Number Of Fuzzy Rules Research Articles

Study of tensor product model alternatives

AbstractA tensor product (TP) model has an infinite number of alternatives. These variants can be readily derived by the TP model transformation that can variate the number of fuzzy rules, the number of antecedent and consequent sets and, further, the shape of the antecedent fuzzy sets. The related literature has quite deep analysis that modifying these features of a TP model has a crucial role in further design. The latest variants of the TP model transformation, emerged about a year ago, are capable of variating the input space of a TP model. The goal of this paper is to analyse this recently emerged new feature through the example of the gantry crane state space model.

A Wavelet-Based Robust Adaptive T-S Fuzzy Controller Design for Synchronization of Faulty Chaotic Gyrostat Systems

In this study, the synchronization problem of the faulty chaotic gyrostat master–slave systems using a wavelet-based robust adaptive T-S fuzzy control is investigated. This control system is comprised of a wavelet T-S fuzzy network (TSFN) controller, a feedback controller and a robust controller. Within this scheme, the wavelet TSFN is used in two separate approaches. At the first approach, it is utilized to approximate the nonlinear functions of the gyrostat systems, and at the second approach, it is used to approximate the lumped fault function of the control system. The feedback controller is developed to initially control the underlying system, and a robust controller is an adaptive controller which is used to dispel the effects of the approximation errors on the tracking performance. The parameters of wavelet TSFN and the bound parameter of the robust controller are tuned on-line by the derived adaptive laws based on Lyapunov stability analysis. The wavelet block acts as a feature extractor, reduces the number of fuzzy rules and also acts as a normalization block. The Lyapunov stability of the closed-loop system, robustness against the parameters uncertainties, the external disturbances and the approximation errors, as well as the convergence of the tracking errors and boundedness of all signals in the closed-loop system, are guaranteed. Finally, the synchronization problem of the unknown chaotic gyrostat systems in the presence of parameter uncertainties, external disturbances and actuator faults is simulated to illustrate the effectiveness of the proposed control scheme.

Cooperative Fuzzy-Neural Control for Wastewater Treatment Process

Wastewater treatment process, including multiple biochemical reactions, is a complex industrial process with strong nonlinearity and time-varying dynamics. It is a challenge to design an effective controller for this kind of process. To solve this problem, a cooperative fuzzy-neural controller is proposed to improve the operation performance of wastewater treatment process in this article. The main advantages of cooperative fuzzy-neural controller contain the following three parts: first, a structure cooperative strategy is developed to adjust the number of fuzzy rules in the controller by coordinating the indexes of similarity and independent contributions. Then, the structure of cooperative fuzzy-neural controller with the balanced redundant degree and efficiency can be adapted to satisfy the different operation conditions of wastewater treatment process. Second, a parameter cooperative strategy is proposed to coordinate the global and local parameters of controller. Then, the parameters can be optimized together to meet the control requirements. Third, the stability of control strategy is given in details. Then, the corresponding stability conditions are shown to guide its application. Finally, the control performance is confirmed on the benchmark simulation model and real wastewater treatment process. The results demonstrate that the proposed cooperative fuzzy-neural controller can achieve superior control precision and low computational burden.

Autonomous omnidirectional mobile robot navigation based on hierarchical fuzzy systems

PurposeThis paper aims to propose a one-layer Mamdani hierarchical fuzzy system (HFS) to navigate autonomously an omnidirectional mobile robot to a target with a desired angle in unstructured environment. To avoid collision with unknown obstacles, Mamdani limpid hierarchical fuzzy systems (LHFS) are developed based on infrared sensors information and providing the appropriate linear speed controls.Design/methodology/approachThe one-layer Mamdani HFS scheme consists of three fuzzy logic units corresponding to each degree of freedom of the holonomic mobile robot. This structure makes it possible to navigate with an optimized number of rules. Mamdani LHFS for obstacle avoidance consists of a number of fuzzy logic units of low dimension connected in a hierarchical structure. Hence, Mamdani LHFS has the advantage of optimizing the number of fuzzy rules compared to a standard fuzzy controller. Based on sensors information inputs of the Mamdani LHFS, appropriate linear speed controls are generated to avoid collision with static obstacles.FindingsSimulation results are performed with MATLAB software in interaction with the environment test tool “Robotino Sim.” Experiments have been done on an omnidirectional mobile robot “Robotino.” Simulation results show that the proposed approaches lead to satisfied performances in navigation between static obstacles to reach the target with a desired angle and have the advantage that the total number of fuzzy rules is greatly reduced. Experimental results prove the efficiency and the validity of the proposed approaches for the navigation problem and obstacle avoidance collisions.Originality/valueBy comparing simulation results of the proposed Mamdani HFS to another navigational controller, it was found that it provides better results in terms of path length in the same environment. Moreover, it has the advantage that the number of fuzzy rules is greatly reduced compared to a standard Mamdani fuzzy controller. The use of Mamdani LHFS in obstacle avoidance greatly reduces the number of involved fuzzy rules and overcomes the complexity of high dimensionality of the infrared sensors data information.

Sink selection and clustering using fuzzy‐based controller for wireless sensor networks

SummaryApplying multiple sink nodes in a large‐scale wireless sensor networks (WSN) can increase the scalability and lifetime of the network. The current sink selection mechanisms assume an unlimited amount of buffer and bandwidth for the sink nodes. This can be problematic in real‐world applications, especially when many cluster heads select a specific sink node and send their data to the sink at the same time. In this situation, the sink node may not have enough buffer to receive and process data; consequently, some packets are dropped. To mitigate these occasions, a fuzzy‐based controller with reduced rules is proposed for sink selection by considering the capacity of the sink nodes. The capacity of the sink nodes is estimated using the long short‐term memory (LSTM) technique. Then another fuzzy‐based controller with reduced rules is designed to select the cluster head. The fuzzy rules are reduced by employing R‐implications method. Reducing the number of fuzzy rules decreases the complexity of the fuzzy controllers. The results show the efficiency of the proposed sink selection and clustering techniques in terms of consumed energy, remaining energy, first node dead (FND), half nodes dead (HND), last node dead (LND), packet loss, and delay.

Fuzzy-PID based control scheme for PMDC series motor speed control

Background/Objectives: PID controllers are widely used in different industrial appliations especially in achieving stable speed control of DC motors. Hower, due to their limitations, most often other methods like Sliding Mode controller, or fuzzy based controller are used. Since the Fuzzy controlers are more adaptive to non-linearity. This study is to analyse a fuzzy-based speed control scheme for tuning/adusting the performance of PID controller for the purpose of speed control of DC motor under the load condition. Methods/Statistical Analysis: Because of low precision and slow response in different control schemes, a performance comparison is shown between three different control approaches for the DC motor speed control. MATLAB’s Simulink platform is used to realize DC Motor and to implement the PID, Fuzzy and Fuzzy-based PID controllers to run the DC motor on the desired speed. Fuzzy controller is based on very few rule & performance is analyzed considering the load. Findings: The performance of three controllers is evaluated in terms of transient domain characteristics like Percentage overshoot, settling and rise times and percentage error under load (2000 rpm). The PID controller has the highest overshoot and hence a faster rise time while FLC has significantly reduced the overshoot, therefore causing rise time to increase. For the Fuzzy-PID controller the percentage overshoot has almost vanished. The rise time also decreased as compared to the FLC. The simulated controller’s responses confirm that Fuzzy-based PID controller has better performance comparing to independent PID and FLC controllers. Novel/Applications: In this work, the design of an intelligent Fuzzy-PID controller for the speed control of the DC motor with reduced complexity and a faster response using with minimum number of Fuzzy rules producing more optimized performance is presented. The design of a control strategy that has capability to control nonlinear behaviors and to stabilize the performance of linear systems specially to provide optimized performance for speed tracking system which is an important aspect in real time system design. Keywords: PMDC motor; PID Controller; fuzzy controller; fuzzy-based PID controller; transient response

Intelligent forecasting of time series based on evolving distributed Neuro‐Fuzzy network

AbstractAn evolving methodology based on Neuro‐Fuzzy Takagi‐Sugeno network (NF‐TS) for distributed forecasting of univariate time series, is proposed. First, the unobservable components, or hidden patterns, are extracted from experimental data of the time series. Then, a distributed forecasting is performed separately for each component, considering an evolving NF‐TS associated with each extracted pattern. The evolving NF‐TS uses components data to adapt and adjust its structure, as the number of fuzzy rules increases or decreases according the behavior of the unobservable components. A recursive version of singular spectral analysis (SSA) technique is formulated, as one of the main contributions of this article, and it is applied to extract the components. The efficiency of proposed methodology is illustrated from results of comparison to others state‐of‐the‐art techniques for forecasting of various univariate time series.

On the Accuracy–Complexity Tradeoff of Fuzzy Broad Learning System

The fuzzy broad learning system (FBLS) is a recently proposed neuro-fuzzy model that shares the similar structure of a broad learning system (BLS). It shows high accuracy in both classification and regression tasks and inherits the fast computational nature of a BLS. However, the ensemble of several fuzzy subsystems in an FBLS decreases the possibility of understanding the fuzzy model since the fuzzy rules from different fuzzy systems are difficult to combine together while keeping the consistence. To balance the model accuracy and complexity, a synthetically simplified FBLS with better interpretability, named compact FBLS (CFBLS), is developed in this article, which can generate much fewer and more explainable fuzzy rules for understanding. In such a way, only one traditional Takagi–Sugeno–Kang fuzzy system is employed in the feature layer of a CFBLS, and the input universe of discourse is equally partitioned to obtain the fuzzy sets with proper linguistic labels accordingly. The random feature selection matrix and rule combination matrix are employed to reduce the total number of fuzzy rules and to avoid the “curse of dimensionality.” The enhancement layer is kept in the CFBLS that helps to add a nonlinear transformation of input features to the traditional first-order polynomial used in the consequent part of a fuzzy rule. The pseudoinverse is also used to determine the parameters of CFBLS guaranteeing its fast computational nature. The experiments on the popular UCI and KEEL datasets indicate that the CFBLS can generate a smaller set of comprehensible fuzzy rules and achieve much higher accuracy than some state-of-the-art neuro-fuzzy models. Moreover, the advantage of CFBLS is also verified in a real-world application.

A novel control method for roll gap of roller crusher based on Fuzzy-PID with decision factor self-correction

Roller crusher is widely used in solid and block material pulverizing. Roll gap between the rollers is usually adjusted to satisfy the particle size of output material. In order to realize convenient adjustment, a roll gap control scheme based on electro-hydraulic technology is designed and optimized. And Fuzzy-PID is applied to realize the automatic process. Moreover, decision factor self-correction is introduced to balance the number of Fuzzy rules and system precision. Finally, an experiment platform and some simulations are conducted to validate the performance of the proposed approach.

An intelligent approach for predicting resource usage by combining decomposition techniques with NFTS network

Time sensitive virtual machines that run real-time control tasks are constrained by hard timing requirements. Optimal resource management and guarantee the hard timing requirements of virtual machines are critical goals. Basically, cloud resource usage predicting and resource reservation play a crucial role to achieve these two goals. So, we propose a predicting approach based on two-phase decomposition method and hybrid neural network to predict future resource usage. This paper uses a clustering method based on the AnYa algorithm in an on-line manner in order to obtain the number of fuzzy rules and the initial value of the premise and consequent parameters. Since cloud resource usage varies widely from time to time and server to server, extracting the best time series model for predicting cloud resource usage depend not only on time but on the cloud resource usage trend. For this, we present a recursive hybrid technique based on singular spectrum analysis and adaptively fast ensemble empirical mode decomposition to identify the hidden characteristics of the time series data. This method tries to extract seasonal and irregular components of the time series. According to the simulation results, it can be found that the proposed model can have significantly better performance than the three comparison models from one-step to six-step CPU usage predictions with the MAPE of 33.83% average performance promotion, MAE of 36.54% average performance promotion, RMSE of 36.70% average performance promotion.

FUZZY INFERENCE SYSTEMS BASE ON POLYNOMIALCONSEQUENTS OF FUZZY RULES

Various fuzzy inference systems that operate on the basis of polynomial consequents of fuzzy rules. As well as inference methods for such systems, in particular, Takagi-Sugeno fuzzy inference systems, their differences from other popular fuzzy systems, such as Mamdani systems, etc., are considered. The attention is focused on the features of the functioning of such systems both in the construction of elementary fuzzy systems. The Systems for which the calculation of the general logical conclusion involves intermediate levels of logical inference with many hierarchically interconnected blocks of fuzzy rules. Fuzzy sets of type 2 are considered, the membership index of which is a fuzzy term of the first type. This allows you to take into account the secondary fuzziness of linguistic concepts in the design of intelligent systems based on fuzzy inference. Fuzzy systems of the second type based on Takagi-Sugeno systems and the iterative Karnik-Mendel algorithm are considered to obtain a logical conclusion for fuzzy systems with the interval membership functions of the second type in the antecedents of fuzzy rules. The proposed procedure for lowering the order of fuzzy rules for higher-order Takagi-Sugeno fuzzy systems is described and justified. A fuzzy inference method for higher-order fuzzy systems based on the partition of a set of input variables is proposed. It is proposed to build a separate block of fuzzy rules for each of the input subspaces in the presence of a common polynomial. Which is a higher-order consequent, that reduces the total number of fuzzy rules in blocks.

An ELM-based single input rule module and its application in power generation

Extreme Learning Machine (ELM) is widely known as an effective learning algorithm than the conventional learning methods from the point of learning speed as well as generalization. In traditional fuzzy inference method which was the "if-then" rules, all the input and output objects were assigned to antecedent and consequent component respectively. However, a major dilemma was that the fuzzy rules' number kept increasing until the system and arrangement of the rules became complicated. Therefore, the single input rule modules connected type fuzzy inference (SIRM) method where consociated the output of the fuzzy rules modules significantly. In this paper, we put forward a novel single input rule modules based on extreme learning machine (denoted as SIRM-ELM) for solving data regression problems. In this hybrid model, the concept of SIRM is applied as hidden neurons of ELM and each of them represents a single input fuzzy rules. Hence, the number of fuzzy rule and the number of hidden neuron of ELM are the same. The effectiveness of proposed SIRM-ELM model is verified using sigmoid activation functions based on several benchmark datasets and a NOx emission of power generation plant. Experimental results illustrate that our proposed SIRM-ELM model is capable of achieving small root mean square error, i.e., 0.027448 for prediction of NO<sub>x</sub> emission.

Hybrid adaptive neuro-fuzzy inference systems for forecasting benzene, toluene & m-xylene removal from aqueous solutions by HZSM-5 nano-zeolite synthesized from coal fly ash

In this research study, a mesoporous HZSM-5 nano-zeolite (SiO2/Al2O3=40) was hydrothermally synthesized from a type of coal fly ash containing high amounts of muscovite plates. The physicochemical properties of coal fly ash and HZSM-5 were examined by various characterization techniques. The synthesized HZSM-5 was applied in simultaneous removal of benzene (B), toluene (T) and m-xylene (X) from aqueous solutions. The effect of adsorption parameters such as solution pH, adsorbent dosage, contact time, initial concentration and temperature on the removal efficiencies of benzene, toluene and m-xylene were evaluated in batch-scale experiments. The maximum adsorption capacity (qmax) of synthesized HZSM-5 was achieved at optimum conditions; pH=7 and t=90 min qmax;B=9.03<T=9.16<X=9.37 mg/g. The kinetic and isotherm studies revealed that the adsorption data were well fitted with pseudo-first order kinetic and Freundlich isotherm models and the equilibrium adsorption was attained within 90 min. Thermodynamic assessments at three different temperatures of 25, 45 and 65 °C displayed that the uptakes of benzene, toluene and m-xylene onto HZSM-5 were exothermic, feasible and spontaneous at ambient temperature. Furthermore, three hybrid intelligence models comprising adaptive neuro-fuzzy inference system integrated with grid partition, subtractive clustering and fuzzy c-means were employed to estimate the removal efficiencies of benzene, toluene and m-xylene. Statistical analysis clearly proved the acceptable performance of all developed hybrid models. The highest accuracy was obtained by ANFIS-FCM models R2 >0.98 with minimum number of fuzzy rules (nR−FCM=10) which is indicative of the superiority of this method over others. The overall results suggested that the synthesized mesoporous HZSM-5 nano-zeolite could be an efficient and cost-effective adsorbent to eliminate the contamination of benzene, toluene and m-xylene from aqueous solutions.

Short-term load forecast using ensemble neuro-fuzzy model

In this paper, Takagi-Sugeno-Kang neuro-fuzzy model is trained using locally linear model tree (LOLIMOT) method to forecast day-ahead hourly load profile. The proposed approach is applied to a real load profile measured in Iran as a geographically spread case study. The effects of partitioning the power system to smaller regions on the load forecasting and its advantages, such as practical consideration of daily average temperature data, are also shown. Moreover, a set of preprocessing approaches is proposed and implemented on historical load data to improve forecasting results. It is shown that by using LOLIMOT, the neuro-fuzzy model does not need the predetermined settings, such as the number of neurons, membership functions or fuzzy rules by an expert because all the parameters are set by the LOLIMOT method. This approach leads to the flexible network topology of the trained model for different days, which leads to extract the load profile trends more effectively.

T-S Fuzzy Adaptive Control Based on Small Gain Approach for an Uncertain Robot Manipulators

In this paper, a T–S (Takagi–Sugeno) adaptive tracking algorithm control based on small gain theorem is proposed for an uncertain robot system with $$n$$-link manipulators. A nonzero time-varying parameter is introduced in the common T–S fuzzy logic system, the T–S type fuzzy logic system with updated parameters laws is build, then the new and original universal approximation with parameter is introduced. The approximation accuracy can be updated on-line by the parameters, which is not limited by the number of fuzzy rules. With the novel property of universal approximation, the proposed adaptive control can be synthetized to overcome the limitations such as on-line learning computation burden in conventional fuzzy logic systems. The originality T–S fuzzy logic system is used to compensate the unknown model of robot manipulators and the adaptive tracking control algorithm is designed with the new property of universal approximation. Based on the analysis of small gain theorem and ISS theory (input-to-state stability), all signals in closed-loop system can be guaranteed to be bounded, and the system can be extended from semi-global stability to global stability by employing the proposed adaptive control scheme. Finally, simulation results are shown to demonstrate the effectiveness of the adaptive control scheme.

Recurrent neuro-fuzzy model of pneumatic artificial muscle position

In this paper, a dynamic neuro-fuzzy system is proposed toward modeling the pneumatic artificial muscle, which are widely used in robotics and rehabilitation. To benefit from the outstanding advantages of the pneumatic actuators such as high softness and low weight-to-force ratio, efficient control of the actuator force as well as its displacement is essential. Attaining a comprehensive model with a satisfactory accuracy in the entire course of the muscle is the most important challenge regarding utilization of the pneumatic artificial muscle in a wide range of the applications. Therefore, an adaptive neuro-fuzzy inference system has been developed for pneumatic artificial muscle modeling. The subtractive clustering method is applied to reduce the number of fuzzy rules without loss of accuracy. To verify the effectiveness of the proposed modeling approach, an experimental setup has been constructed using a vertically suited pneumatic artificial muscle which holds a mass. Input-output data are collected for training and testing the recurrent neuro-fuzzy model. The experimental results demonstrate the desirable performance of the proposed adaptive neuro-fuzzy inference system method in modeling the pneumatic artificial muscle as well as its superiority compared to the mathematical model.

Genetic optimised serial hierarchical fuzzy classifier for breast cancer diagnosis

Accurate early-stage medical diagnosis of breast cancer can improve the survival rates and fuzzy rule-base system (FRBS) has been a promising classification system to detect breast cancer. However, the existing classification systems involves large number of input variables for training and produces a large number of fuzzy rules, which lead to high complexity and barely acceptable accuracy. In this paper, we present a genetic optimised serial hierarchical FRBS, which incorporates lateral tuning of membership functions and optimisation of the rule base. The serial hierarchical structure of FRBS allows selecting and ranking the input variables, which reduces the system complexity and distinguish the importance of attributes in datasets. We conduct an experimental study on Original Wisconsin Breast Cancer Database and Wisconsin Breast Cancer Diagnostic Database from UCI Machine Learning Repository, and show that the proposed system can classify breast cancer accurately and efficiently.

A New Monotone Fuzzy Rule Relabeling Framework With Application to Failure Mode and Effect Analysis Methodology

A monotone fuzzy rule relabeling (MFRR) algorithm has been introduced previously for tackling the issue of a non-monotone fuzzy rule base in the Takagi-Sugeno-Kang (TSK) Fuzzy Inference System (FIS). In this paper, we further propose a new three-stage framework to develop a computationally efficient MFRR algorithm. The first stage determines the combinations of fuzzy rules to be relabeled by exploiting the prior information derived from a given non-monotone fuzzy rule base. This prior information includes the minimum number of fuzzy rules to be relabeled (denoted as $k$ ), as well as the states of fuzzy rules that must be, must not be, or may be relabeled. The second stage relabels the consequent parts of multiple sets of $k$ noisy fuzzy rules obtained from the first stage, such that a monotone fuzzy rule base is produced. The third stage selects the most suitable relabeled fuzzy rule base among the potential monotone fuzzy rule bases obtained from the second stage, either objectively or subjectively. We provide insights into MFRR and discuss its practical implementation. In addition, a network flow method is fused with the proposed MFRR framework, resulting in an efficient computation scheme. The MFRR framework is applied to Failure Mode and Effect Analysis (FMEA) problems related to a sewage treatment plant and a public hospital. It is also evaluated with real FMEA information from a semiconductor plant. The results are analyzed and discussed, which positively demonstrate the effectiveness of the proposed MFRR framework in formulating a monotone TSK-FIS model for undertaking FMEA problems.

Review and Investigation of Simplified Rules Fuzzy Logic Speed Controller of High Performance Induction Motor Drives

The use of Fuzzy Logic Controller (FLC) as a speed controller for Induction Motor (IM) drives is garnering strong researchers’ interest since it has proven to achieve superior performance compared to conventional controllers. The aim of this study is to review and investigate the design, operations, and effects of rules reduction for FLC in IM drives. Based on the literature, the most commonly used technique to design FLC Membership Functions (MFs) rule-base and control model is based on engineering skills and experienced behavioral aspects of the controlled system. Simplified fuzzy rules approaches have been introduced to reduce the number of fuzzy rules in order to realize hardware implementation. This study discusses different simplified rules methods applied to IM drives. Most of the proposed methods shared a common drawback in that they lacked systematic procedures for designing FLC rule base. Therefore, this research proposed a methodological approach to designing and simplifying the FLC rule-base for IM drives based on dynamic step response and phase plane trajectory of the second order representation of IM drives systems. The proposed method presents guidance for designing FLC rule-base based on the general dynamic step response of the controlled system. Following the proposed method procedures, a (9, 25, 49) rules size has been designed and simplified to a (5, 7, 9) rules size. The effectiveness and accuracy of the designed rules as well as the simplified rules were verified by conducting simulation analysis of IM drives using MATLAB/Simulink environment. Step speed command performance comparisons were achieved with both standard designed and simplified rules at various speed demands. The simulation results showed that the simplified rules maintain the drive performance and produced similar behavior as the standard designed rules.

Genetic optimised serial hierarchical fuzzy classifier for breast cancer diagnosis

Accurate early-stage medical diagnosis of breast cancer can improve the survival rates and fuzzy rule-base system (FRBS) has been a promising classification system to detect breast cancer. However, the existing classification systems involves large number of input variables for training and produces a large number of fuzzy rules, which lead to high complexity and barely acceptable accuracy. In this paper, we present a genetic optimised serial hierarchical FRBS, which incorporates lateral tuning of membership functions and optimisation of the rule base. The serial hierarchical structure of FRBS allows selecting and ranking the input variables, which reduces the system complexity and distinguish the importance of attributes in datasets. We conduct an experimental study on Original Wisconsin Breast Cancer Database and Wisconsin Breast Cancer Diagnostic Database from UCI Machine Learning Repository, and show that the proposed system can classify breast cancer accurately and efficiently.