An Interval Type-2 Neural Fuzzy System for Online System Identification and Feature Elimination

Nonsingular Gradient Descent Algorithm for Interval Type-2 Fuzzy Neural Network

Interval type-2 fuzzy neural network (IT2FNN) is widely used to model nonlinear systems. Unfortunately, the gradient descent-based IT2FNN with uncertain variances always suffers from low convergence speed due to its inherent singularity. To cope with this problem, a nonsingular gradient descent algorithm (NSGDA) is developed to update IT2FNN in this article. First, the widths of type-2 fuzzy rules are transformed into root inverse variances (RIVs) that always satisfy the sufficient condition of differentiability. Second, the singular RIVs are reformulated by the nonsingular Shapley-based matrices associated with type-2 fuzzy rules. It averts the convergence stagnation caused by zero derivatives of singular RIVs, thereby sustaining the gradient convergence. Third, an integrated-form update strategy (IUS) is designed to obtain the derivatives of parameters, including RIVs, centers, weight coefficients, deviations, and proportionality coefficient of IT2FNN. These parameters are packed into multiple subvariable matrices, which are capable to accelerate gradient convergence using parallel calculation instead of sequence iteration. Finally, the experiments showcase that the proposed NSGDA-based IT2FNN can improve the convergence speed through the improved learning algorithm.

Self-Organizing Interval Type-2 Fuzzy Neural Network Using Information Aggregation Method

Interval type-2 fuzzy neural networks (IT2FNNs) usually stack adequate fuzzy rules to identify nonlinear systems with high-dimensional inputs, which may result in an explosion of fuzzy rules. To cope with this problem, a self-organizing IT2FNN, based on the information aggregation method (IA-SOIT2FNN), is developed to avoid the explosion of fuzzy rules in this article. First, a relation-aware strategy is proposed to construct rotatable type-2 fuzzy rules (RT2FRs). This strategy uses the individual RT2FR, instead of multiple standard fuzzy rules, to interpret interactive features of high-dimensional inputs. Second, a comprehensive information evaluation mechanism, associated with the interval information and rotation information of RT2FR, is developed to direct the structural adjustment of IA-SOIT2FNN. This mechanism can achieve a compact structure of IA-SOIT2FNN by growing and pruning RT2FRs. Third, a multicriteria-based optimization algorithm is designed to optimize the parameters of IA-SOIT2FNN. The algorithm can simultaneously update the rotatable parameters and the conventional parameters of RT2FR, and further maintain the accuracy of IA-SOIT2FNN. Finally, the experiments showcase that the proposed IA-SOIT2FNN can compete with the state-of-the-art approaches in terms of identification performance.

T-S fuzzy model identification based on an improved interval type-2 fuzzy c-regression model

Fuzzy clustering has been widely applied in T-S fuzzy model identification for nonlinear systems, however, tradition type-1 fuzzy clustering algorithms can’t deal with uncertainties in real world, an improved interval type-2 fuzzy c-regression model (IT2-FCRM) clustering is proposed for T-S fuzzy model identification in this paper. The improved IT2-FCRM adapts a new objective function, which makes the boundary of clustering more clearly and reduces the influence of outliers or noisy data on clustering results. The premise parameters of T-S fuzzy model are upper and lower hyperplanes obtained by improved IT2-FCRM, and the upper and lower hyperplanes are used to build hyper-plane-shaped type-2 Gaussian membership function. Compared with the hyper-sphere-shaped membership function of tradition IT2-FCRM, the hyper-plane-shaped membership function is more coincided with point to plane sample distance described by FCRM clustering. The simulation results of several benchmark problems and a real bed temperature in circulating fluidized bed plant show that the identification algorithm has higher accuracy.

A Novel Interval Type-2 Fuzzy System Identification Method Based on the Modified Fuzzy C-Regression Model

In this article, a novel interval type-2 Takagi-Sugeno fuzzy c -regression modeling method with a modified distance definition is proposed. The modified distance definition is developed to describe the distance between each data point and the local type-2 fuzzy model. To improve the robustness of the proposed identification method, a modified objective function is presented. In addition, different from most previous studies that require numerous free parameters to be determined, an interval type-2 fuzzy c -regression model is developed to reduce the number of such free parameters. Furthermore, an improved ratio between the upper and lower weights is proposed based on the upper and lower membership function with each input data, and the ordinary least-squares method is adopted to establish the type-2 fuzzy model. The Box-Jenkins model and two numerical models are given to illustrate the effectiveness and robustness of the proposed results.

Sensory evaluation of customer satisfaction using type-2 fuzzy logic

Sensory experiences that include vision, hearing, touching, smelling and tasting are important parameters that enable people to trade effectively in retail stores. In this study, based on multisensory attributes the evaluation of customer satisfaction is considered using fuzzy set theory and conjoint analysis. Fuzzy set theory is one of the best methodologies for describing the meaning of linguistic values that express customer preferences. However, there may be different customer and expert opinions in the evaluation of preferences by expressing linguistic values. In the paper, a type-2 fuzzy set is used to handle these uncertainties. This paper proposes the combination of type-2 fuzzy sets and conjoint analysis in order to evaluate customer satisfaction using customer opinions about sensory variables such as sight, sound, taste, touch and smell when purchasing goods in retail stores. For this purpose, using statistical survey results and type-2 fuzzy sets the customer satisfaction degrees were determined. The methodology used for the determination of customer satisfaction is based on conjoint analysis that uses the similarity measure to determine the closest opinions of the customers and experts for the evaluation of customer satisfaction degrees. The obtained experimental results indicate the efficiency of the presented approach in the determination of customer satisfaction in retail markets.

A novel interval type-2 fuzzy Kalman filtering and tracking of experimental data

In this paper, a methodology for design of fuzzy Kalman filter, using interval type-2 fuzzy models, in discrete time domain, via spectral decomposition of experimental data, is proposed. The adopted methodology consists of recursive parametric estimation of local state space linear submodels of interval type-2 fuzzy Kalman filter for tracking and forecasting of the dynamics inherited to experimental data, using an interval type-2 fuzzy version of Observer/Kalman Filter Identification (OKID) algorithm. The partitioning of the experimental data is performed by interval type-2 fuzzy Gustafson-Kessel clustering algorithm. The interval Kalman gains in the consequent proposition of interval type-2 fuzzy Kalman filter are updated according to unobservable components computed by recursive spectral decomposition of experimental data. Computational results illustrate the efficiency of proposed methodology for filtering and tracking the time delayed state variables of Chen's chaotic attractor in a noisy environment, and experimental results illustrate its applicability for adaptive and real time forecasting the dynamic spread behavior of novel Coronavirus 2019 (COVID-19) outbreak in Brazil.

Reinforcement Learning-Based Differential Evolution With Cooperative Coevolution for a Compensatory Neuro-Fuzzy Controller

This paper presents the integration of reinforcement learning-based differential evolution (DE) with the cooperative coevolution (R-CCDE) method in a compensatory neuro-fuzzy controller (CNFC). The CNFC model employs compensatory fuzzy operations, which increase the adaptability and effectiveness of the controller. The R-CCDE method was used to determine an adequate control policy for nonlinear system problems. The evolution of a population involved the use of DE with cooperative coevolution to adjust CNFC parameters, and the fitness function of the R-CCDE method is used by a reinforcement signal to determine the controller that can be used to solve the control problem. This paper identified the best performing controller to solve nonlinear system problems. The simulation results of the proposed R-CCDE method were compared with those of various DE methods and the performance of the proposed R-CCDE method was superior to that of the other methods.

Hybrid Fuzzy Wavelet Neural Networks Architecture Based on Polynomial Neural Networks and Fuzzy Set/Relation Inference-Based Wavelet Neurons

This paper presents a hybrid fuzzy wavelet neural network (HFWNN) realized with the aid of polynomial neural networks (PNNs) and fuzzy inference-based wavelet neurons (FIWNs). Two types of FIWNs including fuzzy set inference-based wavelet neurons (FSIWNs) and fuzzy relation inference-based wavelet neurons (FRIWNs) are proposed. In particular, a FIWN without any fuzzy set component (viz., a premise part of fuzzy rule) becomes a wavelet neuron (WN). To alleviate the limitations of the conventional wavelet neural networks or fuzzy wavelet neural networks whose parameters are determined based on a purely random basis, the parameters of wavelet functions standing in FIWNs or WNs are initialized by using the C-Means clustering method. The overall architecture of the HFWNN is similar to the one of the typical PNNs. The main strategies in the design of HFWNN are developed as follows. First, the first layer of the network consists of FIWNs (e.g., FSIWN or FRIWN) that are used to reflect the uncertainty of data, while the second and higher layers consist of WNs, which exhibit a high level of flexibility and realize a linear combination of wavelet functions. Second, the parameters used in the design of the HFWNN are adjusted through genetic optimization. To evaluate the performance of the proposed HFWNN, several publicly available data are considered. Furthermore a thorough comparative analysis is covered.

Efficient Approach for RLS Type Learning in TSK Neural Fuzzy Systems

This paper presents an efficient approach for the use of recursive least square (RLS) learning algorithm in Takagi-Sugeno-Kang neural fuzzy systems. In the use of RLS, reduced covariance matrix, of which the off-diagonal blocks defining the correlation between rules are set to zeros, may be employed to reduce computational burden. However, as reported in the literature, the performance of such an approach is slightly worse than that of using the full covariance matrix. In this paper, we proposed a so-called enhanced local learning concept in which a threshold is considered to stop learning for those less fired rules. It can be found from our experiments that the proposed approach can have better performances than that of using the full covariance matrix. Enhanced local learning method can be more active on the structure learning phase. Thus, the method not only can stop the update for insufficiently fired rules to reduce disturbances in self-constructing neural fuzzy inference network but also raises the learning speed on structure learning phase by using a large backpropagation learning constant.