Optimization of interval type-2 fuzzy logic controllers for a perturbed autonomous wheeled mobile robot using genetic algorithms

We describe a tracking controller for the dynamic model of a unicycle mobile robot by integrating a kinematic and a torque controller based on type-2 fuzzy logic theory and genetic algorithms. Computer simulations are presented confirming the performance of the tracking controller and its application to different navigation problems.     

一种改进的区间二型模糊控制器设计

针对二型模糊控制器设计中出现的降型计算方法损失不确定性信息的问题,提出一种改进的区间二型模糊控制器．该控制器在充分利用二型模糊推理结果的前提下,对区间模糊输出进行再次优化,其优化指标可直接与被控系统性能相关,由此可得到更有利于提高系统整体性能的准确输出量．最后,将改进的控制器用于汽车非线性悬架系统的控制,仿真结果验证了所提出方法的有效性．     

Experimental study of intelligent controllers under uncertainty using type-1 and type-2 fuzzy logic

Uncertainty is an inherent part in control systems used in real world applications. The use of new methods for handling incomplete information is of fundamental importance. Type-1 fuzzy sets used in conventional fuzzy systems cannot fully handle the uncertainties present in control systems. Type-2 fuzzy sets that are used in type-2 fuzzy systems can handle such uncertainties in a better way because they provide us with more parameters and more design degrees of freedom. This paper deals with the design of control systems using type-2 fuzzy logic for minimizing the effects of uncertainty produced by the instrumentation elements, environmental noise, etc. The experimental results are divided in two classes, in the first class, simulations of a feedback control system for a non-linear plant using type-1 and type-2 fuzzy logic controllers are presented; a comparative analysis of the systems’ response in both cases was performed, with and without the presence of uncertainty. For the second class, a non-linear identification problem for time-series prediction is presented. Based on the experimental results the conclusion is that the best results are obtained using type-2 fuzzy systems.     

Computing derivatives in interval type-2 fuzzy logic systems

This paper makes type-2 fuzzy logic systems much more accessible to fuzzy logic system designers, because it provides mathematical formulas and computational flowcharts for computing the derivatives that are needed to implement steepest-descent parameter tuning algorithms for such systems. It explains why computing such derivatives is much more challenging than it is for a type-1 fuzzy logic system. It provides derivative calculations that are applicable to any kind of type-2 membership functions, since the calculations are performed without prespecifying the nature of those membership functions. Some calculations are then illustrated for specific type-2 membership functions.     

Dynamic parameter adaptation in particle swarm optimization using interval type-2 fuzzy logic

In this paper, we propose a new method for dynamic parameter adaptation in particle swarm optimization (PSO). PSO is an optimization method inspired in social behavior, which has been applied to different optimization problems obtaining good results. In this paper, we propose an improvement to the convergence and diversity of the swarm in PSO using interval type-2 fuzzy logic. Simulation results show that the proposed approach improves the performance of PSO. A comparison of the proposed method using type-2 fuzzy logic with the original PSO approach, and with PSO using type-1 fuzzy logic for dynamic parameter adaptation is presented.     

Improving risk-adjusted performance in high frequency trading using interval type-2 fuzzy logic

In this paper, we investigate the ability of higher order fuzzy systems to handle increased uncertainty, mostly induced by the market microstructure noise inherent in a high frequency trading (HFT) scenario. Whilst many former studies comparing type-1 and type-2 Fuzzy Logic Systems (FLSs) focus on error reduction or market direction accuracy, our interest is predominantly risk-adjusted performance and more in line with both trading practitioners and upcoming regulatory regimes. We propose an innovative approach to design an interval type-2 model which is based on a generalisation of the popular type-1 ANFIS model. The significance of this work stems from the contributions as a result of introducing type-2 fuzzy sets in intelligent trading algorithms, with the objective to improve the risk-adjusted performance with minimal increase in the design and computational complexity. Overall, the proposed ANFIS/T2 model scores significant performance improvements when compared to both standard ANFIS and Buy-and-Hold methods. As a further step, we identify a relationship between the increased trading performance benefits of the proposed type-2 model and higher levels of microstructure noise. The results resolve a desirable need for practitioners, researchers and regulators in the design of expert and intelligent systems for better management of risk in the field of HFT.     

A simple design method for interval type-2 fuzzy pid controllers

In this study, a design method for single Input interval type-2 fuzzy PID controller has been developed. The most important feature of the proposed type-2 fuzzy controller is its simple structure consisting of a single input variable. The presented simple structure gives an opportunity to the designer to form the type-2 fuzzy controller output in closed form formulation for the first time in literature. This formulation cannot be achieved with present type-2 fuzzy PID controller structures which have employed the Karnik-Mendel type reduction. The closed form solution is derived in terms of the tuning parameters which are chosen as the heights of lower membership functions of the antecedent interval type-2 fuzzy sets. Elaborations are done on the derived closed form output and a simple strategy is presented for a single input type-2 fuzzy PID controller design. The presented interval type-2 fuzzy controller structure still keeps the most preferred features of the PID controller such as simplicity and easy design. We will illustrate how the extra degrees of freedom provided by the antecedent interval type-2 fuzzy sets can be used to enhance the control performance on linear and nonlinear benchmark systems by simulations. Moreover, the type-2 fuzzy controller structure has been implemented on experimental pH neutralization. The simulation and experimental results will illustrate that the proposed type-2 fuzzy controller produces superior control performance and can handle nonlinear dynamics, parameter uncertainties, noise and disturbances better in comparison with the standard PID controllers. Hence, the results and analyses of this study will give the control engineers an opportunity to draw a bridge and connect the type-2 fuzzy logic and control theory.     

An interval type-2 fuzzy logic system-based method for prediction interval construction

This paper introduces a new non-parametric method for uncertainty quantification through construction of prediction intervals (PIs). The method takes the left and right end points of the type-reduced set of an interval type-2 fuzzy logic system (IT2FLS) model as the lower and upper bounds of a PI. No assumption is made in regard to the data distribution, behaviour, and patterns when developing intervals. A training method is proposed to link the confidence level (CL) concept of PIs to the intervals generated by IT2FLS models. The new PI-based training algorithm not only ensures that PIs constructed using IT2FLS models satisfy the CL requirements, but also reduces widths of PIs and generates practically informative PIs. Proper adjustment of parameters of IT2FLSs is performed through the minimization of a PI-based objective function. A metaheuristic method is applied for minimization of the non-linear non-differentiable cost function. Performance of the proposed method is examined for seven synthetic and real world benchmark case studies with homogenous and heterogeneous noise. The demonstrated results indicate that the proposed method is capable of generating high quality PIs. Comparative studies also show that the performance of the proposed method is equal to or better than traditional neural network-based methods for construction of PIs in more than 90% of cases. The superiority is more evident for the case of data with a heterogeneous noise.     

A review on the design and optimization of interval type-2 fuzzy controllers

A review of the methods used in the design of interval type-2 fuzzy controllers has been considered in this work. The fundamental focus of the work is based on the basic reasons for optimizing type-2 fuzzy controllers for different areas of application. Recently, bio-inspired methods have emerged as powerful optimization algorithms for solving complex problems. In the case of designing type-2 fuzzy controllers for particular applications, the use of bio-inspired optimization methods have helped in the complex task of finding the appropriate parameter values and structure of the fuzzy systems. In this review, we consider the application of genetic algorithms, particle swarm optimization and ant colony optimization as three different paradigms that help in the design of optimal type-2 fuzzy controllers. We also mention alternative approaches to designing type-2 fuzzy controllers without optimization techniques. We also provide a comparison of the different optimization methods for the case of designing type-2 fuzzy controllers.     

Control of a non-isothermal continuous stirred tank reactor by a feedback-feedforward structure using type-2 fuzzy logic controllers

A control system that uses type-2 fuzzy logic controllers (FLC) is proposed for the control of a non-isothermal continuous stirred tank reactor (CSTR), where a first order irreversible reaction occurs and that is characterized by the presence of bifurcations. Bifurcations due to parameter variations can bring the reactor to instability or create new working conditions which although stable are unacceptable. An extensive analysis of the uncontrolled CSTR dynamics was carried out and used for the choice of the control configuration and the development of controllers. In addition to a feedback controller, the introduction of a feedforward control loop was required to maintain effective control in the presence of disturbances. Simulation results confirmed the effectiveness and the robustness of the type-2 FLC which outperforms its type-1 counterpart particularly when system uncertainties are present.     

Optimization of interval type-2 fuzzy systems for image edge detection

This paper presents the optimization of a fuzzy edge detector based on the traditional Sobel technique combined with interval type-2 fuzzy logic. The goal of using interval type-2 fuzzy logic in edge detection methods is to provide them with the ability to handle uncertainty in processing real world images. However, the optimal design of fuzzy systems is a difficult task and for this reason the use of meta-heuristic optimization techniques is also considered in this paper. For the optimization of the fuzzy inference systems, the Cuckoo Search (CS) and Genetic Algorithms (GAs) are applied. Simulation results show that using an optimal interval type-2 fuzzy system in conjunction with the Sobel technique provides a powerful edge detection method that outperforms its type-1 counterparts and the pure original Sobel technique.     

A new gaussian noise filter based on interval type-2 fuzzy logic systems

In this paper, a new selective feedback fuzzy neural network (SFNN) based on interval type-2 fuzzy logic systems is introduced by partitioning input and output spaces and based upon which a new FLS filter is further studied. The experimental results demonstrate that this new FLS filter outperforms other filters (e.g. the mean filter and the Wiener filter) in suppressing Gaussian noise and maintaining the original structure of an image.     

Web shopping expert using new interval type-2 fuzzy reasoning

Finding a product with high quality and reasonable price online is a difficult task due to uncertainty of Web data and queries. In order to handle the uncertainty problem, the Web Shopping Expert, a new type-2 fuzzy online decision support system, is proposed. In the Web Shopping Expert, a fast interval type-2 fuzzy method is used to directly use all rules with type-1 fuzzy sets to perform type-2 fuzzy reasoning efficiently. The parameters of type-2 fuzzy sets are optimized by a least square method. The Web Shopping Expert based on the interval type-2 fuzzy inference system provides reasonable decisions for online users.     

Conceptual design evaluation using interval type-2 fuzzy information axiom

Concept selection is the most critical part of the design process as it determines the direction of subsequent design stages. In addition, it is a difficult task because available information for decision-making at this stage is imprecise and subjective. This necessitates the need for fuzzy decision models for selecting the best conceptual design among a set of alternatives. Although ordinary fuzzy sets cover uncertainties of linguistic words to some extent, it is recommended to use interval type-2 fuzzy sets (IT2FS) to capture potential uncertainties of words. This paper presents a new concept selection methodology that extends the fuzzy information axiom (FIA) approach to incorporate IT2FSs. The proposed methodology is called interval-type-2 fuzzy information axiom (IT2-FIA). IT2-FIA method is also enriched by using ordered weighted geometric aggregation operator to include the decision maker's attitude during the aggregation process. A case study is given to demonstrate the potential of the methodology.     

Finishing mill strip gage setup and control by interval type-1 non-singleton type-2 fuzzy logic systems

The setup and control of the finishing mill roll gap positions required to achieve the desired strip head thickness as measured by the finish mill exit X-ray gauge sensor is made by an intelligent controller based on an interval type-2 fuzzy logic system. The controller calculates the finishing mill stand screw positions required to achieve the strip finishing mill exit target thickness. The interval type-2 fuzzy head gage controller uses as inputs the transfer bar thickness, the width and the temperature at finishing mill entry, the strip target thickness, the width and the temperature at finishing mill exit, the stand work roll diameter, the stand work roll speed, the stand entry thickness, the stand exit thickness, the stand rolling force, and the %C of the strip. Taking into account that the measurements and inputs to the proposed system are modeled as type-1 non-singleton fuzzy numbers, we present the so called interval type-1 non-singleton type-2 fuzzy logic roll gap controller. As reported in the literature, interval type-2 fuzzy logic systems have greater non-linear approximation capacity than that of its type-1 counterpart and it has the advantage to develop more robust and reliable solutions than the latter. The experiments of these applications were carried out for three different types of coils, from a real hot strip mill. The results proved the feasibility of the developed system for roll gap control. Comparison against the mathematical based model shows that the proposed interval type-2 fuzzy logic system equalizes the performance in finishing mill stand screw positions setup and enhances the achieved strip thickness under the tested conditions characterized by high uncertainty levels.     

Designing fuzzy logic controllers using a multiresolutional searchparadigm

A multiresolutional search paradigm is employed to design optimal fuzzy logic controllers in a variable structure simulation environment. The initial search space is evaluated with a coarse resolution and some of the subspaces are selected as candidate regions for global optimum. New optimization processes are then created to investigate the candidate search spaces in detail, a process which continues until a solution is found. This search paradigm was implemented using hierarchical distributed genetic algorithms (HDGAs)-search agents solving different degrees of abstracted problems. Creation/destruction of agents is executed dynamically during the operation based on their performance. In the application to fuzzy systems, the HDGA investigates design alternatives such as different types of membership functions and the number of the fuzzy labels, as well as their optimal parameter settings, all at the same time. This paradigm is demonstrated with an application to the design of a fuzzy controller for an inverted pendulum     

Uncertainty bounds and their use in the design of interval type-2 fuzzy logic systems

We derive inner- and outer-bound sets for the type-reduced set of an interval type-2 fuzzy logic system (FLS), based on a new mathematical interpretation of the Karnik-Mendel iterative procedure for computing the type-reduced set. The bound sets can not only provide estimates about the uncertainty contained in the output of an interval type-2 FLS, but can also be used to design an interval type-2 FLS. We demonstrate, by means of a simulation experiment, that the resulting system can operate without type-reduction and can achieve similar performance to one that uses type-reduction. Therefore, our new design method, based on the bound sets, can relieve the computation burden of an interval type-2 FLS during its operation, which makes an interval type-2 FLS useful for real-time applications.     

Modeling the permeability of carbonate reservoir using type-2 fuzzy logic systems

In this work, the use of type-2 fuzzy logic systems as a novel approach for predicting permeability from well logs has been investigated and implemented. Type-2 fuzzy logic system is good in handling uncertainties, including uncertainties in measurements and data used to calibrate the parameters. In the formulation used, the value of a membership function corresponding to a particular permeability value is no longer a crisp value; rather, it is associated with a range of values that can be characterized by a function that reflects the level of uncertainty. In this way, the model will be able to adequately account for all forms of uncertainties associated with predicting permeability from well log data, where uncertainties are very high and the need for stable results are highly desirable. Comparative studies have been carried out to compare the performance of the proposed type-2 fuzzy logic system framework with those earlier used methods, using five different industrial reservoir data. Empirical results from simulation show that type-2 fuzzy logic approach outperformed others in general and particularly in the area of stability and ability to handle data in uncertain situations, which are common characteristics of well logs data. Another unique advantage of the newly proposed model is its ability to generate, in addition to the normal target forecast, prediction intervals as its by-products without extra computational cost.     

Design of interval type-2 fuzzy sliding-mode controller

In this paper, an interval type-2 fuzzy sliding-mode controller (IT2FSMC) is proposed for linear and nonlinear systems. The proposed IT2FSMC is a combination of the interval type-2 fuzzy logic control (IT2FLC) and the sliding-mode control (SMC) which inherits the benefits of these two methods. The objective of the controller is to allow the system to move to the sliding surface and remain in on it so as to ensure the asymptotic stability of the closed-loop system. The Lyapunov stability method is adopted to verify the stability of the interval type-2 fuzzy sliding-mode controller system. The design procedure of the IT2FSMC is explored in detail. A typical second order linear interval system with 50% parameter variations, an inverted pendulum with variation of pole characteristics, and a Duffing forced oscillation with uncertainty and disturbance are adopted to illustrate the validity of the proposed method. The simulation results show that the IT2FSMC achieves the best tracking performance in comparison with the type-1 Fuzzy logic controller (T1FLC), the IT2FLC, and the type-1 fuzzy sliding-mode controller (T1FSMC).