a complex multi-step process in which we encounter a large number of parameters such as type and number of membership functions, fuzzy operators, defuzzification and implication methods and etc. There is currently very little literature on the topic of the best selection of parameters for development of expert based inference models. In this study we developed a fuzzy rule based model, which uses available farm management data as required inputs, for the environmental assessment of farming systems. We also tried to make an analysis on the efficiency of current mathematical parameters in the development of our fuzzy model. Finally, in a practical example we demonstrate the applicability of the developed model for improvement of environmental status of the cane farming in Iran.A Mamdani fuzzy inference model with two inference engines was developed to combine five basic input indexes, which were selected as indicators of farms environmental status based on the experts' interview and scientific knowledge. To validate the developed model, we inserted several cycles of analysis using graphical and global sensitivity methods on the model and compared the model outcomes with experts' viewpoints. Using these analysis methods, we also evaluated the effects of changes in operators, membership function shape and defuzzification methods, on the model outcomes and their sensitivities.In this study, fuzzy inference emerged as a suitable, uncomplicated and effective tool for development of environmental assessment models. Totally, performance of one parameter was highly influenced by other parameters. For the selection of one parameter its interaction with other parameters had to be considered. Type, shape and the number of membership functions were from the most effective parameters for development of the model and significantly influenced the other factors. Case study results showed that environmental indexes of sugarcane production can enhance between 37 and 59% using simple improving strategies.     

A NEURO‐FUZZY SYSTEM DESIGN METHODOLOGY FOR VIBRATION CONTROL

Fuzzy system has been known to provide a framework for handling uncertainties and imprecision by taking linguistic information from human experts. However, difficulties arise in determining effectively the fuzzy system configuration, i.e., the number of rules, input and output membership functions. A neuro‐fuzzy system design methodology by combining neural network and fuzzy logic is developed in this paper to adaptively adjust the fuzzy membership functions and dynamically optimize the linguistic‐fuzzy rules. The structure of a five‐layer feedforward network is shown to determine systematically the correct fuzzy logic rules, tune optimally (in the sense of local region) the parameters of the membership functions, and perform accurately the fuzzy inference. It is shown both numerically and experimentally that engineering applications of the neuro‐fuzzy system to vibration control have been very successful.     

Development of a systematic methodology of fuzzy logic modeling

This paper proposes a systematic methodology of fuzzy logic modeling for complex system modeling. It has a unified parameterized reasoning formulation, an improved fuzzy clustering algorithm, and an efficient strategy of selecting significant system inputs and their membership functions. The reasoning mechanism introduces 4 parameters whose variation provides a continuous range of inference operation. As a result, we are no longer restricted to standard extremes in any step of reasoning. The fuzzy model itself can then adjust the reasoning process by optimizing the inference parameters based on input-output data. The fuzzy rules are generated through fuzzy c-means (FCM) clustering. Major bottlenecks are addressed and analytical solutions are suggested. We also address the classification process to extend the derived fuzzy partition to the entire output space. In order to select suitable input variables among a finite number of candidates (unlike traditional approaches) we suggest a new strategy through which dominant input parameters are assigned in one step and no iteration process is required. Furthermore, a clustering technique called fuzzy fine clustering is introduced to assign the input membership functions. In order to evaluate the proposed methodology, two examples-a nonlinear function and a gas furnace dynamic procedure-are investigated in detail. The significant improvement of the model is concluded compared to other fuzzy modeling approaches     

Circuit implementation of linguistic-hedge fuzzy logic controller in current-mode approach

In this paper, a novel fuzzy logic controller called linguistic-hedge fuzzy logic controller in a mixed-signal circuit design is discussed. The linguistic-hedge fuzzy logic controller has the following advantages: 1) it needs only three simple-shape membership functions for characterizing each variable prior to the linguistic-hedge modifications; 2) it is sufficient to adopt nine rules for inference; 3) the rules are developed intuitively without heavy dependence on the endeavors of experts; 4) it performs better than conventional fuzzy logic controllers; and 5) it can be realized with a lower design complexity and a smaller hardware overhead as compared with the controllers that required more than nine rules. In this implementation, a current-mode approach is adopted in designing the signal processing portions to simplify the circuit complexity; digital circuits are adopted to implement the programmable units. This design was fabricated with a TSMC 0.35 /spl mu/m single-polysilicon-quadruple-metal CMOS process. In this chip, the LHFLC processes two input variables and one output variable. Each variable is specified using three membership functions. Nine inference rules, scheduled in a rule table with a dimension of 3 /spl times/ 3, define the relationship implications between these three variables. Under a supply voltage of 3.3 V, the measurement results show that the measured control surface and the control goal are consistent. The speed of inference operation goes up to 0.5M FLIPS that is fast enough for the control application of the cart-pole balance system. The cart-pole balance system experimental results show that this chip works with nine inference rules. Furthermore, by performing some off-chip modifications, such as shifting and scaling on the input signals and output signal of this design, according to the specifications defined by the controlled plants, this design is suitable for many control applications.     

Heuristic constraints enforcement for training of and ruleextraction from a fuzzy/neural architecture. II. Implementation andapplication

For part I, see ibid., p.143-50. This paper is the second of two companion papers. The foundations of the proposed method of heuristic constraint enforcement on membership functions for knowledge extraction from a fuzzy/neural architecture was given in Part I. Part II develops methods for forming constraint sets using the constraints and techniques for finding acceptable solutions that conform to all available a priori information Moreover, methods of integration of enforcement methods into the training of the fuzzy-neural architecture are discussed. The proposed technique is illustrated on a fuzzy-AND classification problem and a motor fault detection problem. The results indicate that heuristic constraint enforcement on membership functions leads to extraction of heuristically acceptable membership functions in the input and output spaces. Although the method is described on a specific fuzzy/neural architecture, it is applicable to any realization of a fuzzy inference system, including adaptive and/or static fuzzy inference systems     

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.     

Fuzzy functions with LSE

“Fuzzy Functions” are proposed to be determined by the least squares estimation (LSE) technique for the development of fuzzy system models. These functions, “Fuzzy Functions with LSE” are proposed as alternate representation and reasoning schemas to the fuzzy rule base approaches. These “Fuzzy Functions” can be more easily obtained and implemented by those who are not familiar with an in-depth knowledge of fuzzy theory. Working knowledge of a fuzzy clustering algorithm such as FCM or its variations would be sufficient to obtain membership values of input vectors. The membership values together with scalar input variables are then used by the LSE technique to determine “Fuzzy Functions” for each cluster identified by FCM. These functions are different from “Fuzzy Rule Base” approaches as well as “Fuzzy Regression” approaches. Various transformations of the membership values are included as new variables in addition to original selected scalar input variables; and at times, a logistic transformation of non-scalar original selected input variables may also be included as a new variable. A comparison of “Fuzzy Functions-LSE” with Ordinary Least Squares Estimation (OLSE)” approach show that “Fuzzy Function-LSE” provide better results in the order of 10% or better with respect to RMSE measure for both training and test cases of data sets.     

Analytical structure and stability analysis of a fuzzy PID controller

Analytical structure for a fuzzy PID controller is introduced by employing two fuzzy sets for each of the three input variables and four fuzzy sets for the output variable. This structure is derived via left and right trapezoidal membership functions for inputs, trapezoidal membership functions for output, algebraic product triangular norm, bounded sum triangular co-norm, Mamdani minimum inference method, and center of sums (COS) defuzzification method. Conditions for bounded-input bounded-output (BIBO) stability are derived using the Small Gain Theorem. Finally, two numerical examples along with their simulation results are included to demonstrate the effectiveness of the simplest fuzzy PID controller.