IT2 FLS Research Articles

A New Fuzzy Bayesian Inference Approach for Risk Assessments

Bayesian network (BN) inference is an important statistical tool with additive symmetry. However, BN inference cannot deal with the uncertain, fuzzy, random, and conflicting information from experts’ knowledge in the process of conducting a risk assessment. To tackle this issue, a new fuzzy BN inference approach for risk assessments was proposed based on cloud model (CM), interval type-2 fuzzy set (IT2 FS), interval type-2 fuzzy logic system (IT2 FLS), modified Dempster–Shafer (D-S) evidence theory (ET), and Latin hypercube sampling (LHS) methods along the following lines. Firstly, CM was integrated into IT2 FS, and CM-based IT2 FS (CM-IT2 FS) was defined in the IT2 FLS. Secondly, modified D-S ET was utilized to determine the CM-IT2 FS-based a priori probabilities, and the CM-IT2 FS-based BN model was established. Thirdly, the CM-IT2 FS-based a priori probabilities were reduced to the CM-IT1 FS-based ones using a type reducer in the IT2 FLS, LHS was applied to propose a new fuzzy BN inference algorithm, and then, the new algorithm was used in a typical case to perform the fuzzy BN positive inference for risk prediction and the fuzzy BN reverse inference for risk sensitivity analysis. Finally, the BN inference results were analyzed using the proposed algorithm and the two common BN inference algorithms, and the effectiveness of the proposed approach was validated. It can be concluded that the proposed approach was both accurate and promising.

Adaptive type-2 fuzzy output feedback control using nonlinear observers for permanent magnet synchronous motor servo systems

This paper investigates the accurate servo position control of the permanent magnet synchronous motor (PMSM)-driven system under varying external disturbance and unknown mechanical friction. Firstly, to overcome the difficulty of state observer design caused by uncertainties, the interval type-2 fuzzy logic system (IT2 FLS) is introduced to approximate the nonlinear friction. Meanwhile, the nonlinear disturbance observer (NDO) is employed to estimate the lumped disturbance. Then aiming to solve the problem of explosion of complexity and filtering error, a finite-time (FT) adaptive IT2 fuzzy output feedback controller is proposed by combining the error compensation mechanism and FT control. In addition, to further improve the performance of the closed-loop system, the adaptive law is updated by the compensation error signal. By means of Lyapunov stability theory, all signals in the closed loop system can be guaranteed to be finite-time stable. Numerical simulations and real-time experiments are presented to demonstrate the effectiveness and superiority of the proposed controller.

Interval Type-2 Fuzzy Relation Matrix Model via Semitensor Product

A new modeling idea of interval type-2 fuzzy logic system (IT2 FLS) is proposed on the basis of matrix semi-tensor product (STP) fuzzy representation technique, to construct an interval type-2 fuzzy relationship matrix (IT2 FRM) model. The model naturally inherits the advantages of STP theory, which enables the fuzzy logic reasoning process to be translated into algebraic form for computation. In most cases, the fuzzy rules in the IT2 FRM are generally unknown. To address the above situation, the parameters of this model can be trained with observed data pairs. Firstly, the fuzzy rules are generated by the space division method, and the initial parameters of the model are determined. Secondly, the parameters in the model are trained using the steepest descent algorithm. Finally, the IT2 FRM model is validated by simulation, and the results demonstrate that the IT2 FLS can be designed using the STP method.

Event-Triggered Prespecified Performance Control for Steer-by-Wire Systems With Input Nonlinearity

This paper addresses the prescribed tracking performance control problem for uncertain steer-by-wire (SbW) systems with input nonlinearity (including dead-zone and actuator fault) and the limitation of controller-area-network (CAN) bandwidth. An adaptive interval type-2 fuzzy logic system (IT2 FLS) is introduced to approximate the lumped model uncertainty, and a switching event-triggering mechanism (ETM) is applied to save the communication resources. Combining the backstepping approach and barrier Lyapunov function techniques, a prescribed tracking performance control method is proposed for SbW systems, where the initial values of state errors are no longer required in the controller design. Theoretical analysis shows that the tracking error can converge to the predefined residual set within preset time instead of the time tending infinite, while the closed-loop system is semi-globally stable. Simulations and vehicle experiments are presented to verify the effectiveness of the proposed control method.

Observer-based fixed-time adaptive fuzzy control for SbW systems with prescribed performance

This paper addresses a tracking control problem for Steer-by-Wire (SbW) systems with unmeasurable states, model uncertainty, and limited communication resources. An interval type-2 fuzzy logic system (IT2 FLS)-based fixed-time state observer are proposed to estimate the unavailable state. Different from the accurate model-based state observers and the observers with some additional assumptions, under the proposed observer, the extra conditions can be removed and the fixed-time convergence of observation error can be guaranteed. To save communication resources of the controller-to-actuator channels and achieve the prescribed tracking performance, an event-triggered prescribed performance control (PPC) scheme is proposed. Compared with these existing PPC methods, the computational complexity is reduced and a new prescribed performance function with fixed-time convergence is suggested to improve the steady-state and transient performance of the closed-loop system. The Zeno behavior of the event-triggered communication can be avoided. Simulations and experiments are carried out to demonstrate the effectiveness and superiority of the proposed control technique.

Event-triggered adaptive fuzzy control for automated vehicle steer-by-wire system with prescribed performance: Theoretical design and experiment implementation

Steer-by-wire (SbW) systems substitute the typical mechanical linkage between the steering wheel and the front wheel with electromechanical actuators, resulting in that the steering performance of SbW systems depends on the control of electromechanical actuators. To guarantee the transient and steady-state performance of SbW systems, this paper proposes an event-triggered adaptive fuzzy control for the SbW system subject to the unavailable steering angular velocity, the time-varying disturbance, and the limited communication resources. First, to solve the problem of uncertainty modeling and external interference, an interval type-2 fuzzy logic system (IT2 FLS) and a disturbance observer are used to approximate the unknown SbW system dynamics and disturbance, respectively. Second, considering the angular velocity of the front wheels is difficult to measure, an adaptive observer is developed to estimate the steering angular velocity. The observation error is proved by the Lyapunov theory to converge in finite time. Third, to guarantee the transient and steady-state performance of the SbW system, this paper develops an output feedback controller for the automated vehicles based on event-triggered control (ETC) and prescribed performance control (PPC). Theoretical analysis proves that the tracking error can converge to a preset range within the set time, and the communication data between the controller and the actuator is reduced. Finally, simulation and experiment verify the effectiveness and superiority of the proposed method. From the analysis of the estimation performance, the designed observer has strong adaptability, which can ensure better observation accuracy even if the system has uncertainty. From the analysis of control performance, the proposed controller can guarantee the output trajectory tracking performance attributes (maximum overshoot, convergence time, maximum steady-state error). More specifically, in the experiment, the tracking error can converge to within 0.075 rad in 5 s. Additionally, the RMSE of the experimental results of the designed method is 44.7% higher than that of the output-feedback adaptive neural controller. From the perspective of communication data, the control signal transmitted to the motor driver is effectively saved by 19.3 %.

Event-triggered type-2 fuzzy-based sliding mode control for steer-by-wire systems

This paper proposes an event-triggered higher-order sliding mode control for steer-by-wire (SbW) systems subject to limited communication resources and uncertain nonlinearity. First, an interval type-2 fuzzy logic system (IT2 FLS) is adopted to approximate the uncertain nonlinearities. A fuzzy-based state observer is developed to estimate unavailable states of the extended SbW system. Then, to save communication resources and eliminate chattering, an event-triggered higher-order sliding mode control is proposed for the SbW system. The key advantage is that the proposed control scheme can offset the observation error and the event-triggering error. After that, the practical finite-time stability of the closed-loop SbW system is proved in the framework of the Lyapunov theory. Finally, numerical simulations and vehicle experiments are given to evaluate the effectiveness and superiority of the proposed scheme.

Observer-based event-triggered type-2 fuzzy control for uncertain steer-by-wire systems

This paper addresses the tracking control problem for the uncertain steer-by-wire (SbW) system with the controller area network (CAN) communication and unavailable variables. First, an adaptive interval type-2 fuzzy logic system (IT2 FLS) and sliding mode observer are constructed to estimate the uncertain nonlinearity and unavailable variables of SbW control systems. Further, an event-triggered sliding mode control (ET-SMC) is presented to achieve the transient steering performance of SbW systems while saving CAN communication resources. Much importantly, the dynamic gain and nested technologies are incorporated in this scheme to deal with estimation error and the chattering phenomenon of the sliding mode control system. It is shown that the practical fixed-time stability of the closed-loop system can be guaranteed without the initial condition of tracking errors. Finally, simulations and vehicle experiments are presented to verify the designed scheme.

Observer-based event-triggered control of steer-by-wire systems with prespecified tracking accuracy

This paper addresses the event-triggered tracking control problem of the SbW system subject to unavailable steering angular velocity of front-wheels, time-varying external disturbance, and uncertain dynamics, including friction torque and self-aligning torque. First, an adaptive state observer is proposed to estimate the unavailable steering angular velocity of front-wheels. The uncertain nonlinearity and time-varying disturbance can be estimated by the adaptive interval type-2 fuzzy logic system (IT2 FLS) and the disturbance observer, respectively. An event-triggered control is proposed for SbW systems to guarantee the prespecified control performance and save communication resources in the controller-to-actuator channel. Much importantly, the nested robust terms are incorporated in the control scheme to counteract the observation error and overcome the negative influence of the event-triggering error. Theoretical analysis shows that the prespecified arbitrary tracking accuracy can be guaranteed within finite time, and the Zeno-behavior can be strictly avoided while saving communication resources in the controller-to-actuator channel. Finally, simulation and vehicle experiment results and some comparisons are given to evaluate the effectiveness of the proposed method.

Observer-based interval type-2 fuzzy friction modeling and compensation control for steer-by-wire system

This paper studies the tracking control of the SbW system with unknown nonlinear friction torque and the unmeasured angular velocity. An observer-based adaptive interval type-2 fuzzy logic system controller is proposed to eliminate the adverse influence of the friction torque on the SbW system. Firstly, the angular velocity of the front wheels is estimated via the observer, such that the system sensitivity to measurement noise, the hardware cost, and the structural complexity are reduced. Then, an interval type-2 fuzzy logic system (IT2 FLS) is used to model the friction torque, in which the model and parameters are not effectively identified. IT2 FLS has a more exceptional ability to deal with uncertainties than the traditional type-1 fuzzy logic system (T1 FLS), so the friction modeling based on IT2 FLS has more satisfactory effect in practical application. Finally, an adaptive interval type-2 fuzzy logic system controller is proposed to achieve excellent tracking performance. The tracking error can be guaranteed to converge asymptotically to zero by the Lyapunov stability theory. The numerical simulations and hardware-in-loop (HIL) experiments verify the effectiveness and superiority of the proposed friction modeling method and control strategy.

Adaptive type-2 fuzzy sliding mode control of steer-by-wire systems with event-triggered communication

The steering-by-wire (SbW) system is one of the main subsystems of automatic vehicles, realizing the steering control of autonomous vehicles. This paper proposes an event-triggered adaptive sliding mode control for the SbW system subject to the uncertain nonlinearity, time-varying disturbance, and limited communication resources. Firstly, an event-triggered nested adaptive sliding mode control is proposed for SbW systems. The uncertain nonlinearity is approximated by the interval type-2 fuzzy logic system (IT2 FLS). The time-varying disturbance, modeling error, and event-triggering error can be offset by robust terms of sliding mode control. The key advantage is that the high-frequency switching of sliding mode control only appears on the time derivate of control input without increasing the input-output relative degree of closed-loop SbW systems, such that the chattering phenomenon can be eliminated. Finally, theoretical analysis shows that the practical finite-time stability of the closed-loop SbW system can be achieved, and communication resources in the controller-to-actuator channels can be saved while avoiding the Zeno-behavior. Numerical simulations and experiments are given to evaluate the effectiveness of the proposed method.

Improvement of Enhanced Opposite Direction Searching Algorithm

Type-reduction is an important part of the interval type-2 fuzzy logic system (IT2 FLS), which is also the main factor that influences the effectiveness of IT2 FLS. The enhanced opposite direction searching (EODS) algorithm is currently the fastest form of the Karnik–Mendel algorithm, but it requires a large number of iterations. In this article, an improvement of the enhanced opposite direction searching (IEODS) algorithm is presented to obtain the type reduced set more efficiently. The IEODS algorithm improves the iterative process of the original EODS algorithm through the width of the upper and lower member functions of the IT2 FS. In this way, the IEODS algorithm uses a single-sided iteration process. It has a better initial point to greatly reduce the number of iterations. Quantitative analysis and simulation based experiments show that the IEODS algorithm can save more than 90% of the iterations required in the EODS algorithm. It makes the IEODS algorithm more suitable for practical applications, especially to various development platforms with an explanatory programming language as a tool, greatly expanding the application range of the IT2 FLS.

A new interval type-2 fuzzy logic system under dynamic environment: Application to financial investment

This paper proposes a new interval type-2 fuzzy logic system (IT2 FLS) for financial investment with time-varying parameters adaptive to real-time data streams by using an on-line learning method based on a state-space framework. Particularly, our state-space approach regards the parameters of IT2 FLSs as state variables to sequentially learn by Bayesian filtering algorithms under dynamic environments, where time-series data are continuously observed with occasional structural changes. Moreover, our proposal is effective for financial investment, which often involves various practical complex constraints, because general state-space model makes it possible to flexibly deal with non-linearities. In our empirical experiment with time-series data of global financial assets, our approach is applied to on-line parameter learning of type-1 and type-2 FLSs for portfolio decision making. As a result, it is shown that the IT2 FLS holds its advantage against the type-1 FLS, even though both of the type-1 and type-2 models have the adaptive time-varying parameters, which is an unexplored topic for empirical studies of this area.

Interval type-2 fuzzy logic system based similarity evaluation for image steganography

Similarity measure, also called information measure, is a concept used to distinguish different objects. It has been studied from different contexts by employing mathematical, psychological, and fuzzy approaches. Image steganography is the art of hiding secret data into an image in such a way that it cannot be detected by an intruder. In image steganography, hiding secret data in the plain or non-edge regions of the image is significant due to the high similarity and redundancy of the pixels in their neighborhood. However, the similarity measure of the neighboring pixels, i.e., their proximity in color space, is perceptual rather than mathematical. Thus, this paper proposes an interval type-2 fuzzy logic system (IT2 FLS) to determine the similarity between the neighboring pixels by involving an instinctive human perception through a rule-based approach. The pixels of the image having high similarity values, calculated using the proposed IT2 FLS similarity measure, are selected for embedding via the least significant bit (LSB) method. We term the proposed procedure of steganography as ‘IT2 FLS-LSB method’. Moreover, we have developed two more methods, namely, type-1 fuzzy logic system based least significant bits (T1FLS-LSB) and Euclidean distance based similarity measures for least significant bit (SM-LSB) steganographic methods. Experimental simulations were conducted for a collection of images and quality index metrics, such as PSNR (peak signal-to-noise ratio), UQI (universal quality index), and SSIM (structural similarity measure) are used. All the three steganographic methods are applied on dataset and the quality metrics are calculated. The obtained stego images and results are shown and thoroughly compared to determine the efficacy of the IT2 FLS-LSB method. We have also demonstrated the high payload capacity of our proposed method. Finally, we have done a comparative analysis of the proposed approach with the existing well-known steganographic methods to show the effectiveness of our proposed steganographic method.

A New Interval Type-2 Fuzzy Logic System Under Dynamic Environment: Application to Financial Investment

This paper proposes a new interval type-2 fuzzy logic system (IT2 FLS) for financial investment with time-varying parameters adaptive to real-time data streams by using an on-line learning method based on a state-space framework. Particularly, our state-space approach regards parameters of IT2 FLSs as state variables to sequentially learn by Bayesian filtering algorithms under dynamic environment, where time-series data are continuously observed with occasional structural changes. Moreover, our proposal is helpful for financial applications, which often involve various practical complex constraints, because general state-space model makes it possible to flexibly deal with non-linearities. In our empirical experiment with time-series data of financial assets, our approach is applied to on-line parameter learning of type-1 and type-2 FLSs for portfolio decision making. As a result, it is shown that the IT2 FLS holds its advantage against the type-1 FLS, even though the both type-1 and type-2 models have the adaptive time-varying parameters, which is an unexplored topic for empirical studies of this area.

Hybrid Learning for Interval Type-2 Intuitionistic Fuzzy Logic Systems as Applied to Identification and Prediction Problems

This paper presents a novel application of a hybrid learning approach to the optimisation of membership and nonmembership functions of a newly developed interval type-2 intuitionistic fuzzy logic system (IT2 IFLS) of a Takagi–Sugeno–Kang (TSK) fuzzy inference system with neural network learning capability. The hybrid algorithms consisting of decoupled extended Kalman filter (DEKF) and gradient descent (GD) are used to tune the parameters of the IT2 IFLS for the first time. The DEKF is used to tune the consequent parameters in the forward pass while the GD method is used to tune the antecedents parts during the backward pass of the hybrid learning. The hybrid algorithm is described and evaluated, prediction and identification results together with the runtime are compared with similar existing studies in the literature. Performance comparison is made among the proposed hybrid learning model of IT2 IFLS, a TSK-type-1 intuitionistic fuzzy logic system (IFLS-TSK), and a TSK-type interval type-2 fuzzy logic system (IT2 FLS-TSK) on two instances of the datasets under investigation. The empirical comparison is made on the designed systems using three artificially generated datasets and three real world datasets. Analysis of results reveal that IT2 IFLS outperforms its type-1 variants, IT2 FLS and most of the existing models in the literature. Moreover, the minimal run time of the proposed hybrid learning model for IT2 IFLS also puts this model forward as a good candidate for application in real time systems.

Interval Type-2 Fuzzy Logic Modeling and Control of a Mobile Two-Wheeled Inverted Pendulum

This paper presents an integrated interval type-2 fuzzy logic approach that simultaneously models and controls an underactuated mobile two-wheeled inverted pendulum (MTWIP), which suffers from modeling uncertainties and external disturbances. The control objective is to attain the desired position and direction while keeping the MTWIP balanced. It is achieved by integrating four interval type-2 fuzzy logic systems (IT2 FLSs): the first IT2 FLS describes the dynamics of the MTWIP using a Takagi–Sugeno model, the second IT2 FLS controls the balance of the MTWIP using also a Takagi–Sugeno model, and the third and fourth IT2 FLSs control its position and direction, respectively, using a Mamdani model. A linear matrix inequality based design approach is also proposed to guarantee the stability of the balance controller. The proposed approach is compared with a type-1 FLS in real-world experiments. All results demonstrate that the IT2 FLS outperforms the type-1 FLS, especially under modeling uncertainties and external disturbances.

Optimized Interval Type-II Fuzzy Controller-Based STATCOM for Voltage Regulation in Power Systems With Photovoltaic Farm

The intermittent characteristics and high penetration of renewables (such as photovoltaic and wind powers) cause voltage and stability problems in power systems. The static synchronous compensator (STATCOM) has recently acquired attention on account of its ability to regulate system voltages and improve system stability. This paper presents a novel interval type-II fuzzy logic system (IT2 FLS)-based controller, which consists of current and voltage regulators, applied to the STATCOM, to mitigate bus voltage variations caused by large disturbances (such as intermittent generation of photovoltaic arrays). The current regulator is used to produce the phase angle at the voltage-source converter in the STATCOM while the voltage regulator outputs the current reference on the quadrature axis for the STATCOM. The parameters of the upper/lower membership functions and control gains are optimized by particle swarm optimization. A realistic 10-bus distribution system is used to demonstrate the effectiveness of the proposed method. Comparative studies reveal that the proposed method outperforms traditional PI and type-I FLS-based methods.

Interval type-2 fuzzy logic system for diagnosis coronary artery disease

Coronary artery disease (CAD) is a disease that has been the deadliest disease in Indonesia. The ratio of cardiologists over potential patients is not appropriate either. Intelligent system which can help doctors or patients for cheap and efficient diagnosing CAD is needed. Medical record data, acquisition of cardiologist knowledge and computing technology can be utilized for developing fuzzy logic based intelligent system. Type-1 fuzzy logic system (T1 FLS) has been widely used in various fields. T1 FS has limitation in representing and modelling uncertainty and minimize the impact. Whereas, type-2 fuzzy set (T2 FS) was also introduced as fuzzy set that can model uncertainty more sophisticated. T2 FLS does have a higher degree of freedom when modeling uncertainty but it is quite difficult to make the membership function. An interval T2 FS is a T2 FS in which the membership grade on third dimension is the same everywhere so it is simpler than T2 FS. This paper aims to clarify the better capability of IT2 FLS over T1 FLS on the development of CAD diagnosis system. Rules and membership function were formulated with the help of fuzzy c-means. This study illustrated the causes of CAD risk factors, fuzzification, type reduction and defuzzification. The resulted system was tested with percentage split method (50%-50%) to produce training data and testing data. This test is performed ten times with random seed to separate the data set. The resulted system generates an average of 73.78% accuracy, 71.94% sensitivity and 76.52% specificity.

On the justification to use a novel simplified interval type-2 fuzzy logic system

Wu-Mendel Uncertainty Bounds WM UB is a viable inference engine for interval type-2 fuzzy logic systems IT2 FLS. This engine; however, has a complex structure and hence performing analysis using this mechanism is difficult. Moreover, when WM UB is used for control, one cannot guarantee stability. As such, a new IT2 FLS, called an m--n IT2 FLS, that is a simplified version of the WM UB IT2 FLS, has been recently introduced in the literature. The m--n IT2 FLS has enabled rigorous analyses of IT2 fuzzy controllers, has recently been used in several applications and has shown great promise to be used as a viable IT2 FLS that is not limited just to control. In this paper, we mathematically analyze the structure of the m--n IT2 FLS and through bounds approach find the conditions upon which the m--n IT2 FLS gets close to the WM UB. These conditions will also provide guidelines for the design parameters of the m--n IT2 FLS that will ultimately help designers to choose these parameters for their applications. The results presented in this paper should lead to wider applications of the novel and simplified m--n IT2 FLS.