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

• Published in: IEEE transactions on fuzzy systems Vol. 27; no. 2; pp. 333 - 347
• Main Authors: Rubio-Solis, Adrian, Melin, Patricia, Martinez-Hernandez, Uriel, Panoutsos, George
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.02.2019; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Basis functions; Chaos theory; Frequency selective surfaces; Fuzzy logic; fuzzy modelling; Fuzzy sets; Fuzzy systems; General Type-2 FLSs; Granulation; Iterative algorithms; Iterative methods; Neural networks; Nonlinear systems; Optimization; Parameter estimation; Radial basis function; Radial basis function networks; Radial Basis Function Neural Networks; Uncertainty; α-plane representation
• ISSN: 1063-6706; 1941-0034
• DOI: 10.1109/TFUZZ.2018.2858740

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 used. Hence, this paper provides four different architectures of the GT2-RBFNN and their parametric optimisation. Such optimisation is a two-stage methodology that first implements an Iterative Information Granulation (IIG) approach to estimate the antecedent parameters of each fuzzy rule. Secondly, each consequent part and the fuzzy rule base of the GT2-RBFNN is optimised using an Adaptive Gradient Descent method (AGD) respectively. A number of popular benchmark data sets, the identification of a nonlinear system and the prediction of 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.