Deep Structure Optimization for Incremental Hierarchical Fuzzy Systems Using Improved Differential Evolution Algorithm

The optimization of the rule base of a fuzzy logic system (FLS) based on evolutionary algorithm has achievednotable results. However, due to the diversity of the deep structure in the hierarchical fuzzy system (HFS) and thecorrelation of each sub fuzzy system, the uncertainty of the HFS’s deep structure increases. For the HFS, a largenumber of studies mainly use fixed structures, which cannot be selected automatically. To solve this problem, thispaper proposes a novel approach for constructing the incremental HFS. During system design, the deep structureand the rule base of the HFS are encoded separately. Subsequently, the deep structure is adaptively mutated basedon the fitness value, so as to realize the diversity of deep structures while ensuring reasonable competition amongthe structures. Finally, the differential evolution (DE) is used to optimize the deep structure of HFS and theparameters of antecedent and consequent simultaneously. The simulation results confirm the effectiveness of themodel. Specifically, the root mean square errors in the Laser dataset and Friedman dataset are 0.0395 and 0.0725,respectively with rule counts of rules is 8 and 12, respectively.When compared to alternative methods, the resultsindicate that the proposed method offers improvements in accuracy and rule counts.

Robust fault detection for delta operator switched fuzzy systems with bilateral packet losses

Considering packet losses, time-varying delay, and parameter uncertainty in the switched fuzzy system, this paper designs a robust fault detection filter at any switching rate and analyzes the H∞ performance of the system. Firstly, the Takagi-Sugeno(T-S) fuzzy model is used to establish a global fuzzy model for the uncertain nonlinear time-delay switched system,and the packet loss process is modeled as a mathematical model satisfying Bernoulli distribution. Secondly, through the average dwell time method and multiple Lyapunov functions, the exponentially stable condition of the nonlinear network switched system is given. Finally, specific parameters of the robust fault detection filter can be obtained by solving linear matrix inequalities(LMIs). The effectiveness of the method is verified by simulation results.

Cross-Domain TSK Fuzzy System Based on Semi-Supervised Learning for Epilepsy Classification

Through semi-supervised learning and knowledge inheritance,a novel Takagi-Sugeno-Kang(TSK)fuzzy system framework is proposed for epilepsy data classification in this study.The new method is based on the maximum mean discrepancy(MMD)method and TSK fuzzy system,as a basic model for the classification of epilepsy data.First,formedical data,the interpretability of TSK fuzzy systems can ensure that the prediction results are traceable and safe.Second,in view of the deviation in the data distribution between the real source domain and the target domain,MMD is used to measure the distance between different data distributions.The objective function is constructed according to the MMD distance,and the distribution distance of different datasets is minimized to find the similar characteristics of different datasets.We introduce semi-supervised learning to further explore the relationship between data.Based on the MMD method,a semi-supervised learning(SSL)-MMD method is constructed by using pseudo-tags to realize the data distribution alignment of the same category.In addition,the idea of knowledge dissemination is used to learn pseudo-tags as additional data features.Finally,for epilepsy classification,the cross-domain TSK fuzzy system uses the cross-entropy function as the objective function and adopts the back-propagation strategy to optimize the parameters.The experimental results show that the new method can process complex epilepsy data and identify whether patients have epilepsy.

Output Linearization of Single-Input Single-Output Fuzzy System to Improve Accuracy and Performance

For fuzzy systems to be implemented effectively,the fuzzy membership function(MF)is essential.A fuzzy system(FS)that implements precise input and output MFs is presented to enhance the performance and accuracy of single-input single-output(SISO)FSs and introduce the most applicable input and output MFs protocol to linearize the fuzzy system’s output.Utilizing a variety of non-linear techniques,a SISO FS is simulated.The results of FS experiments conducted in comparable conditions are then compared.The simulated results and the results of the experimental setup agree fairly well.The findings of the suggested model demonstrate that the relative error is abated to a sufficient range(≤±10%)and that the mean absolute percentage error(MPAE)is reduced by around 66.2%.The proposed strategy to reduceMAPE using an FS improves the system’s performance and control accuracy.By using the best input and output MFs protocol,the energy and financial efficiency of every SISO FS can be improved with very little tuning of MFs.The proposed fuzzy system performed far better than other modern days approaches available in the literature.

Genetics Based Compact Fuzzy System for Visual Sensor Network

As a component of Wireless Sensor Network(WSN),Visual-WSN(VWSN)utilizes cameras to obtain relevant data including visual recordings and static images.Data from the camera is sent to energy efficient sink to extract key-information out of it.VWSN applications range from health care monitoring to military surveillance.In a network with VWSN,there are multiple challenges to move high volume data from a source location to a target and the key challenges include energy,memory and I/O resources.In this case,Mobile Sinks(MS)can be employed for data collection which not only collects information from particular chosen nodes called Cluster Head(CH),it also collects data from nearby nodes as well.The innovation of our work is to intelligently decide on a particular node as CH whose selection criteria would directly have an impact on QoS parameters of the system.However,making an appropriate choice during CH selection is a daunting task as the dynamic and mobile nature of MSs has to be taken into account.We propose Genetic Machine Learning based Fuzzy system for clustering which has the potential to simulate human cognitive behavior to observe,learn and understand things from manual perspective.Proposed architecture is designed based on Mamdani’s fuzzy model.Following parameters are derived based on the model residual energy,node centrality,distance between the sink and current position,node centrality,node density,node history,and mobility of sink as input variables for decision making in CH selection.The inputs received have a direct impact on the Fuzzy logic rules mechanism which in turn affects the accuracy of VWSN.The proposed work creates a mechanism to learn the fuzzy rules using Genetic Algorithm(GA)and to optimize the fuzzy rules base in order to eliminate irrelevant and repetitive rules.Genetic algorithmbased machine learning optimizes the interpretability aspect of fuzzy system.Simulation results are obtained using MATLAB.The result shows that the classification accuracy increase along with minimizing fuzzy rules count and thus it can be inferred that the suggested methodology has a better protracted lifetime in contrast with Low Energy Adaptive Clustering Hierarchy(LEACH)and LEACHExpected Residual Energy(LEACH-ERE).

Prediction Model of Dissolved Oxygen Fuzzy System in Aquaculture Pond Based on Neural Network

A dissolved oxygen fuzzy system predicting model based on neural network was put forward in this study. 106 groups of data were used to confirm the fitness of the predicting model. The first 80 groups of data were acted as training input and the other 26 groups of data were acted as the confirmed data in the system. The result showed that the testing data was approximately the same as the predicted data. So it gave a new way to solve the problem that the status of the water quality couldn＇t be predicted in time and it＇s hard to watching and measuring the factors dynamic.

Stability analysis for affine fuzzy system based on fuzzy Lyapunov functions

An analysis method based on the fuzzy Lyapunov functions is presented to analyze the stability of the continuous affine fuzzy systems. First, a method is introduced to deal with the consequent part of the fuzzy local model. Thus, the stability analysis method of the homogeneous fuzzy system can be used for reference. Stability conditions are derived in terms of linear matrix inequalities based on the fuzzy Lyapunov functions and the modified common Lyapunov functions, respectively. The results demonstrate that the stability result based on the fuzzy Lyapunov functions is less conservative than that based on the modified common Lyapunov functions via numerical examples. Compared with the method which does not expand the consequent part, the proposed method is simpler but its feasible region is reduced. Finally, in order to expand the application of the fuzzy Lyapunov functions, the piecewise fuzzy Lyapunov function is proposed, which can be used to analyze the stability for triangular or trapezoidal membership functions and obtain the stability conditions. A numerical example validates the effectiveness of the proposed approach.

Study on Prediction of Pesticide Residues Based on Fuzzy System

This study was aimed to do the prediction of pesticide residues based on fuzzy system. Taking chlorpyrifos as an example, the Mathematic Fuzzy System was established by using the MRL values （maximum residue limits of all kinds of pesticides in food） of the Matlab Fuzzy Toolbox to analyze and predict the degra- dation degree of pesticide residues of the same crop at different time periods of bagging treatment, with the aim to provide some theoretical guidances for solving practical problems in real life.

New sufficient conditions for general linear SISO Takagi-Sugeno fuzzy systems as universal approximators

By the best approximation theory, it is first proved that the SISO （single-input single-output） linear Takagi-Sugeno （TS） fuzzy systems can approximate an arbitrary polynomial which, according to Weierstrass approximation theorem, can uniformly approximate any continuous functions on the compact domain. Then new sufficient conditions for general linear SISO TS fuzzy systems as universal approximators are obtained. Formulae are derived to calculate the number of input fuzzy sets to satisfy the given approximation accuracy. Then the presented result is compared with the existing literature＇s results. The comparison shows that the presented result needs less input fuzzy sets, which can simplify the design of the fuzzy system, and examples are given to show its effectiveness.

Research of robust adaptive trajectory linearization control based on T-S fuzzy system

A robust adaptive trajectory linearization control （RATLC） algorithm for a class of nonlinear systems with uncertainty and disturbance based on the T-S fuzzy system is presented. The unknown disturbance and uncertainty are estimated by the T-S fuzzy system, and a robust adaptive control law is designed by the Lyapunov theory. Irrespective of whether the dimensions of the system and the rules of the fuzzy system are large or small, there is only one parameter adjusting on line. Uniformly ultimately boundedness of all signals of the composite closed-loop system are proved by theory analysis. Finally, a numerical example is studied based on the proposed method. The simulation results demonstrate the effectiveness and robustness of the control scheme.

Robust Controller Design of a Class of Uncertain Switched Fuzzy Systems with Delays

The robust control problem for a class of uncertain switched fuzzy systems with delays is investigated. Firstly,the model of the switched fuzzy system is presented and the parallel distributed compensation( PDC) technology is employed to design fuzzy controllers. Then, based on the convex combination method, a sufficient condition for robust stabilization in terms of linear matrix inequalities( LMIs) is obtained and a switching law is presented.Meanwhile,the Lyapunov-Krasovskii functional is taken to deal with time varying delays. Moreover,an algorithm is applied to finding a solution for a group of convex combination coefficient. Finally,a numerical example is given to demonstrate the effectiveness of the proposed method.

Prediction of representative deformation modulus of longwall panel roof rock strata using Mamdani fuzzy system

Deformation modulus is the important parameter in stability analysis of tunnels, dams and mining struc- tures. In this paper, two predictive models including Mamdani fuzzy system （MFS） and multivariable regression analysis （MVRA） were developed to predict deformation modulus based on data obtained from dilatometer tests carried out in Bakhtiary dam site and additional data collected from longwall coal mines. Models inputs were considered to be rock quality designation, overburden height, weathering, unconfined compressive strength, bedding inclination to core axis, joint roughness coefficient and fill thickness. To control the models performance, calculating indices such as root mean square error （RMSE）, variance account for （VAF） and determination coefficient （R^2） were used. The MFS results show the significant prediction accuracy along with high performance compared to MVRA results. Finally, the sensitivity analysis of MFS results shows that the most and the least effective parameters on deformation modulus are weatherin~ and overburden height, respectively.

CASCADED FUZZY SYSTEM AND ITS ROBUST ANALYSIS BASED ON SYLLOGISTIC FUZZY REASONING

Syllogistic fuzzy reasoning is introduced into fuzzy system, and the new Cascaded Fuzzy System(CFS) is presented. The thoroughly theoretical analysis and experimental results show that syllogistic fuzzy reasoning is more robust than all other implication inferences for noise data and that CFS has better robustness than conventional fuzzy systems, which provide the solid foundation for CFS's potential application in fuzzy control and modeling and so on.

Functional-type Single-input-rule-modules Connected Neural Fuzzy System for Wind Speed Prediction

Wind is one kind of clean and free renewable energy sources. Wind speed plays a pivotal role in the wind power output. However, due to the random and unstable nature of the wind, accurate prediction of wind speed is a particularly challenging task. This paper presents a novel neural fuzzy method for the hourly wind speed prediction. Firstly, a neural structure is proposed for the functional-type single-input-rule-modules(FSIRMs) connected fuzzy inference system(FIS) to combine the merits of both the FSIRMs connected FIS and the neural network. Then, in order to achieve both the smallest training errors and the smallest parameters, a least square method based parameter learning algorithm is presented for the proposed FSIRMs connected neural fuzzy system(FSIRMNFS). Further,the proposed FSIRMNFS and its parameter learning algorithm are applied to the hourly wind speed prediction. Experiments and comparisons are also made to show the effectiveness and advantages of the proposed approach. Experimental results verified that our study has presented an effective approach for the hourly wind speed prediction. The proposed approach can also be used for the prediction of wind direction, wind power and some other prediction applications in the research field of renewable energy.

On Methodology of Fuzzy Systems

Fuzziness is one of the general characteristics of human thinking and objective things.Fuzzy systems are efficient tools to simulate human thinking and execute fuzzy information processing. This paper discusses several fundamental problems on methodology of fuzzy systems briefly,including generalized fuzzy entropy, generalized defuzzification strategies and fuzzy consistent relation.

Neuro-fuzzy system modeling based on automatic fuzzy clustering

A neuro-fuzzy system model based on automatic fuzzy dustering is proposed. A hybrid model identification algorithm is also developed to decide the model structure and model parameters. The algorithm mainly includes three parts：1） Automatic fuzzy C-means （AFCM）, which is applied to generate fuzzy rttles automatically, and then fix on the size of the neuro-fuzzy network, by which the complexity of system design is reducesd greatly at the price of the fitting capability; 2） R.ecursive least square estimation （RLSE）. It is used to update the parameters of Takagi-Sugeno model, which is employed to describe the behavior of the system;3） Gradient descent algorithm is also proposed for the fuzzy values according to the back propagation algorithm of neural network. Finally,modeling the dynamical equation of the two-link manipulator with the proposed approach is illustrated to validate the feasibility of the method.

Delay-dependent robust H_∞control of convex polyhedral uncertain fuzzy systems

The robust H∞ control problem for a class of uncertain Takagi-Sugeno fuzzy systems with timevarying state delays is studied. The uncertain parameters are supposed to reside in a polytope. Based on the delay-dependent Lyapunov functional method, a new delay-dependent robust H∞ fuzzy controller, which depends on the size of the delays and the derivative of the delays, is presented in term of linear matrix inequalities （LMIs）. For all admissible uncertainties and delays, the controller guarantees not only the asymptotic stability of the system but also the prescribed H∞ attenuation level. In addition, the effectiveness of the proposed design method is demonstrated by a numerical example.

Guaranteed cost control for T-S fuzzy systems with time-varying delays

This paper deals with the problem of guaranteed cost control for nonlinear systems with time-varying delays which is represented by Takagi-Sugeno （T-S） fuzzy models with time-varying delays.The derivatives of time-varying delay are not necessary to be bounded.Based on the free weighting matrix method,sufficient conditions for the existence of fuzzy guaranteed cost controller via state feedback are given in terms of linear matrix inequalities （LMIs）.A minimizing method is also proposed to search the suboptimal upper bound of the guaranteed cost function.The results are delay-dependent but contain delay-independent criteria as a special case.A numerical example is presented to demonstrate the effectiveness and less conservativeness of our work.

Novel robust approach for constructing Mamdani-type fuzzy system based on PRM and subtractive clustering algorithm

A novel approach for constructing robust Mamdani fuzzy system was proposed, which consisted of an efficiency robust estimator(partial robust M-regression, PRM) in the parameter learning phase of the initial fuzzy system, and an improved subtractive clustering algorithm in the fuzzy-rule-selecting phase. The weights obtained in PRM, which gives protection against noise and outliers, were incorporated into the potential measure of the subtractive cluster algorithm to enhance the robustness of the fuzzy rule cluster process, and a compact Mamdani-type fuzzy system was established after the parameters in the consequent parts of rules were re-estimated by partial least squares(PLS). The main characteristics of the new approach were its simplicity and ability to construct fuzzy system fast and robustly. Simulation and experiment results show that the proposed approach can achieve satisfactory results in various kinds of data domains with noise and outliers. Compared with D-SVD and ARRBFN, the proposed approach yields much fewer rules and less RMSE values.

Fuzzy System Design Using Current Amplifier for 20 nm CMOS Technology

In the recent decade,different researchers have performed hardware implementation for different applications covering various areas of experts.In this research paper,a novel analog design and implementation of different steps of fuzzy systems with current differencing buffered amplifier(CDBA)are proposed with a compact structure that can be used in many signal processing applications.The proposed circuits are capable of wide input current range,simple structure,and are highly linear.Different electrical parameters were compared for the proposed fuzzy system when using different membership functions.The novelty of this paper lies in the electronic implementation of different steps for realizing a fuzzy system using current amplifiers.When the power supply voltage of CDBA is 2V,it results in 155mW,power dissipation;4.615KΩ,input resistance;366KΩ,output resistances;and 189.09 dB,common-mode rejection ratio.A 155.519 dB,voltage gain,and 0.76V/μs,the slew rate is analyzed when the power supply voltage of CDBAis 3V.The fuzzy system is realized in 20nm CMOS technology and investigated with an output signal of high precision and high speed,illustrating that it is suitable for realtime applications.In this research paper,a consequence of feedback resistance on the adder circuit and the defuzzified circuit is also analyzed and the best results are obtained using 100K resistance.The structure has a low hardware complexity leading to a low delay and a rather high quality.