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

Fuzzy logic systems have been extensively applied for solving many real world application problems because they are found to be universal approximators and many methods, particularly, gradient descent (GD) methods have been widely adopted for the optimization of fuzzy membership functions. Despite its popularity, GD still suffers some drawbacks in terms of its slow learning and convergence. In this study, the use of decoupled extended Kalman filter (DEKF) to optimize the parameters of an interval type-2 intuitionistic fuzzy logic system of Tagagi-Sugeno-Kang (IT2IFLS-TSK) fuzzy inference is proposed and results compared with IT2IFLS gradient descent learning. The resulting systems are evaluated on a real world dataset from Australia's electricity market. The IT2IFLS-DEKF is also compared with its type-1 variant and interval type-2 fuzzy logic system (IT2FLS). Analysis of results reveal performance superiority of IT2IFLS trained with DEKF (IT2IFLS-DEKF) over IT2IFLS trained with gradient descent (IT2IFLS-GD). The proposed IT2IFLS-DEKF also outperforms its type-1 variant and IT2FLS on the same learning platform.

This paper studies the continuity of the input-output mappings of fuzzy logic systems (FLSs), including both type-1 (T1) and interval type-2 (IT2) FLSs. We show that a T1 FLS being an universal approximator is equivalent to saying that a T1 FLS has a continuous input-output mapping. We also derive the condition under which a T1 FLS is discontinuous. For IT2 FLSs, we consider six type-reduction and defuzzification methods (the Karnik-Mendel method, the uncertainty bound method, the Wu-Tan method, the Nie-Tan method, the Du-Ying method, and the Begian-Melek-Mendel method) and derive the conditions under which continuous and discontinuous input-output mappings can be obtained. Guidelines for designing continuous IT2 FLSs are also given. This paper is to date the most comprehensive study on the continuity of FLSs. Our results will be very useful in the selection of the parameters of the membership functions to achieve a desired continuity (e.g., for most traditional modeling and control applications) or discontinuity (e.g., for hybrid and switched systems modeling and control).

Studies on interval type-2 TSK fuzzy logic system is a hot topic in the current academic area. Parameter identification is very important for system design. Commonly used parameter identification methods are the least-square algorithm, BP algorithm, etc., few scholars use QPSO algorithm for parameter identification. In this paper, we propose a design of interval type-2 TSK fuzzy logic system based on quantum behaved particle swarm optimization (QPSO) intelligent algorithm. Firstly, by combining the A1–C1, A2–C0, A2–C1 interval type-2 TSK fuzzy logic system with neural network, the fuzzy neural network system is designed. Then, the QPSO intelligent algorithm was used to tune the fuzzy neural network system parameters, and the designed system model is applied to predict the Nasdaq Composite Index and International Gold Prices. Both QPSO algorithm and BP algorithm have been used to train the system model. By comparing QPSO algorithm and BP algorithm, the performance index and simulation results illustrated the proposed model is effective and feasible, which can achieve a better performance. Finally, compare the performance of the four fuzzy logic systems, it can be seen the effect of A2–C1 fuzzy logic system is better than that of the other three fuzzy logic systems.

An interval type-2 fuzzy logic system (IT2FLS) can function well with uncertain data, with which a type-1 fuzzy logic system (T1FLS) is ineffective because its membership function rests upon crisp values. However, similar to T1FLSs, there are challenges associated with IT2FLSs in selecting parameters, which can significantly affect the accuracy of the classification results with their relatively high sensitivity. This paper discusses and proposes a hybrid model based on IT2FLS and particle swarm optimization (PSO) for prediction problems. The main objective of this paper is to find the optimal solution for the unknown fuzzy systems using labelled data for training the fuzzy system. The PSO technique was used to find the optimal parameters of the Gaussian membership functions which utilized for IT2FLSs. The authors tested two data sets for each of the two prediction problems, namely: burnt forest area prediction and wine quality prediction. The predictive results were compared with other predictive methods including random forest (RF), support vector machines (SVM), artificial neural network (ANN), adaptive neuro fuzzy inference system (ANFIS) and IT2FLS with parameters generated by using the fuzzy c-means algorithm (IT2FLS-FCM). Experiment results showed that the proposed method could significantly improve accuracy compared to several other predictive techniques.

In this paper, we present a new approach for sensed signal strength forecasting in wireless sensors using interval type-2 fuzzy logic system (FLS). We show that a type-2 fuzzy membership function, i.e., a Gaussian MF with uncertain mean is most appropriate to model the sensed signal strength of wireless sensors. We demonstrate that the sensed signals of wireless sensors are self-similar, which means it can be forecasted. An interval type-2 FLS is designed for sensed signal forecasting and is compared against a type-1 FLS. Simulation results show that the interval type-2 FLS performs much better than the type-1 FLS in sensed signal forecasting. This application can be further used for power on/off control in wireless sensors to save battery energy.

In this study, interval type2 fuzzy logic (IT2FL) and PID controller is designed for swing-up position control of double inverted pendulum (DIP) system. The double inverted pendulum system consists of two rigid bars connected by a revolute joint. Mass of the revolute joint is included in the dynamic model.Rigid bars in the system are assumed to experience planar motion. The pendulum system is connected to the base by means of a revolute joint. Torque provided through a motor mounted to the base is used for position control of the system. PID (Proportional-Derivative-Integral) and interval type2 fuzzy logic controllers are developed by using the same performance criteria for position control of double inverted pendulum system. IT2FL controller is similar with type1 fuzzy logic controller. IT2FL system provides soft decision boundaries, whereas a type-1 fuzzy logic system provides a hard decision boundary. Membership function in interval type2 fuzzy logic set as an area called Footprint of Uncertainty (FOU) which limited by two type1 membership function those are upper membership function (UMF) and lower membership function (LMF).System behaviour is obtained by computer simulation using developed controllers respectively. Computer simulation results are compared in order to evaluate applicability of developed controllers. MATLAB/Simulink software is used in computer simulations.

In this paper, simulated annealing algorithm is used to design general type-2 fuzzy logic systems (GT2FLS) with the aid of interval type-2 fuzzy logic systems (IT2FLS). The proposed practical design methodology aims to reduce computations needed to get the best footprint of uncertainty (FOU) using IT2FLS. Simulated annealing is used to learn IT2FLS followed by learning the secondary membership functions in GT2FLS using a novel parameterization method. This methodology has been applied to four bench-mark problems. some practical issues have been discussed and some analysis of the results obtained by IT2FLS and GT2FLS has been drawn.

Interval type-2 fuzzy logic systems (IT2 FLSs) have become increasingly popular in the last decade, and have demonstrated superior performance in a number of applications. However, the computations in an IT2 FLS are more complex than those in a type-1 FLS, and there are many choices to be made in designing an IT2 FLS, including the shape of membership functions (Gaussian or trapezoidal), number of membership functions, type of fuzzifier (singleton or non-singleton), kind of rules (Mamdani or Takagi-Sugeno-Kang), type of i-norm (minimum or product), method to compute the output (type-reduction or not), and methods for tuning the parameters (gradient-based methods or evolutionary computation algorithms; one-step or two-step). While these choices give an experienced IT2 FLS researcher extensive freedom to design the optimal IT2 FLS, they may look overwhelming and confusing to IT2 beginners. Such a beginner may make an inappropriate choice, obtain unexpected results, and lose interest, which will hinder the wider applications of IT2 FLSs. In this paper we try to help IT2 beginners navigate through the maze by recommending some representative choices for an IT2 FLS design. We also clarify two myths about IT2 FLSs. This paper will make IT2 FLSs more accessible to IT2 beginners.

Fire-rule-based direct adaptive type-2 fuzzy H∞ tracking control

In this paper, a hybrid training model for interval type-2 fuzzy logic system is proposed. The hybrid training model uses extreme learning machine to tune the consequent part parameters and genetic algorithm to optimize the antecedent part parameters. The proposed hybrid learning model of interval type-2 fuzzy logic system is tested on the prediction of Mackey-Glass time series data sets with different levels of noise. The results are compared with the existing models in literature; extreme learning machine and Kalman filter based learning of consequent part parameters with randomly generated antecedent part parameters. It is observed that the interval type-2 fuzzy logic system provides improved performance with the proposed hybrid learning model.

Clustering is an effective method for reducing energy consumption in wireless sensor networks (WSNs). In a multihop clustered network scenario, each sensor node transmits data to its own cluster head (CH), and the CH aggregates the data from its member nodes and forwards it to the base station (BS) via other CHs. However, the “hot spot” problem is prone to occur in clustered WSNs because CHs closer to the BS have heavier intercluster forwarding tasks. To address this problem, this paper proposes an unequal clustering algorithm based on interval type-2 TSK fuzzy logic theory (UCT2TSK). The relative distance to the BS (RDB), residual energy (RE), and node density (ND) are considered as the inputs of an interval type-2 fuzzy logic system (FLS). Through fuzzy reasoning, outputs are acquired that can be used to optimize the CHs and determine the cluster sizes. Simulation results verify that UCT2TSK can effectively balance energy consumption and enhance energy efficiency because it has better performance in network lifetime and network throughput than other classical and recent clustering algorithms.

Learning of fuzzy parameters for system modeling using evolutionary algorithms is an interesting topic. In this paper, two optimal design and tuning of Interval type-2 fuzzy logic system are proposed using hybrid learning algorithms. The consequent parameters of the interval type-2 fuzzy logic system in both the hybrid algorithms are tuned using Kalman filter. Whereas the antecedent parameters of the system in the first hybrid algorithm is optimized using the multi-objective particle swarm optimization (MOPSO) and using the multi-objective evolutionary algorithm Based on Decomposition (MOEA/D) in the second hybrid algorithm. Root mean square error and maximum absolute error as the two accuracy objective are utilized to find the Pareto-optimal solution with the MOPSO and MOEA/D respectively. The proposed hybrid multi-objective designs of the interval type-2 fuzzy logic system are utilized to the prediction of solar photovoltaic output. It is observed that MOEA/D outperforms MOPSO in this case in terms of quality of results and its diversity. Finally, one point is selected from the obtained Pareto front and its performance is illustrated.

Power load forecasting is very important in power industry, which can ensure power network runs safely and economically. A novel method for forecasting power load based on interval type-2 fuzzy logic system is proposed in this paper. The fuzzy system is trained by steepest descent algorithm to optimize parameters of membership function so as to produce an output with minimum error. Simulation results show that the interval type-2 FLS performs much better than the type-1 FLS in power load forecasting.

The application interval type-2 fuzzy inference systems (IT2FIS) has been attention for a short-term load forecasting problems solution. This paper present optimization membership function of antecedent (X,Y) and consequent (Z) interval type-2 Fuzzy Logic System using Big Bang – Big Crunch Algorithm for application short term load forecasting on national holiday. This method has implemented on the historical peak load data during 14 national holiday case study in South and Central Kalimantan – Indonesia electrical power system on year 2008. The Big Bang–Big Crunch (BB–BC) algorithm will applied to optimization interval footprint of uncertainty (FOU) membership functions of interval type-2 fuzzy logic system. BB-BC Algorithm is a global optimization algorithm and has a low computational cost and a high convergence speed, so very efficient in this research. The test result showed main absolute percentage error (MAPE) less than interval type-2 fuzzy inference system (FIS) and type-1 fuzzy inference system (FIS). Finally, this paper defined main absolute percentage error (MAPE) 0.58045% for type-1 FIS, 0.53906% for interval type-2 FIS, and 0.52421% for optimization interval type-2 FIS-Big Bang Big Crunch Algorithm.

Design of an interval Type-2 fuzzy model with justifiable uncertainty