Interval Type-2 Fuzzy Logic System Research Articles

Application of ANOVA in interval type-2 fuzzy logic systems for modeling the process of ceramic coating preparation in the foundry industry

Application of ANOVA in interval type-2 fuzzy logic systems for modeling the process of ceramic coating preparation in the foundry industry

Investigation on the influence of a new trapezoidal-triangular membership function in IT2FLS with type-reductions for a manufacturing application

The performance of Interval type-2 fuzzy logic system (IT2FLS) can be affected by many factors including the type of reduction methodology followed and the kind of membership function applied. Further, a particular membership function is influenced by its construction, the type of optimisation and adaptiveness applied, and the learning scheme adopted. The available literature lags in providing detailed information about such factors affecting the performance of IT2FLS. In this work, an attempt has been made to comprehensively study the factors affecting the performance of IT2FLS by introducing a new trapezoidal-triangular membership function (TTMF). A real-time application of drilling operation has been considered as an example for predicting temperature of the job, which is considered as one of the key state variables to evaluate. A detailed comparison based on membership functions (MFs) such as triangular membership function (TrMF), trapezoidal membership function (TMF), the newly introduced trapezoidal-triangular membership function (TTMF), semi-elliptic membership function (SEMF), and Gaussian membership function (GMF) has been performed and presented. Further, the average error rate obtained with two “type-reduction” methods such as “Wu-Mendel” uncertainty bounds and Center of sets type reduction (COS TR) has also been discussed. This study provides information for selecting a particular MF and “type reduction” scheme for the implementation of IT2FLS. Also, concludes that MF having fewer parameters such as GMF and SEMF possess significant advantages in terms of computation complexity compared to others.

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.

An Interval Type-2 Fuzzy Logic Approach for Dynamic Parameter Adaptation in a Whale Optimization Algorithm Applied to Mathematical Functions

In this paper, an improved whale optimization algorithm (WOA) based on the utilization of an interval type-2 fuzzy logic system (IT2FLS) is presented. The main idea is to present a proposal for adjusting the values of the r→1 and r→2 parameters in the WOA using an IT2FLS to achieve excellent results in the execution of the WOA. The original WOA has already proven itself as an algorithm with excellent results; therefore, a wide variety of improvements have been made to it. Herein, the main purpose is to provide a hybridization of the WOA algorithm employing fuzzy logic to find the appropriate values of the r→1 and r→2 parameters that can optimize the mathematical functions used in this study, thereby providing an improvement to the original WOA algorithm. The performance of the fuzzy WOA using IT2FLS (FWOA-IT2FLS) shows good results in the case study of the benchmark function optimization. An important comparative with other metaheuristics is also presented. A statistical test and the comparative with other bio-inspired algorithms, namely, the original WOA with type-1 FLS (FWOA-T1FLS) are analyzed. The performance index used is the average of the minimum errors in each proposed method.

Elliptic interval Type-2 intuitionistic fuzzy logic system for non-linear system identification

An elliptic membership function has been proposed in the literature for interval type-2 fuzzy logic system. In this paper, elliptic non- membership function is incorporated into the conventional elliptic membership function model to obtain elliptic interval type-2 intuitionistic fuzzy sets for the first time. The elliptic interval type-2 intuitionistic fuzzy logic system so formed is applied for the prediction of two benchmark non-linear systems and results compared with Gaussian interval type-2 intuitionistic fuzzy logic system. Experimental results show that the elliptic interval type-2 intuitionistic fuzzy logic system outperforms the traditional Gaussian interval type-2 intuitionistic fuzzy logic system in the problem instances investigated.

Interval Type-2 Fuzzy PID Controller Using Disassembled Gradational Optimization.

This paper presents an interval type-2 fuzzy proportional-integral-derivative (IT2F-PID) controller that is designed using a new disassembled gradational optimization (D-GO) method. A PID controller is first optimized using the D-GO method and then connected to a type-1 fuzzy logic system (T1-FLS). The parameters of the T1-FLS are optimized, and the T1-FLS is blurred into the interval type-2 fuzzy logic system (IT2-FLS). Finally, the IT2F-PID controller is formed. The proposed method is compared with the concurrent and general optimization methods. The simulation results show that the D-GO method reduces the optimization time by over 90% compared with the general method, and decreases the integral-of-time-absolute-error (ITAE) by 30%. Beyond that, compared with the concurrent optimization method, the D-GO method reduces time by over 25%, and the ITAE value by about 95%. In the normal case, model uncertainty, target uncertainty, and external disturbance, the control ability of the IT2F-PID controller designed using the D-GO method is verified via simulations using a nonlinear forced closed-loop system. The results show that the overshoot is reduced by 80% and the fluctuation is reduced by 67% compared with a traditional PID controller and an IT2F-PID controller built using the general method.

Towards capsule endoscope locomotion in large volumes: design, fuzzy modeling, and testing

AbstractWe present the design and deployment of a capsule endoscope via external electromagnets for locomotion in large volumes alongside its digital twin implementation based on interval type-2 fuzzy logic systems (IT2-FLSs). To perform locomotion, we developed an external mechanism comprising five external electromagnets on a two-dimensional translational platform that is to be placed underneath the patients’ bed and integrated multiple Neodymium magnets into the capsule. The interaction between the central bottom external electromagnet and the internal magnet forms a fixed body frame at the capsule center, allowing rotation. The interaction between the external electromagnets and the two internal magnets results in rotation. The elevation of the capsule is accomplished due to the interaction between the upper external electromagnet and the internal magnets. Through simulations, we model the capsule rotation as a function of torque and drive voltages. We validated the proposed locomotion approach experimentally and observed that the results are highly nonlinear and uncertain. Thus, we define a regression problem in which IT2-FLSs, capable of representing nonlinearity and uncertainty, are learned. To verify the proposed locomotion approach and test the IT2-FLS, we leverage our experimental effort to a stomach phantom and finally to an ex vivo bovine stomach. The experimental results validate the locomotion capability and show that the IT2-FLS can capture uncertainties while resulting in satisfactory prediction performance. To showcase the benefit in a clinical scenario, we present a digital twin implementation of the proposed approach in a virtual environment that can link physical and virtual worlds in real time.

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.

Adaptive interval type-2 fuzzy fixed-time control for nonlinear MIMO fast-slow coupled systems with user-defined tracking performance

This paper focuses on the adaptive interval type-2 (IT2) fuzzy fixed-time self-triggered control issue for a class of multi-input and multi-output (MIMO) nonlinear fast-slow coupled systems (FSCSs) with preassigned tracking performance requirements. At first, the steady-state error and dynamic response of the investigated system are synthetically weighed by introducing an improved fixed-time prescribed performance function into coordinate transformation. Second, an IT2 fuzzy adaptive self-trigged controller is designed, where the unknown continuous functions are approximated by the interval type-2 fuzzy logic systems (IT2FLSs). In addition, the 1-bit encoding-decoding mechanism (EDM) is embedded in the signal transmission channel between the controller and the actuator, which also provides a feasible solution to further reduce network bandwidth consumption under the framework of the self-triggered protocol. Stability analysis indicates that the developed control method ensures that all states of the closed-loop system are practical fixed-time bounded, and the tracking error evolves to a pre-specified performance envelope within a predetermined time. Finally, a numerical example and an application example are provided to demonstrate the effectiveness and superiority of the proposed method.

A hybrid search mode-based differential evolution algorithm for auto design of the interval type-2 fuzzy logic system

This article proposed a hybrid search mode-based differential evolution (HSM-DE) algorithm to overcome the complex design of an interval type-2 fuzzy logic system (IT2FLS). First, transform complex design processes of the IT2FLS into optimization problems for our proposed evolutionary algorithm by decoding the whole system into design parameters regarded as search objectives. Then, the DE algorithm with a rapid convergence characteristic is adopted as a global search method for exploration according to a memetic algorithm (MA) structure. Considering the conventional DE algorithm is lack of escaping ability for the local optimal solution, a local search method combined with a simulated binary crossover (SBX) and polynomial mutation (PM) is utilized to enhance the exploitation behavior of our proposed method. In addition, simple constraints on the design parameters of the membership function are added to balance the searching freedom of the HSM-DE algorithm and the readability of the optimal IT2FLS. Finally, a simulation of a mobile two-wheel vehicle (MTWV) under a goal search task is performed to verify the effectiveness of the optimal IT2FLS auto designed by HSM-DE. All results demonstrate that the HSM-DE realizes auto design for the IT2FLS with high-performance control and outperforms the comparative methods. Moreover, four comparison methods are performed to validate the high-performance of the proposed HSM-DE on the search ability of the optimal solution.

Mobbing among seafarers: Scale development and application of an interval type-2 fuzzy logic system

Mobbing is a universal problem in every industry, but it is a particularly serious problem for seafarers who are tied to their work 24 h a day, 7 days a week. In this study, it was first aimed to develop a mobbing scale for seafarers from Turkey as one of the countries that provide the most seafarers to the international maritime sector and to examine their mobbing behaviors. A total of 518 people participated in the development of the scale, while 211 participated in a validation study. Factors were determined using exploratory factor analysis and then the validity of the developed scale was verified utilizing confirmatory factor analysis. Secondly, an interval type-2 fuzzy logic system was designed based on the developed scale to deal with the imprecision and vagueness inherent to the answers to the questions. To our knowledge, this is the first study to employ interval type-2 fuzzy sets to measure mobbing behavior. The results of the study demonstrate that there are inverse relationships between the age, professional experience, and position of seafarers and the severity of the mobbing to which they are exposed. The study recommends that the awareness of mobbing be promoted among seafarers.

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.

Interval type-2 fuzzy logic control for a space nuclear reactor core power system

The uncertain environment and delayed communications bring great challenges for the space nuclear reactor core power control. The imprecise knowledge about nonlinear and time varying parameters of the reactor make the problem further difficult. In this work, an anti-interference method is proposed for the core power control of space reactors. A new core power controller is designed to compensate the power deviation caused by model uncertainties and external disturbances. To further approximate nonlinear mapping functions between the control drum angle position and the deviation of the reactor core power, an interval type-2 fuzzy logic system is employed to deduce the correction of control drum angle position for its general approximation ability. Moreover, in order to solve control difficulties caused by physical constraints of the control drum and high stability requirements of the core power control system, an optimized iteration algorithm is proposed to ensure convergence to the optimal solution. A 1MWe space nuclear reactor is used as a reference object to carry out the research and verification of the newly proposed power control scheme. The numerical results verify the feasibility of the novel controller and show that load tracking performance of the system can be realized effectively.

Comparative Study of Type-1 and Interval Type-2 Fuzzy Logic Systems in Parameter Adaptation for the Fuzzy Discrete Mycorrhiza Optimization Algorithm

The Fuzzy Discrete Mycorrhiza Optimization (FDMOA) Algorithm is a new hybrid optimization method using the Discrete Mycorrhiza Optimization Algorithm (DMOA) in combination with type-1 or interval type-2 fuzzy logic system. In this new research, when using T1FLS, membership functions are defined by type-1 fuzzy sets, which allows for a more flexible and natural representation of uncertain and imprecise data. This approach has been successfully applied to several optimization problems, such as in feature selection, image segmentation, and data clustering. On the other hand, when DMOA is using IT2FLS, membership functions are represented by interval type-2 fuzzy sets, which allows for a more robust and accurate representation of uncertainty. This approach has been shown to handle higher levels of uncertainty and noise in the input data and has been successfully applied to various optimization problems, including control systems, pattern recognition, and decision-making. Both DMOA using T1FLS and DMOA using IT2FLS have shown better performance than the original DMOA algorithm in many applications. The combination of DMOA with fuzzy logic systems provides a powerful and flexible optimization framework that can be adapted to various problem domains. In addition, these techniques have the potential to more efficiently and effectively solve real-world problems.

Enhancing Positional Accuracy of the XY-Linear Stage Using Laser Tracker Feedback and IT2FLS

This paper proposes a calibration algorithm to improve the positional accuracies of an industrial XY-linear stage. Precision positioning of these linear stages is required to maintain highly accurate object handling and manipulation. However, due to imprecisions in linear motor stages and the gearbox, static and dynamic errors exist within these manipulators that cannot be adjusted internally. In this paper, to improve the positioning accuracy of these manipulators, measurements from a laser tracker are used within an interval type-2 fuzzy logic system. The laser tracker used in this experiment is an AT960-MR, which is a highly accurate noncontact coordinate metrology equipment capable of performing highly accurate robotic measurements. To perform calibration, we use an IT2FLS to find a nonlinear correcting relationship to compensate for position errors. The IT2FLS acts on the commands given to the move stage to find the accurate position of the move stage. To train the IT2FLS, we use particle swarm optimization (PSO) for the antecedent part parameters and Moore–Penrose generalized inverse to estimate the consequent part parameters. Data are split into train/test data to test the efficacy of the proposed algorithm. It is shown that by using the proposed IT2FLS-based calibration approach, the standard deviation of the position errors can be decreased from 86.1μm to 55.9μm, which is a 35.1% improvement. Comparison results with a multilayer perceptron neural network reveal that the proposed IT2FLS-based calibration algorithm outperforms multilayer perceptron neural network for positional calibration purposes.

More Than Accuracy: A Composite Learning Framework for Interval Type-2 Fuzzy Logic Systems

In this article, we propose a novel composite learning framework for interval type-2 (IT2) fuzzy logic systems (FLSs) to train regression models with a high accuracy performance and capable of representing uncertainty. In this context, we identify three challenges, first, the uncertainty handling capability, second, the construction of the composite loss, and third, a learning algorithm that overcomes the training complexity while taking into account the definitions of IT2-FLSs. This article presents a systematic solution to these problems by exploiting the type-reduced set of IT2-FLS via fusing quantile regression and deep learning (DL) with IT2-FLS. The uncertainty processing capability of IT2-FLS depends on employed center-of-sets calculation methods, while its representation capability is defined via the structure of its antecedent and consequent membership functions. Thus, we present various parametric IT2-FLSs and define the learnable parameters of all IT2-FLSs alongside their constraints to be satisfied during training. To construct the loss function, we define a multiobjective loss and then convert it into a constrained composite loss composed of the log-cosh loss for accuracy purposes and a tilted loss for uncertainty representation, which explicitly uses the type-reduced set. We also present a DL approach to train IT2-FLS via unconstrained optimizers. In this context, we present parameterization tricks for converting the constraint optimization problem of IT2-FLSs into an unconstrained one without violating the definitions of fuzzy sets. Finally, we provide comprehensive comparative results for hyperparameter sensitivity analysis and an inter/intramodel comparison on various benchmark datasets.

Application of Interval Type-2 Fuzzy Logic System and Ant Colony Optimization for Hydropower Dams Displacement Forecasting

Forecasting the dam displacement is an important problem in dam monitoring. By using multi-temporal monitoring data to make predictions and forecast dam structure health, it is possible to detect abnormalities over time of the dam so that remedial measures can be taken promptly to minimize risks. The paper proposes a method of applying the interval type-2 fuzzy logic system (IT2FLS) and ant colony optimization (ACO) technique to forecast hydroelectric dams’ displacement. The method consists of two stages: The first is to design an IT2FLS according to the input and output data with base rules and newly constructed membership functions. The second is to find the optimal parameters for an interval type-2 fuzzy logic system based on the ACO technique and give the final fuzzy forecasting system. Experimental data are measured from hydroelectricity monitoring data of Ialy, Gia Lai Province, Vietnam, in the period from 2004 to 2016. The proposed method is compared with some other methods to compare prediction efficiency and accuracy. The experimental results show that the proposed model has the best performance compared to other standard methods in both accuracy and stability of prediction. This shows that a predictive model based on the IT2FLS is a promising method and can be used for forecasting time-series data.

An interpretable predictive modelling framework for the turning process by the use of a compensated fuzzy logic system

ABSTRACT This research presents a compensated fuzzy logic system that integrates an interval type-2 fuzzy logic system (IT2FLS) with the Gaussian mixture model (GMM) to model the turning process. First, an IT2FLS is elicited to model the turning process by mapping its input variables to the cutting force and the surface quality. Second, the GMM is incorporated in the IT2FLS structure to compensate for the error residuals. The idea of such an incorporation stems from the fact that the majority of the models are constructed based on the normality assumption of the error. The GMM is developed in a way that refines the extracted rules and considers stochastic unmodelled behaviours. Validated on real experiments, it has been demonstrated that the compensated fuzzy logic system has the ability to accurately predict the cutting force and the surface quality; deal with uncertainties; and provide users with comprehensive understanding of the turning process.

Metaheuristic Optimization Algorithm for Optimal Design of Type-2 Fuzzy Controller

The utilization of Le`vy flight to create new candidate solutions is one of the most powerful elements of CS. Candidate solutions are modified using this method by making a lot of minor modifications and a few big jumps. As a result, CS will be able to significantly increase the link between exploration and exploitation while also improving its search capabilities. The cuckoo search optimization (CSO) algorithm is applied to interval type-2 fuzzy logic controller (IT2FLC) in this research to determine the optimal parameters of membership functions (MFs) of interval type-2 fuzzy logic systems (IT2FLSs). The study takes into account two forms of MFs: triangular and trapezoidal. When perturbations are applied during the execution of each control issue, the CSO algorithm's performance and efficiency improve significantly. The proposed approach is tested using two benchmark control problems: water tank controller and inverted pendulum controller.

Optimization of Interval Type-2 Fuzzy Logic System By using A New Hybrid Method of Whale Optimization algorithm and Extreme Learning Machine

The problem of searching for the best values ​​of the fuzzy logic parameters (T1FLS) is consider complex problems, and for type-2 fuzzy logic system (T2FLS) the problem is more complex, in special case interval type-2 fuzzy logic system (IT2FLS). The Researchers have used many methods and algorithms to solve this problem, and among the most important algorithms used in this field are the)Meta-heuristic) algorithms. Because Meta-heuristic algorithms have a high capacity in the practical field, so we used one of the modern algorithms in this field, which is the Whale Optimization algorithm (WOA). We are used the (WOA) algorithm together with the Extreme Learning Machine (ELM) algorithm as a hybrid algorithm to find the best parameters ​​for the IT2FLS. Whereas, the (WOA) algorithm was used to estimate the values of the antecedent for the system, and the (ELM) algorithm was used to find the values ​​of the consequent parts in the system. The simulation results show that the proposed algorithm is effective for a system (IT2FLS).