Type-2 fuzzy logic-based classifier fusion for support vector machines

As a machine-learning tool, support vector machines (SVMs) have been gaining popularity due to their promising performance. However, the generalization abilities of SVMs often rely on whether the selected kernel functions are suitable for real classification data. To lessen the sensitivity of different kernels in SVMs classification and improve SVMs generalization ability, this paper proposes a fuzzy fusion model to combine multiple SVMs classifiers. To better handle uncertainties existing in real classification data and in the membership functions (MFs) in the traditional type-1 fuzzy logic system (FLS), we apply interval type-2 fuzzy sets to construct a type-2 SVMs fusion FLS. This type-2 fusion architecture takes considerations of the classification results from individual SVMs classifiers and generates the combined classification decision as the output. Besides the distances of data examples to SVMs hyperplanes, the type-2 fuzzy SVMs fusion system also considers the accuracy information of individual SVMs. Our experiments show that the type-2 based SVM fusion classifiers outperform individual SVM classifiers in most cases. The experiments also show that the type-2 fuzzy logic-based SVMs fusion model is better than the type-1 based SVM fusion model in general.     

Type-2 fuzzy logic systems

We introduce a type-2 fuzzy logic system (FLS), which can handle rule uncertainties. The implementation of this type-2 FLS involves the operations of fuzzification, inference, and output processing. We focus on “output processing,” which consists of type reduction and defuzzification. Type-reduction methods are extended versions of type-1 defuzzification methods. Type reduction captures more information about rule uncertainties than does the defuzzified value (a crisp number), however, it is computationally intensive, except for interval type-2 fuzzy sets for which we provide a simple type-reduction computation procedure. We also apply a type-2 FLS to time-varying channel equalization and demonstrate that it provides better performance than a type-1 FLS and nearest neighbor classifier     

A hierarchical type-2 fuzzy logic control architecture for autonomous mobile robots

Autonomous mobile robots navigating in changing and dynamic unstructured environments like the outdoor environments need to cope with large amounts of uncertainties that are inherent of natural environments. The traditional type-1 fuzzy logic controller (FLC) using precise type-1 fuzzy sets cannot fully handle such uncertainties. A type-2 FLC using type-2 fuzzy sets can handle such uncertainties to produce a better performance. In this paper, we present a novel reactive control architecture for autonomous mobile robots that is based on type-2 FLC to implement the basic navigation behaviors and the coordination between these behaviors to produce a type-2 hierarchical FLC. In our experiments, we implemented this type-2 architecture in different types of mobile robots navigating in indoor and outdoor unstructured and challenging environments. The type-2-based control system dealt with the uncertainties facing mobile robots in unstructured environments and resulted in a very good performance that outperformed the type-1-based control system while achieving a significant rule reduction compared to the type-1 system.     

Application of type-2 fuzzy logic system for load frequency control using feedback error learning approaches

In this paper, the type-2 fuzzy logic system (T2FLS) controller using the feedback error learning (FEL) strategy has been proposed for load frequency control (LFC) in the restructure power system. The original FEL strategy consists of an intelligent feedforward controller (INFC) (i.e. artificial neural network (ANN)) and the conventional feedback controller (CFC). The CFC acting as a general feedback controller to guarantee the stability of the system plays a crucial role in the transient state. The INFC is adopted in forward path to take over the control problem in the steady state. In this work, to improve the performance of the FEL strategy, the T2FLS is adopted instead of ANN in the INFC part due to its ability to model uncertainties, which may exist in the rules and measured data of sensors more effectively. The proposed FEL controller has been compared with a type-1 fuzzy logic system (T1FLS) – based FEL controller and the proportional, integral and derivative (PID) controller to highlight the effectiveness of the proposed method.     

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.     

Type-2 fuzzy wavelet networks (T2FWN) for system identification using fuzzy differential and Lyapunov stability algorithm

We propose a novel method for the identification of non-linear system by utilizing some of the important properties of wavelets like denoising, compression, multiresolution along with the concepts of fuzzy logic. Two new type-2 fuzzy wavelet networks (T2FWNs) are proposed here. These T2FWNs can handle rule uncertainties in a better way because of using the type-2 fuzzy sets in modeling and fuzzy differential (FD) and Lyapunov stability during learning. Lot of work has been done in the identification of non-linear system by using the models based on type-1 fuzzy logic system (FLS). But in practice they are unable to handle uncertainties in the rules. The robustness of the system is assured by Lyapunov stability (LS). Also we have explored the properties of wavelets and FLS to handle the uncertainties efficiently. As the stability of the model is highly dependent on the learning of the system we use Lyapunov stability in combination with fuzzy differential. FD gives the range of variation of parameters having lower and upper bound in which the system is stable. The performance of T2FWN is compared with type-1 FLS, FWN [D.W.C. Ho, P.-A. Zhang, J. Xu, Fuzzy wavelet networks for function learning, IEEE Trans. Fuzzy Syst. 9 (February (1)) 2000] and FWNN [S. Srivastava, M. Singh, M. Hanmandlu, A.N. Jha, New fuzzy wavelet neural networks for system identification and control, Intl. J. Appl. Soft Comput. 6 (November (I)) 2005, 1–17]. It is shown that noise and disturbance in the reference signal are reduced with wavelets. A comparison of three learning algorithms: (i) gradient descent (GD) (ii) a combination of Lyapunov stability and fuzzy differential (LSFD) and, (iii) a combination of (i) and (ii) is done.     

Type-2 hierarchical fuzzy system for high-dimensional data-based modeling with uncertainties

A type-2 hierarchical fuzzy system (T2HFS) is presented for the high-dimensional data-based modeling with uncertainties. Type-2 fuzzy logic system (T2FLS) is a powerful tool to handle uncertainties in complex processes. However, the operation of type-reduction has greatly increased the computational burden of T2FLSs. By integrating the T2FLS with hierarchical structure, a systematic design methodology of T2HFS is proposed to avoid the rule explosion and to simplify the computation complexity. The design methodology has included several procedures to establish the T2HFS. Firstly, the PCA-based method is developed to capture the prominent component from training data, and to determine the hierarchical structure of T2HFS. Furthermore, a novel clustering method is proposed to design the basic type-2 fuzzy logic unit (T2FLU) in uncertain environments. Finally, a hybrid-learning method is presented to fine-tune the parameters for the global optimization where the statistical and deterministic optimization methods are developed for the nominal and auxiliary performance, respectively. Simulation results have shown that the proposed T2HFS is very effective for the high-dimensional data-based modeling and control in uncertain environment.     

Polynomial regression interval-valued fuzzy systems

In recent years, the type-2 fuzzy sets theory has been used to model and minimize the effects of uncertainties in rule-base fuzzy logic system (FLS). In order to make the type-2 FLS reasonable and reliable, a new simple and novel statistical method to decide interval-valued fuzzy membership functions and probability type reduce reasoning method for the interval-valued FLS are developed. We have implemented the proposed non-linear (polynomial regression) statistical interval-valued type-2 FLS to perform smart washing machine control. The results show that our quadratic statistical method is more robust to design a reliable type-2 FLS and also can be extend to polynomial model.     

Least squares support vector regression and interval type-2 fuzzy density weight for scene denoising

Support vector machines are the popular machine learning techniques. Its variant least squares support vector regression (LS-SVR) is effective for image denoising. However, the fitting of the samples contaminated by noises in the training phase will result in the fact that LS-SVR cannot work well when noise level is too far from it or noise density is high. Type-2 fuzzy sets and systems have been shown to be a more promising method to manifest the uncertainties. Various noises would be taken as uncertainties in scene images. By integrating the design of learning weights with type-2 fuzzy sets, a systematic design methodology of interval type-2 fuzzy density weighted support vector regression (IT2FDW-SVR) model for scene denoising is presented to address the problem of sample uncertainty in scene images. A novel strategy is used to design the learning weights, which is similar to the selection of human experience. To handle the uncertainty of sample density, interval type-2 fuzzy logic system (IT2FLS) is employed to deduce the fuzzy learning weights (IT2FDW) in the IT2FDW-SVR, which is an extension of the previously weighted SVR. Extensive experimental results demonstrate that the proposed method can achieve better performances in terms of both objective and subjective evaluations than those state-of-the-art denoising techniques.     

Type-2 FLCs: A New Generation of Fuzzy Controllers

Type-1 fuzzy logic controllers (FLCs) have been applied to date with great success to many different applications. However, for dynamic unstructured environments and many real-world applications, there is a need to cope with large amounts of uncertainties. The traditional type-1 FLC using crisp type-1 fuzzy sets cannot directly handle such uncertainties. A type-2 FLC using type-2 fuzzy sets can handle such uncertainties to produce a better performance. Hence, type-2 FLCs will have the potential to overcome the limitations of type-1 FLCs and produce a new generation of fuzzy controllers with improved performance for many applications, which require handling high levels of uncertainty. This paper introduces briefly the interval type-2 FLC and its benefits. We also present briefly the type-2 FLC application to three challenging domains: industrial control, mobile robots control and ambient intelligent environments control     

Interval type-2 fuzzy weighted support vector machine learning for energy efficient biped walking

An interval type-2 fuzzy weighted support vector machine (IT2FW-SVM) is proposed to address the problem of high energy consumption for biped walking robots. Different from the traditional machine learning method of ‘copy learning’, the proposed IT2FW-SVM obtains lower energy cost and larger zero moment point (ZMP) stability margin using a novel strategy of ‘selective learning’, which is similar to human selections based on experience. To handle the uncertainty of the experience, the learning weights in the IT2FW-SVM are deduced using an interval type-2 fuzzy logic system (IT2FLS), which is an extension of the previous weighted SVM. Simulation studies show that the existing biped walking which generates the original walking samples is improved remarkably in terms of both energy efficiency and biped dynamic balance using the proposed IT2FW-SVM.     

Designing an adaptive type-2 fuzzy logic system load frequency control for a nonlinear time-delay power system

In this paper, a combination of type-2 fuzzy logic system (T2FLS) and a conventional feedback controller (CFC) has been designed for the load frequency control (LFC) of a nonlinear time-delay power system. In this approach, the T2FLS controller which is designed to overcome the uncertainties and nonlinearites of the controlled system is in the feedforward path and the CFC which plays an important role in the transient state is in the feedback path. A Lyapunov–Krasovskii functional has been used to ensure the stability of the system and the parameter adjustment laws for the T2FLS controller are derived using this functional. In this training method, the effect of delay has been considered in tuning the T2FLS controller parameters and thus the performance of the system has been improved. The T2FLS controller is used due to its ability to effectively model uncertainties, which may exist in the rules and data measured by the sensors. To illustrate the effectiveness of the proposed method, a two-area nonlinear time-delay power system has been used and compared with the controller that uses the gradient-descend (GD) algorithm to tune the T2FLS controller parameters.     

Three-dimensional fuzzy logic system for process modeling and control

The traditional fuzzy logic system (FLS) can only model and control the process in two-dimensional nature. Many of real-world systems are of multidimensional features, such as, thermal and fluid processes with spatiotemporal dynamics, biological systems, or decision-making processes that contain stochastic and imprecise uncertainties. These types of systems are difficult for the traditional FLS to model and control because they require a third dimension for spatial or probabilistic information. The type-2 fuzzy set provides the possibility to develop a three-dimensional fuzzy logic system for modeling and controlling these processes in three-dimensional nature.     

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.     

Designing interval type‐2 fuzzy logic systems using an SVD‐QR method: Rule reduction

A type‐2 fuzzy logic system (FLS) can handle numerical and linguistic uncertainties, but, like a type‐1 FLS, rule explosion is one of its major disadvantages. In this paper, we present a design method which can tremendously reduce rule number for interval type‐2 fuzzy logic systems using an SVD‐QR method. The SVD‐QR method is performed after extracting two fuzzy basis function expansions from the interval type‐2 FLS. We evaluate this method by applying it to a time‐series forecasting problem in conjunction with back‐propagation training, and demonstrate that tremendous rule number reduction ratio is achieved with very little performance degradation. © 2000 John Wiley & Sons, Inc.     

A probabilistic fuzzy logic system for modeling and control

In this paper, a probabilistic fuzzy logic system (PFLS) is proposed for the modeling and control problems. Similar to the ordinary fuzzy logic system (FLS), the PFLS consists of the fuzzification, inference engine and defuzzification operation to process the fuzzy information. Different to the FLS, it uses the probabilistic modeling method to improve the stochastic modeling capability. By using a three-dimensional membership function (MF), the PFLS is able to handle the effect of random noise and stochastic uncertainties existing in the process. A unique defuzzification method is proposed to simplify the complex operation. Finally, the proposed PFLS is applied to a function approximation problem and a robotic system. It shows a better performance than an ordinary FLS in stochastic circumstance.     

Direct adaptive interval type-2 fuzzy control of multivariable nonlinear systems

A fuzzy logic controller equipped with a training algorithm is developed such that the H^∞ tracking performance should be satisfied for a model-free nonlinear multiple-input multiple-output (MIMO) system, with external disturbances. Due to universal approximation theorem, fuzzy control provides nonlinear controller, i.e., fuzzy logic controllers, to perform the unknown nonlinear control actions and the tracking error, because of the matching error and external disturbance is attenuated to arbitrary desired level by using H^∞ tracking design technique. In this paper, a new direct adaptive interval type-2 fuzzy controller is developed to handle the training data corrupted by noise or rule uncertainties for nonlinear MIMO systems involving external disturbances. Therefore, linguistic fuzzy control rules can be directly incorporated into the controller and combine the H^∞ attenuation technique. Simulation results show that the interval type-2 fuzzy logic system can handle unpredicted internal disturbance, data uncertainties, very well, but the adaptive type-1 fuzzy controller must spend more control effort in order to deal with noisy training data. Furthermore, the adaptive interval type-2 fuzzy controller can perform successful control and guarantee the global stability of the resulting closed-loop system and the tracking performance can be achieved.     

A Probabilistic Neural-Fuzzy Learning System for Stochastic Modeling

A probabilistic fuzzy neural network (PFNN) with a hybrid learning mechanism is proposed to handle complex stochastic uncertainties. Fuzzy logic systems (FLSs) are well known for vagueness processing. Embedded with the probabilistic method, an FLS will possess the capability to capture stochastic uncertainties. Further enhanced with the neural learning, it will be able to work under time-varying stochastic environment. Integrated with a statistical process control (SPC) based monitoring method, the PFNN can maintain the robust modeling performance. Finally, the successful simulation demonstrates the modeling effectiveness of the proposed PFNN under the time-varying stochastic conditions.      

基于TS模型的二型模糊控制器和观测器分析与设计

主要探讨一种新的系统方法——二型模糊系统在控制上的应用．文章先介绍了二型模糊集合和系统的基本概念和基本方法，然后集中推导TS模型下规则的输出形式，推广一型系统的特性，从而获得二型模糊控制器和观测器的表达式、稳定性以及其它特性分析方法，并以小车倒立摆仿真验证．最后文章从整体上分析和比较了传统系统、一型模糊系统和二型模糊系统的主要特点和不同点．