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.     

A hybrid model through the fusion of type-2 fuzzy logic systems and extreme learning machines for modelling permeability prediction

Extreme learning machines (ELM), as a learning tool, have gained popularity due to its unique characteristics and performance. However, the generalisation capability of ELM often depends on the nature of the dataset, particularly on whether uncertainty is present in the dataset or not. In order to reduce the effects of uncertainties in ELM prediction and improve its generalisation ability, this paper proposes a hybrid system through a combination of type-2 fuzzy logic systems (type-2 FLS) and ELM; thereafter the hybrid system was applied to model permeability of carbonate reservoir. Type-2 FLS has been chosen to be a precursor to ELM in order to better handle uncertainties existing in datasets beyond the capability of type-1 fuzzy logic systems. The type-2 FLS is used to first handle uncertainties in reservoir data so that its final output is then passed to the ELM for training and then final prediction is done using the unseen testing dataset. Comparative studies have been carried out to compare the performance of the proposed T2-ELM hybrid system with each of the constituent type-2 FLS and ELM, and also artificial neural network (ANN) and support Vector machines (SVM) using five different industrial reservoir data. Empirical results show that the proposed T2-ELM hybrid system outperformed each of type-2 FLS and ELM, as the two constituent models, in all cases, with the improvement made to the ELM performance far higher against that of type-2 FLS that had a closer performance to the hybrid since it is already noted for being able to model uncertainties. The proposed hybrid also outperformed ANN and SVM models considered.     

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.     

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.     

Wireless Sensor Network Lifetime Analysis Using Interval Type-2 Fuzzy Logic Systems

Extending the lifetime of the energy constrained wireless sensor networks is a crucial challenge in sensor network research. In this paper, we present a novel approach based on fuzzy logic systems to analyze the lifetime of a wireless sensor network. We demonstrate that a type-2 fuzzy membership function (MF), i.e., a Gaussian MF with uncertain standard deviation (std) is most appropriate to model a single node lifetime in wireless sensor networks. In our research, we study two basic sensor placement schemes: square-grid and hex-grid. Two fuzzy logic systems (FLSs): a singleton type-1 FLS and an interval type-2 FLS are designed to perform lifetime estimation of the sensor network. We compare our fuzzy approach with other nonfuzzy schemes in previous papers. Simulation results show that FLS offers a feasible method to analyze and estimate the sensor network lifetime and the interval type-2 FLS in which the antecedent and the consequent membership functions are modeled as Gaussian with uncertain std outperforms the singleton type-1 FLS and the nonfuzzy schemes.     

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.     

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     

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.     

A type-2 neural fuzzy system learned through type-1 fuzzy rules and its FPGA-based hardware implementation

This paper first proposes a type-2 neural fuzzy system (NFS) learned through its type-1 counterpart (T2NFS-T1) and then implements the built IT2NFS-T1 in a field-programmable gate array (FPGA) chip. The antecedent part of each fuzzy rule in the T2NFS-T1 uses interval type-2 fuzzy sets, while the consequent part uses a Takagi-Sugeno-Kang (TSK) type with interval combination weights. The T2NFS-T1 uses a simplified type-reduction operation to reduce system training time and hardware implementation cost. Given a training data set, a TSK type-1 NFS is first learned through structure and parameter learning. The built type-1 fuzzy logic system (FLS) is then extended to a type-2 FLS, where highly overlapped type-1 fuzzy sets are merged into interval type-2 fuzzy sets to reduce the total number of fuzzy sets. Finally, the rule consequent and antecedent parameters in the T2NFS-T1 are tuned using a hybrid of the gradient descent and rule-ordered recursive least square (RLS) algorithms. Simulation results and comparisons with various type-1 and type-2 FLSs verify the effectiveness and efficiency of the T2NFS-T1 for system modeling and prediction problems. A new hardware circuit using both parallel-processing and pipeline techniques is proposed to implement the learned T2NFS-T1 in an FPGA chip. The T2NFS-T1 chip reduces the hardware implementation cost in comparison to other type-2 fuzzy chips.     

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.     

Interval type-2 fuzzy logic systems: theory and design

We present the theory and design of interval type-2 fuzzy logic systems (FLSs). We propose an efficient and simplified method to compute the input and antecedent operations for interval type-2 FLSs: one that is based on a general inference formula for them. We introduce the concept of upper and lower membership functions (MFs) and illustrate our efficient inference method for the case of Gaussian primary MFs. We also propose a method for designing an interval type-2 FLS in which we tune its parameters. Finally, we design type-2 FLSs to perform time-series forecasting when a nonstationary time-series is corrupted by additive noise where SNR is uncertain and demonstrate an improved performance over type-1 FLSs     

区间Type-2 T-S间接自适应模糊控制

本文在Type-1 T-S间接自适应模糊控制器的基础上,利用Type-2模糊系统理论,提出了区间Type-2 T-S间接自适应模糊控制器的设计方法.由于该系统的规则前件是区间Type-2模糊集合,后件为精确数,使构造的控制方法既具备Type-2模糊集处理诸多不确定性的特点,能够减少由于规则不确定对系统的影响,同时又具有T-S模糊模型后件为各输入变量的线性组合的特点,可以提高系统的建模精度,减少系统的规则数等优点.本文利用Lyapunov合成方法,研究了在所有变量一致有界的意义下,闭环系统的全局稳定性,分析了区间Type-2 T-S间接自适应模糊控制系统的收敛性,并给出了系统参数的自适应律.通过倒立摆跟踪模型进行仿真,验证其有效性和优越性.     

Interval type-2 fuzzy expert system for prediction of carbon monoxide concentration in mega-cities

This paper presents an indirect approach to interval type-2 fuzzy logic system modeling to forecaste the level of air pollutants. The type-2 fuzzy logic system permits us to model the uncertainties among rules and the parameters related to data analysis. In this paper, we propose an indirect method to create an interval type-2 fuzzy logic system from a historical data, where Footprint of Uncertainties of fuzzy sets are extracted by implementation of an interval type-2 FCM algorithm and based on an upper and lower value for the level of fuzziness m in FCM. Finally, the proposed model is applied for prediction of carbon monoxide concentration in Tehran air pollution. It is shown that the proposed type-2 fuzzy logic system is superior in comparison to type-1 fuzzy logic systems in terms of two performance indices.     

输出约束的有限时间自适应区间二型模糊输出反馈PMSM伺服控制

针对永磁同步电机驱动的伺服系统在不确定性摩擦和未知负载的影响下难以达到高精度的控制效果,提出一种基于区间二型模糊系统的带有输出约束的有限时间自适应输出反馈控制方案.首先,构建一个基于非线性扰动观测器的区间二型模糊状态观测器,分别完成对于未知扰动和速度的估计,区间二型模糊系统完成对于非线性摩擦的逼近;然后,在此基础上,结合滤波误差补偿机制和有限时间技术,引入障碍Lyapunov函数和反步控制技术设计输出约束的自适应区间二型模糊输出反馈控制器;最后,根据Lyapunov稳定性理论提出严格的稳定性分析,保证闭环系统的所有信号均是有限时间内有界的,并通过数值仿真和实验验证了所提出方法的有效性.     

Type-2 fuzzy control for a flexible-joint robot using voltage control strategy

Type-1 fuzzy sets cannot fully handle the uncertainties. To overcome the problem, type-2 fuzzy sets have been proposed. The novelty of this paper is using interval type-2 fuzzy logic controller (IT2FLC) to control a flexible-joint robot with voltage control strategy. In order to take into account the whole robotic system including the dynamics of actuators and the robot manipulator, the voltages of motors are used as inputs of the system. To highlight the capabilities of the control system, a flexible joint robot which is highly nonlinear, heavily coupled and uncertain is used. In addition, to improve the control performance, the parameters of the primary membership functions of IT2FLC are optimized using particle swarm optimization (PSO). A comparative study between the proposed IT2FLC and type-1 fuzzy logic controller (T1FLC) is presented to better assess their respective performance in presence of external disturbance and unmodelled dynamics. Stability analysis is presented and the effectiveness of the proposed control approach is demonstrated by simulations using a two-link flexible-joint robot driven by permanent magnet direct current motors. Simulation results show the superiority of the IT2FLC over the T1FLC in terms of accuracy, robustness and interpretability.     

Type-2 fuzzy neural networks with fuzzy clustering and differential evolution optimization

In many real-world problems involving pattern recognition, system identification and modeling, control, decision making, and forecasting of time-series, available data are quite often of uncertain nature. An interesting alternative is to employ type-2 fuzzy sets, which augment fuzzy models with expressive power to develop models, which efficiently capture the factor of uncertainty. The three-dimensional membership functions of type-2 fuzzy sets offer additional degrees of freedom that make it possible to directly and more effectively account for model’s uncertainties. Type-2 fuzzy logic systems developed with the aid of evolutionary optimization forms a useful modeling tool subsequently resulting in a collection of efficient “If-Then” rules.The type-2 fuzzy neural networks take advantage of capabilities of fuzzy clustering by generating type-2 fuzzy rule base, resulting in a small number of rules and then optimizing membership functions of type-2 fuzzy sets present in the antecedent and consequent parts of the rules. The clustering itself is realized with the aid of differential evolution.Several examples, including a benchmark problem of identification of nonlinear system, are considered. The reported comparative analysis of experimental results is used to quantify the performance of the developed networks.     

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．     

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.     

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.     

Data-driven modeling and optimization of thermal comfort and energy consumption using type-2 fuzzy method

In the research domain of intelligent buildings and smart home, modeling and optimization of the thermal comfort and energy consumption are important issues. This paper presents a type-2 fuzzy method based data-driven strategy for the modeling and optimization of thermal comfort words and energy consumption. First, we propose a methodology to convert the interval survey data on thermal comfort words to the interval type-2 fuzzy sets (IT2 FSs) which can reflect the inter-personal and intra-personal uncertainties contained in the intervals. This data-driven strategy includes three steps: survey data collection and pre-processing, ambiguity-preserved conversion of the survey intervals to their representative type-1 fuzzy sets (T1 FSs), IT2 FS modeling. Then, using the IT2 FS models of thermal comfort words as antecedent parts, an evolving type-2 fuzzy model is constructed to reflect the online observed energy consumption data. Finally, a multiobjective optimization model is presented to recommend a reasonable temperature range that can give comfortable feeling while reducing energy consumption. The proposed method can be used to realize comfortable but energy-saving environment in smart home or intelligent buildings.