General Type-2 Radial Basis Function Neural Network: A Data-Driven Fuzzy Model

Abstract

This paper proposes a new General Type-2 Radial Basis Function Neural Network (GT2-RBFNN) that is functionally equivalent to a GT2 Fuzzy Logic System (FLS) of either Takagi-Sugeno-Kang (TSK) or Mamdani type. The neural structure of the GT2-RBFNN is based on the α-planes representation, in which the antecedent and consequent part of each fuzzy rule uses GT2 Fuzzy Sets (FSs). To reduce the iterative nature of the Karnik-Mendel algorithm, the Enhaned-Karnik-Mendel (EKM) type-reduction and three popular direct-defuzzification methods, namely the 1) Nie-Tan approach (NT), the 2) Wu-Mendel uncertain bounds method (WU) and the 3) Biglarbegian-Melek-Mendel algorithm (BMM) are employed. For that reason, this paper provides four different neural structures of the GT2-RBFNN and their structural and parametric optimisation. Such optimisation is a two-stage methodology that first implements an Iterative Information Granulation approach to estimate the antecedent parameters of each fuzzy rule. Secondly, each consequent part and the fuzzy rule base of the GT2-RBFNN is trained and optimised using an Adaptive Gradient Descent method (AGD) respectively. Several benchmark data sets, including a problem of identification of a nonlinear system and a chaotic time series are considered. The reported comparative analysis of experimental results is used to evaluate the performance of the suggested GT2 RBFNN with respect to other popular methodologies.

A Multilayer Interval Type-2 Fuzzy Extreme Learning Machine for the recognition of walking activities and gait events using wearable sensors

“…To reduce the associated computational load that implies the iterative nature of Karnik-Mendel type-reduction methods, a number of close-form algorithms have been suggested [46]. As described in [41], the Nie-Tan is a direct defuzzification process that employs the vertical representation of the Footprint Of Uncertainty (FOU). As illustrated in Fig.…”

“…6, an Interval Type-2 Fuzzy Extreme Learning (IT2-FELM) using a Nie-Tan (NT) direct-defuzzification layer does not require a sorting process. The application of a Nie-Tan layer represents a zero Taylor series approximation of Karnik-Mendel+defuzzification method [41]. Moreover, a Nie-Tan operator is equivalent to an exhaustive and accurate type-reduction for both discrete and continous IT2 Fuzzy Sets (FSs) [15].…”

“…Both models, the RBFNN and the IT2-RBFNN are a class of MIMO ELMs that were initially suggested for function approximation [40]. Based on the functional equivalence between the IT2-RBFNN and IT2 FLSs [39,41], an ELM can be constructed as an MIMO IT2 FLS if its associated inference mechanism is interpreted as an adaptive filter which resembles an additive combination of the MFs (firing strengths). As illustrated in Fig.…”

“…As described in [41], the IT2-RBFNN for classification problems can be viewed as an ensemble of weighted networks that defines the associated uncertainty of each class as a measure for ambiguity as a variation of the output over unlabeled data sharing the same IT2 firing strength.…”

Hysteresis Modelling and Feedforward Control of Piezoelectric Actuator Based on Simplified Interval Type-2 Fuzzy System

“…In fact, IT2 fuzzy system has more freedom of flexibility to describe the complex phenomenon than traditional type-1 fuzzy system, that makes it capable of modelling the nonlinear system more precisely. It has been applied in nonlinear modelling and automatic control in various studies [29][30][31][32][33][34].…”