A new method for constructing membership functions and fuzzy rulesfrom training examples

To extract knowledge from a set of numerical data and build up a rule-based system is an important research topic in knowledge acquisition and expert systems. In recent years, many fuzzy systems that automatically generate fuzzy rules from numerical data have been proposed. In this paper, we propose a new fuzzy learning algorithm based on the alpha-cuts of equivalence relations and the alpha-cuts of fuzzy sets to construct the membership functions of the input variables and the output variables of fuzzy rules and to induce the fuzzy rules from the numerical training data set. Based on the proposed fuzzy learning algorithm, we also implemented a program on a Pentium PC using the MATLAB development tool to deal with the Iris data classification problem. The experimental results show that the proposed fuzzy learning algorithm has a higher average classification ratio and can generate fewer rules than the existing algorithm.     

A study of fuzzy membership functions for dependence decision-making in security robot system

This paper proposes comparison of fuzzy membership functions for decision-making in security robot system. Robot’s decision-making speed depends on fuzzy membership functions. The results of the study indicate that sigmoidal membership function coincide the best, two-sided Gaussian, Gaussian, generalized bell, and zero on both extremes with a rise in the middle member ship function coincide well. However, sigmoidal, with a mirror image membership function that opens to the right, and asymmetrical polynomial membership functions do not coincide well with the trapezoidal membership function. The result of the study indicates that trapezoidal MF gives the best performance, and triangular MF response is very close to that of trapezoidal MF.

     

A general purpose fuzzy controller for monotone functions

In this work, a general purpose fuzzy controller is proposed to handle the class of monotonic functions. A set of rules on the selection of fuzzy subsets and decision tables based on the mean-of-inversion (MOI) defuzzification method for guaranteed convergence and accuracy is given and proved. Unlike the mean-of-maximum (MOM) and the center-of-area (COA) methods, the MOI method defuzzifies each fired rule separately instead of superimposing fired rules before defuzzification     

Maximum entropy membership functions for discrete fuzzy variables

Due to the deficiency of information, the membership function of a fuzzy variable cannot be obtained explicitly. It is a challenging work to find an appropriate membership function when certain partial information about a fuzzy variable is given, such as expected value or moments. This paper solves such problems for discrete fuzzy variables via maximum entropy principle and proves some maximum entropy theorems with certain constraints. A genetic algorithm is designed to solve the general maximum entropy model for discrete fuzzy variables, which is illustrated by some numerical experiments.     

A fuzzy irrigation controller system

The paper presents a solution for an irrigation controller based on the fuzzy-logic methodology. First, it describes the general problem of irrigation. Then, it discusses the physical control model. Following the discussion and the formal presentation of the fuzzy controller, the paper provide examples that will show the simplicity in designing and constructing such a system and other advantages of using fuzzy logic in the feedback control problem.     

Emotion recognition from geometric fuzzy membership functions

The posterity challenging task in the Machine Intelligence field is to design a smarter system to identify the human emotions. Facial Emotion Recognition (FER) is a significant visual based tool to construct a smarter system that can recognize human emotions. The existing methods in FER are based on Action Units (AU), appearance and geometrical parameters. Nearly 7000 different combinations of AUs are used in AU to discriminate the emotions, which can be very expensive and increase processing time. Generalize appearance features across the universe is another challenging task. In this paper, a novel geometrical fuzzy based approach is presented to accurately recognize the emotions. The four corner features from eyes and mouth regions are extracted without considering reference face. The extracted features are used to define the quadrilateral shape that failed to match with the shapes in geometry. The degree of impreciseness exists in the quadrilateral is measured by the proposed Mixed Quadratic Shape Model (MQSM) using fuzzy membership functions. Finally, twelve fuzzy features are extracted from the membership functions and used by the classifier for validation. The CK, JAFFE and ISED datasets are used in the experiment to evaluate the performance of the MSQM. It is observed the proposed method performed better than the contemporary methods using twelve fuzzy features without reference image.

     

A relationship between membership functions and approximationaccuracy in fuzzy systems

This paper presents a relationship between membership functions and approximation accuracy in fuzzy systems. This relationship suggests an idea to design membership functions such that the approximation accuracy of fuzzy systems is improved.     

A method for automatic generation of fuzzy membership functions for mobile device’s characteristics based on Google Trends

While creating a framework for adaptive mobile interfaces for m-learning applications we found that in order to ease the use of our framework we needed to present the mobile device characteristics to non-expert users in a easy to understand manner. Using fuzzy sets to represent the characteristics of mobile devices, non-expert developers such as teachers or instructional designers can actively participate in the development or adaptation of the educational tools. To be able to automatically generate the fuzzy membership functions of the sets we needed the data of the mobile device market, regrettably this information is not publicly available. To tackle this problem we have developed a method to estimate the market share of each mobile device based on the popularity metrics recovered from Google Trends and then we use that estimated value as the input to generate the fuzzy set of each characteristic. The proposed method allows us to not only model the state of the market in different periods of time, but also to localize the results to adapt them to the mobile market of specific countries. In this paper we will describe the proposed algorithm and we will discuss the obtained results.     

Load control of ball mill by a high precision sampling fuzzy logic controller with self‐optimizing

A self‐optimizing, high precision sampling fuzzy logic controller for keeping a ball mill circuit working stably and efficiently is proposed in this paper. The controller is based on fuzzy logic control strategy, and a fuzzy interpolation algorithm is presented to improve the control precision. The final output of the controller is calculated through the interpolation calculation of the observation and its neighboring antecedents, and the interpolation weight coefficients are obtained according to a fuzzy inference algorithm. In the proposed controller, the sampling control strategy is used to deal with a large delay time and a controller set value which can be adjusted by a self‐optimizing algorithm, which can overcome the time‐varying characteristic. Simulation results verify that the controller can control the ball mill circuit effectively and have higher control quality. Field service results also verify that the controller can successfully optimize the control of ball mill circuit. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Supervised Pseudo Self-Evolving Cerebellar algorithm for generating fuzzy membership functions

The proper generation of fuzzy membership function is of fundamental importance in fuzzy applications. The effectiveness of the membership functions in pattern classifications can be objectively measured in terms of interpretability and classification accuracy in the conformity of the decision boundaries to the inherent probabilistic decision boundaries of the training data. This paper presents the Supervised Pseudo Self-Evolving Cerebellar (SPSEC) algorithm that is bio-inspired from the two-stage development process of the human nervous system whereby the basic architecture are first laid out without any activity-dependent processes and then refined in activity-dependent ways. SPSEC first constructs a cerebellar-like structure in which neurons with high trophic factors evolves to form membership functions that relate intimately to the probability distributions of the data and concomitantly reconcile with defined semantic properties of linguistic variables. The experimental result of using SPSEC to generate fuzzy membership functions is reported and compared with a selection of algorithms using a publicly available UCI Sonar dataset to illustrate its effectiveness.     

A fuzzy logic controller for an ABS braking system

Anti-blocking system (ABS) brake controllers pose unique challenges to the designer: a) For optimal performance, the controller must operate at an unstable equilibrium point, b) Depending on road conditions, the maximum braking torque may vary over a wide range, c) The tire slippage measurement signal, crucial for controller performance, is both highly uncertain and noisy, d) On rough roads, the tire slip ratio varies widely and rapidly due to tire bouncing, and e) The braking system contains transportation delays which limit the control system bandwidth. A digital controller design was chosen which combines a fuzzy logic element and a decision logic network. The controller identifies the current road condition and generates a command braking pressure signal, based on current and past readings of the slip ratio and brake pressure. The controller detects wheel blockage immediately and avoids excessive slipping. The ABS system performance is examined on a quarter vehicle model with nonlinear elastic suspension. The parallelity of the fuzzy logic evaluation process ensures rapid computation of the controller output signal, requiring less time and fewer computation steps than controllers with adaptive identification. The robustness of the braking system is investigated on rough roads and in the presence of large measurement noise. This paper describes design criteria, and the decision and rule structure of the control system. The simulation results present the system's performance on various road types and under rapidly changing road conditions     

Incorporating fuzzy membership functions into the perceptron algorithm

The perceptron algorithm, one of the class of gradient descent techniques, has been widely used in pattern recognition to determine linear decision boundaries. While this algorithm is guaranteed to converge to a separating hyperplane if the data are linearly separable, it exhibits erratic behavior if the data are not linearly separable. Fuzzy set theory is introduced into the perceptron algorithm to produce a ``fuzzy algorithm' which ameliorates the convergence problem in the nonseparable case. It is shown that the fuzzy perceptron, like its crisp counterpart, converges in the separable case. A method of generating membership functions is developed, and experimental results comparing the crisp to the fuzzy perceptron are presented.     

Intelligent optimal control system for ball mill grinding process

Operation aim of ball mill grinding process is to control grinding particle size and circulation load to ball mill into their objective limits respectively, while guaranteeing producing safely and stably. The grinding process is essentially a multi-input multi-output system (MIMO) with large inertia, strong coupling and uncertainty characteristics. Furthermore, being unable to monitor the particle size online in most of concentrator plants, it is difficult to realize the optimal control by adopting traditional control methods based on mathematical models. In this paper, an intelligent optimal control method with two-layer hierarchical construction is presented. Based on fuzzy and rule-based reasoning (RBR) algorithms, the intelligent optimal setting layer generates the loops setpoints of the basic control layer, and the latter can track their setpoints with decentralized PID algorithms. With the distributed control system (DCS) platform, the proposed control method has been built and implemented in a concentration plant in Gansu province, China. The industrial application indicates the validation and effectiveness of the proposed method.     

情感智能的球磨机系统内模控制研究

针对球磨机系统控制过程中存在的多变量、强耦合、模型时变性的特点,提出基于情感智能的内模控制方案,采用大脑情感学习模型(BEL模型)对球磨机模型进行在线辨识,根据辨识结果设计BEL控制器,建立球磨机的BEL内模控制系统。仿真结果表明该控制方法跟踪快、解耦性能好,控制品质优于传统的解耦控制方法,能够较好地解决球磨机多变量、时变性、耦合性等问题。     

Determining membership functions and minimum fuzzy support in finding fuzzy association rules for classification problems

This paper propose a new method, that employs the genetic algorithm, to find fuzzy association rules for classification problems based on an effective method for discovering the fuzzy association rules, namely the fuzzy grids based rules mining algorithm (FGBRMA). It is considered that some important parameters, including the number and shapes of membership functions in each quantitative attribute and the minimum fuzzy support, are not easily user-specified. Thus, the above-mentioned parameters are automatically determined by a binary string or chromosome is composed of two substrings: one for each quantitative attribute by the coding method proposed by Ishibuchi and Murata, and the other for the minimum fuzzy support. In each generation, the fitness value, which maximizes the classification accuracy rate and minimizes the number of fuzzy rules, of each chromosome can be obtained. When reaching the termination condition, a chromosome with maximum fitness value is then used to test its performance. For classification generalization ability, the simulation results from the iris data and the appendicitis data demonstrate that proposed method performs well in comparison with other classification methods.     

Study of one class of membership functions of fuzzy sets

A class of everywhere smooth membership functions of fuzzy sets based on the idea of spline functions is proposed. Formulas connecting the parameters of the membership functions and the coefficients defining the values of the membership functions are given. The solution of the problem of the membership function interpolation is presented.     

Design of fuzzy PID controllers using modified triangular membership functions

A design method for fuzzy proportional-integral-derivative (PID) controllers is investigated in this study. Based on conventional triangular membership functions used in fuzzy inference systems, the modified triangular membership functions are proposed to improve a system’s performance according to knowledge-based reasonings. The parameters of the considered controllers are tuned by means of genetic algorithms (GAs) using a fitness function associated with the system’s performance indices. The merits of the proposed controllers are illustrated by considering a model of the induction motor control system and a higher-order numerical model.     

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.     

基于最小二乘拟合的模糊隶属函数构建方法

针对当前模糊隶属函数构造方法中存在的问题,提出一种构造模糊隶属函数方法.采用最小二乘法拟合离散数据来获得隶属函数.为减小拟合误差,采用了3项措施以达到预期目标.所构建的隶属函数,对任意输入物理量可直接得到其对应模糊语言变量的隶属度,从而有效避免专家指定隶属度的主观臆断性及不一致性.该方法简单、求解精度高,具有广泛适用性和较强的应用价值.仿真结果证实了该方法的有效性.