Number Of Fuzzy Rules Research Articles

Comparison of a fuzzy control and the data-driven model for flood forecasting

A novel hybrid of adaptive neuro-fuzzy inference system (ANFIS) and two-dimensional Mamdani fuzzy controller was developed for accurately forecasting the water level at the Three Georges Reservoir during the flood season in China. Using statistical approaches, nine input variables were selected based on the upper water levels in the reservoir and the quantity of interval rainfall. Since rainfall is an important input variable in flood forecasting during the flood season, ANFIS was modified to account for the influence of rainfall. Two sub-models were written, ANFIS 1 with rainfall and ANFIS 2 without rainfall, due to the weak cross-correlation function between the interval rainfall and the forecasted water levels. These two sub-models were trained by adjusting the number of the membership functions and the fuzzy rules. The number of membership functions and fuzzy rules was as selected 5 for ANFIS1, because of the relatively better results obtained based on the evaluation criterion in comparison with the other groups. The two-dimensional Mamdani fuzzy controller was regarded as an updating process for ANFIS forecasting, which controlled the error rate between the observed and forecasted amounts to within 0.05 %. The final forecasted results were acquired through error feedback and proved to be very close to the observed results. These results verified that this novel model has accurate predictive capabilities.

Fault detection for nonlinear networked systems based on quantization and dropout compensation: An interval type-2 fuzzy-model method

This paper investigates the problem of filter-based fault detection for a class of nonlinear networked systems subject to parameter uncertainties in the framework of the interval type-2 (IT2) T–S fuzzy model-based approach. The Bernoulli random distribution process and logarithm quantizer are used to describe the measurement loss and signals quantization, respectively. In the framework of the IT2 T–S fuzzy model, the parameter uncertainty is handled by the membership functions with lower and upper bounds. A novel IT2 fault detection filter is designed to guarantee the residual system to be stochastically stable and satisfy the predefined H∞ performance. It should be mentioned that the proposed filter does not use the same premise variables, number of fuzzy rules and membership functions as the fuzzy model, which will lead to more flexible design. Finally, two illustrative examples are provided to demonstrate the usefulness of the approach proposed in this paper.

Nonparametric techniques to extract fuzzy rules for breast cancer diagnosis problem.

This paper addresses breast cancer diagnosis problem as a pattern classification problem. Specifically, the problem is studied using Wisconsin-Madison breast cancer data set. Fuzzy rules are generated from the input-output relationship so that the diagnosis becomes easier and transparent for both patients and physicians. For each class, at least one training pattern is chosen as the prototype, provided (a) the maximum membership of the training pattern is in the given class, and (b) among all the training patterns, the neighborhood of this training pattern has the least fuzzy-rough uncertainty in the given class. Using the fuzzy-rough uncertainty, a cluster is constructed around each prototype. Finally, these clusters are interpreted as the fuzzy rules that relate the prognostic factors and the diagnosis results. The advantages of the proposed algorithm are, (a) there is no need to know the structure of the training data, (b) the number of fuzzy rules does not increase with the increase of the number of input dimensions, and (c) small number of fuzzy rules is generated. With the three generated fuzzy rules, 96.20% classification efficiency is achieved, which is comparable to other rule generation techniques.

퍼지 클러스터를 이용한 비선형 추론

In this paper, we introduce a fuzzy inference systems for nonlinear inference using fuzzy cluster. Typically, the generation of fuzzy rules for nonlinear inference causes the problem that the number of fuzzy rules increases exponentially if the input vectors increase. To handle this problem, the fuzzy rules of fuzzy model are designed by dividing the input vector space in the scatter form using fuzzy clustering algorithm which expresses fuzzy cluster. From this method, complex nonlinear process can be modeled. The premise part of the fuzzy rules is determined by means of FCM clustering algorithm with fuzzy clusters. The consequence part of the fuzzy rules have four kinds of polynomial functions and the coefficient parameters of each rule are estimated by using the standard least-squares method. And we use the data widely used in nonlinear process for the performance and the nonlinear characteristics of the nonlinear process. Experimental results show that the non-linear inference is possible.

Fuzzy-Logic-based control of payloads subjected to double-pendulum motion in overhead cranes

Abstract Overhead cranes are widely utilized. The use of overhead cranes suffers from the natural sway of payloads. The sway deteriorates not only safety but also throughput. Under certain operating conditions, the sway exhibits double-pendulum motions. The motions complicate crane control. A fuzzy inference model is entitled ‘single-input-rule modules’ (SIRMs). The SIRMs based model is preferable because it can decrease the number of fuzzy rules. This paper develops a SIRMs based fuzzy controller for transport control of double-pendulum-type systems. The controller includes six SIRMs that are dynamically weighted. Genetic algorithm (GA) is adopted to tune some parameters of the controller. Compared with other three controllers, i.e., passivity-based controller, sliding-mode controller and input-shaping controller, simulation results are presented to show the performance and effectiveness of the SIRMs based fuzzy controller for transport control of double-pendulum-type systems.

Fuzzy Solutions for Two-Dimensional Navier-Stokes Equations

AbstractA new methodology via using an adaptive fuzzy algorithm to obtain solutions of “Two-dimensional Navier-Stokes equations” (2-D NSE) is presented in this investigation. The design objective is to find two fuzzy solutions to satisfy precisely the 2-D NSE frequently encountered in practical applications. In this study, a rough fuzzy solution is formulated with adjustable parameters firstly, and then, a set of adaptive laws for optimally tuning the free parameters in the consequent parts of the proposed fuzzy solutions are derived from minimizing an error cost function which is the square summation of approximation errors of boundary conditions, continuum equation and Navier-Stokes equations. In addition, elegant approximated error bounds between the exact solution and the proposed fuzzy solution with respect to the number of fuzzy rules and solution errors have also been proven. Furthermore, the error equations in mesh points can be proven to converge to zero for the 2-D NSE with two sufficient conditions.

A sufficient condition on a general class of interval type-2 Takagi-Sugeno fuzzy systems with linear rule consequent as universal approximators

Whether a rule-based interval type-2 fuzzy system has the ability to approximate any continuous multivariate function arbitrarily well is a fundamentally important question for fuzzy control and modeling. The only approximation results available are the preliminary ones that we previously obtained. They state that two general classes of the interval T2 fuzzy systems, one for the Mamdani type and the other for the TS type, are universal approximators. We now further our investigation on the same T2 TS fuzzy systems to establish a quantitative sufficient approximation condition. These TS fuzzy systems use the linear rule consequent. Their input fuzzy sets are interval T2 and can be in any shape (e.g., Gaussian or trapezoidal) and the fuzzy AND operators in the rules can be any one type or mixed types. We first proved that the fuzzy systems could uniformly approximate any multivariate polynomials arbitrarily accurately and then utilized the Weierstrass approximation theorem to produce the sufficient approximation condition. The condition is a formula calculating the number of the input fuzzy sets needed to achieve any given approximation accuracy (the number of fuzzy rules needed can be easily computed afterward). A numerical example is provided for illustration.

Adaptive Visual Tracking Control for Manipulator With Actuator Fuzzy Dead-Zone Constraint and Unmodeled Dynamic

This paper focuses on a problem of adaptive visual tracking control for an uncalibrated image-based visual servoing manipulator system with actuator fuzzy dead-zone constrain and unknown dynamic. Without a prior knowledge of the system, fuzzy logic systems are employed to approximate the unmodeled nonlinear manipulator dynamics and external disturbances. By using the recursive Newton–Euler method, the total number of fuzzy rules can be reduced significantly as compared with the traditional fuzzy logic system. By defuzzifying the fuzzy slope $\tilde {k}$ of the fuzzy dead-zone model to a deterministic value $\bar {k}$ , a novel fuzzy adaptive controller is constructed to eliminate the harmful effect of fuzzy dead-zone constrain. Lyapunov functions are presented for stability analysis of visual feedback control problem with unknown dynamics and actuator fuzzy dead-zone constrains. Experimental results are carried out to test the visual tracking performance of the proposed controller and the boundedness of the closed-loop system.

Experimental forward and inverse modelling of magnetorheological dampers using an optimal Takagi–Sugeno–Kang fuzzy scheme

An evolving encoding scheme is presented in this article for a fuzzy-based nonlinear system identification scheme, using the subtractive fuzzy C-mean clustering and a modified version of non-dominated sorting genetic algorithm. This method is able to automatically select the best inputs as well as the structure of the fuzzy model such as rules and membership functions. Moreover, three objective functions are considered to satisfy both accuracy and compactness of the model. The developed method is then employed to identify both forward and inverse models of a highly nonlinear structural control device, that is, magnetorheological damper. Experimental results showed that the proposed evolving Takagi–Sugeno–Kang fuzzy model can identify and grasp the nonlinear behaviour of magnetorheological damper very well with minimal number of inputs and fuzzy rules.

A New Two-Stage Fuzzy Inference System-Based Approach to Prioritize Failures in Failure Mode and Effect Analysis

This paper presents a new Fuzzy Inference System (FIS)-based Risk Priority Number (RPN) model for the prioritization of failures in Failure Mode and Effect Analysis (FMEA). In FMEA, the monotonicity property of the RPN scores is important. To maintain the monotonicity property of an FIS-based RPN model, a complete and monotonically-ordered fuzzy rule base is necessary. However, it is impractical to gather all (potentially a large number of) fuzzy rules from FMEA users. In this paper, we introduce a new two-stage approach to reduce the number of fuzzy rules that needs to be gathered, and to satisfy the monotonicity property. In stage-1, a Genetic Algorithm (GA) is used to search for a small set of fuzzy rules to be gathered from FMEA users. In stage-2, the remaining fuzzy rules are deduced approximately by a monotonicity-preserving similarity reasoning scheme. The monotonicity property is exploited as additional qualitative information for constructing the FIS-based RPN model. To assess the effectiveness of the proposed approach, a real case study with information collected from a semiconductor manufacturing plant is conducted. The outcomes indicate that the proposed approach is effective in developing an FIS-based RPN model with only a small set of fuzzy rules, which is able to satisfy the monotonicity property for prioritization of failures in FMEA.

A hybrid neuro-fuzzy power prediction system for wind energy generation

Abstract Wind energy generation is expected to increase in future electric grids. The generated wind power has an intermittent nature which may affect power system stability and increase the risk of blackouts. Therefore, a prediction system for wind power generation is essential for optimum operation of a power system with a significant share of wind energy conversion systems. In this paper, a hybrid neuro-fuzzy wind power prediction system is proposed. A wireless sensor network (WSN) is used to measure and transmit the required parameters for the prediction model at the operator centre. Those parameters are the major factors affecting wind farm output power, namely air temperature, wind speed, air density and air pressure. Considering all these factors will increase the prediction accuracy of the proposed model. The proposed prediction model is designed and tested using fuzzy rules with adaptive network. To decide the optimal number of fuzzy rules, the clustering of the data using modified Fuzzy C-Means (FCM) is used to implement hybrid optimization method. The prediction model is tested using four subsets of data divided into four seasons of year. The proposed prediction model is implemented using Matlab. Analysis of results shows that the proposed model has good prediction accuracy and provides a useful qualitative description of the prediction system.

Research on prediction of traffic flow based on dynamic fuzzy neural networks

Combining the advantages of the neural network and fuzzy system, this paper makes a further research on the dynamic fuzzy neural networks (D-FNN) traffic flow prediction. Instead of being in consistence with growth of the input number, the fuzzy rule number of the D-FNN increases exponentially in the whole training network structure. In particular, this method can establish a required network structure automatically. This method is applied to the traffic flow time series to analyze and compare the predicting performance of the predicting model based on the neural network method and the adaptive neural fuzzy inference system by combining with the chaos theory. The simulation result shows that this method is quite effective and can improve the predicting accuracy.

Enhanced approximation capabilities of the fuzzy systems using variable universes of discourse

The fuzzy systems with variable universe of discourse (VUD) have received increasing attention due to their fine control performance. VUD fuzzy systems are ones in which universes of discourse can be online tuned by means of a set of nonlinear contraction–expansion factors. One advantage of the VUD fuzzy systems lies in that higher control accuracy can be obtained without the aid of integral elements. Another advantage of the VUD fuzzy systems is that the number of fuzzy rules can be reduced significantly for a given application, compared with the fuzzy system based on fixed universes of discourse. Utilizing the multivariable Taylor’s expansion formula, it is proven that the VUD fuzzy system possesses higher approximating power as the input variables approach the equilibrium point. The approximation error converges to zero when the input variables reach the equilibrium point. It is also proven that the same approximating power can be obtained even when two fuzzy sets are applied on any universe of discourse. In addition, a sufficient condition is given for the VUD fuzzy systems as approximators for any given accuracy. Two examples show that the approximating capability of the VUD fuzzy systems can significantly outperform the fuzzy systems with fixed universes of discourse and that the shape of membership functions can influence the approximation effect. This paper provides researchers with some explanations why the VUD fuzzy systems hold the two advantages mentioned above from the standpoint of the functions approximation theories.

Design and Experimental Implementation of DTC of an Induction Machine Based on Fuzzy Logic Control on FPGA

In this paper, a design method of direct torque control (DTC) of an induction machine, which is based on fuzzy logic control (FLC), is proposed. The FLC which is introduced to improve the DTC uses a reduced number of fuzzy inference rules that facilitates the reduction of the FLC computation time. The improvement is performed by reducing the torque and stator flux ripples in the induction machine drive. Then, a hardware description that is based on the VHDL hardware description language of the proposed design is presented and discussed. The techniques of the parallel architecture, direct computation, and modular architecture are adopted for the design of the controller. Simulation and experimental results of the DTFC are compared with those of the conventional DTC. The comparison results illustrate the reduction in the torque and stator flux ripples of the DTFC. The validity of the proposed method is confirmed by the simulation and experimental results.

More relaxed non-quadratic stabilization conditions for TS fuzzy control systems using LMI and GEVP

In this paper, a new systematic approach is presented to further decrease the conservativeness in stability analysis condition and controller design. Non-quadratic Lyapunov function is utilized to derive stability conditions in terms of linear matrix inequalities. Also, the control problem is formulated in a generalized eigenvalue problem. Considering the concept of decay rate and control input constraint, a new systematic procedure is proposed to calculate a maximum bound for the upper bounds of the time derivatives of the membership functions. Moreover, some slack matrices are introduced that help to reduce conservativeness. The number of inequalities is few compared to the existing results in literature, which helps the feasibility in the case of large number of fuzzy rules. Simulation examples and comparison results demonstrate the merits of this method.

Learning a robot controller using an adaptive hierarchical fuzzy rule-based system

The majority of machine learning techniques applied to learning a robot controller generalise over either a uniform or pre-defined representation that is selected by a human designer. The approach taken in this paper is to reduce the reliance on the human designer by adapting the representation to improve the generalisation during the learning process. An extension of a Hierarchical Fuzzy Rule-Based System (HFRBS) is proposed that identifies and refines inaccurate regions of a fuzzy controller, while interacting with the environment, for both supervised and reinforcement learning problems. The paper shows that a controller using an adaptive HFRBS can learn a suitable control policy using a fewer number of fuzzy rules for both a supervised and reinforcement learning problem and is not sensitive to the layout as with a uniform representation. In supervised learning problems, a small number of extra trials are required to find an effective representation but for reinforcement learning problems, the process of adapting the representation is shown to significantly reduce the time taken to learn a suitable control policy and hence open the door to high-dimensional problems.

Filtering of Interval Type-2 Fuzzy Systems With Intermittent Measurements.

In this paper, the problem of fuzzy filter design is investigated for a class of nonlinear networked systems on the basis of the interval type-2 (IT2) fuzzy set theory. In the design process, two vital factors, intermittent data packet dropouts and quantization, are taken into consideration. The parameter uncertainties are handled effectively by the IT2 membership functions determined by lower and upper membership functions and relative weighting functions. A novel fuzzy filter is designed to guarantee the error system to be stochastically stable with H∞ performance. Moreover, the filter does not need to share the same membership functions and number of fuzzy rules as those of the plant. Finally, illustrative examples are provided to illustrate the effectiveness of the method proposed in this paper.

PClass: An Effective Classifier for Streaming Examples

In this paper, a novel evolving fuzzy-rule-based classifier, termed parsimonious classifier (pClass), is proposed. pClass can drive its learning engine from scratch with an empty rule base or initially trained fuzzy models. It adopts an open structure and plug and play concept where automatic knowledge building, rule-based simplification, knowledge recall mechanism, and soft feature reduction can be carried out on the fly with limited expert knowledge and without prior assumptions to underlying data distribution. In this paper, three state-of-the-art classifier architectures engaging multi-input-multi-output, multimodel, and round robin architectures are also critically analyzed. The efficacy of the pClass has been numerically validated by means of real-world and synthetic streaming data, possessing various concept drifts, noisy learning environments, and dynamic class attributes. In addition, comparative studies with prominent algorithms using comprehensive statistical tests have confirmed that the pClass delivers more superior performance in terms of classification rate, number of fuzzy rules, and number of rule-base parameters.

Hierarchical gene selection and genetic fuzzy system for cancer microarray data classification.

This paper introduces a novel approach to gene selection based on a substantial modification of analytic hierarchy process (AHP). The modified AHP systematically integrates outcomes of individual filter methods to select the most informative genes for microarray classification. Five individual ranking methods including t-test, entropy, receiver operating characteristic (ROC) curve, Wilcoxon and signal to noise ratio are employed to rank genes. These ranked genes are then considered as inputs for the modified AHP. Additionally, a method that uses fuzzy standard additive model (FSAM) for cancer classification based on genes selected by AHP is also proposed in this paper. Traditional FSAM learning is a hybrid process comprising unsupervised structure learning and supervised parameter tuning. Genetic algorithm (GA) is incorporated in-between unsupervised and supervised training to optimize the number of fuzzy rules. The integration of GA enables FSAM to deal with the high-dimensional-low-sample nature of microarray data and thus enhance the efficiency of the classification. Experiments are carried out on numerous microarray datasets. Results demonstrate the performance dominance of the AHP-based gene selection against the single ranking methods. Furthermore, the combination of AHP-FSAM shows a great accuracy in microarray data classification compared to various competing classifiers. The proposed approach therefore is useful for medical practitioners and clinicians as a decision support system that can be implemented in the real medical practice.

A new structure identification scheme for ANFIS and its application for the simulation of virtual air pollution monitoring stations in urban areas

Parameter and structure identifications are necessary in any modelling which aims to achieve a generalised model. Although ANFIS (Adaptive Network-based Fuzzy Inference System) employs well-known parameter-identification techniques, it needs to structure identification techniques for the determination of an optimum number of fuzzy rules and the selection of significant input variables from among the candidate input variables. In this study, a new structure identification scheme is developed and introduced, which is simultaneously capable of the selection of significant input variables and the determination of an optimum number of rules. This new structure identification was joined to ANFIS, and this joined modelling framework was applied to the simulation of virtual air-pollution monitoring stations in Berlin. In this study, 18 virtual particulate matter stations were simulated using the particulate matter data of some of the current stations. In other words, the particulate matter monitoring network of Berlin has been intensified. The evaluation of simulated virtual stations shows that, although the uncertainty of daily particulate matter measurement is about 10 percent, the simulated virtual stations can estimate the mean daily particulate matter with less than 10 percent of error. Mean absolute error and root mean square error of the simulations are less than 2.4 and 3.4µg/m3, respectively. The correlation coefficient of the simulation results was more than 0.94. In addition, the range of mean bias error is between −1.0 and 0.5µg/m3, and the range of factor of exceedance is between −14.8 and 10.8 percent. It means that the simulated virtual stations have a small bias. These results demonstrated the appropriate performance of the joined new structure identification scheme and ANFIS for development of a virtual air pollution monitoring network.