Interval Type-2 Radial Basis Function Neural Network: A Modeling Framework

Abstract

In this paper, an interval type-2 radial basis function neural network (IT2-RBF-NN) is proposed as a new modeling framework. We take advantage of the functional equivalence of radial basis function neural networks (RBF-NNs) to a class of type-1 fuzzy logic systems (T1-FLS) to propose a new interval type-2 equivalent system; it is systematically shown that the type equivalence (between RBF and FLS) of the new modeling structure is maintained in the case of the IT2 system. The new IT2-RBF-NN incorporates interval type-2 fuzzy sets within the radial basis function layer of the neural network in order to account for linguistic uncertainty in the system's variables. The antecedent part in each rule in the IT2-RBF-NN is an interval type-2 fuzzy set, and the consequent part is of Mamdani type with interval weights, which are used for the Karnik and Mendel type-reduction process in the output layer of the network. The structural and parametric optimization of the IT2-RBF-NN parameters is carried out by a hybrid approach that is based on estimating the initial rule base and footprint of uncertainty (FOU) directly via a granular computing approach and an adaptive back propagation approach. The effectiveness of the new modeling framework is assessed in two parts. First, the IT2-RBF-NN is tested against a number of popular benchmark datasets, and second, it is demonstrated in a real-world industrial application that has particular challenges that are related to the uncertainty of the raw information. Via simulation results, it isshown that the proposed modeling framework performs well as compared with its T1 equivalent system. In addition, a very good computational efficiency is demonstrated as a result of the systematic and automatic creation of IT2 linguistic information and the FOU. Crucially, the proposed modeling framework opens up a host of opportunities for the academic community that already uses the popular T1-RBF-NN-based structure to try the new IT2-RBF-NN and take advantage of the numerous existing RBF-based adaptive learning algorithms, RBF-based multiobjective optimization techniques, granular computing-based information capture techniques, and real-world FLS implementations, and, in general, take advantage of the computational efficiency of the fusion of IT2-FLS and RBF-NN.Index Terms-Adaptive back propagation (BP), Charpy test, granular computing (GrC), interval type-2 fuzzy systems, radial basis function neural networks (RBF-NNs), steel heat treatment.

Parsimonious random vector functional link network for data streams

“…This concept realises an enhancement layer linking the input layer to the output layer -consistent with the original concept of the RVFLN. Note that recently developed RVFLNs in the literature mostly neglect the direct connection because they are designed with a zero-order output node [8], [11], [14], [15], [17], [41], [50], [51], [63], [66], [67] . The direct connection expands the output node to a higher degree of freedom, which aims to improve the local mapping aptitude of the output node.…”

An ensemble data-driven fuzzy network for laser welding quality prediction

“…Thus, the RBF-NN exploits such a granular signature in order to discriminate the role of each fuzzy set and the input variables while preserving a balance between transparency and interpretability [1]. The parameter identification of the EDDFN follows a Negative Correlation Learning (NCL) [7] and an Adaptive Back Error Propagation (ABEP) approach [11] that we call for short Adaptive Negative Correlation Learning (ANCL). The NCL introduces a penalty term in the cost function of each individual DDFM minimising its Mean Square Error (MSE) together with the correlation of the ensemble network so that every DDFM is finally trained by the ANCL.…”

Iterative information granulation for novelty detection in complex datasets

“…For the training of the NFM-T1, IT2-RBF-NN 50% and 100% out of the total instances were employed. According to [6] and [7], two different phases are involved in order to estimate the final parameters of the NFM-T1 and the IT2-RBF-NN. Firstly, the initial parameters of the NFM-T1 and IT2-RBF-NN are computed by granulating the training data set (50% and 100%), and then a second step based on an adaptive gradient descent approach is employed to optimise the fuzzy inference mechanism.…”

“…In other words, the theoretical structure of granulation involves integration of parts into a whole where granules are drawn together by specific canonical forms usually viewed as fuzzy constraints that lead to a conclusion expressed in natural language [2]. Within this context, several efforts have been devoted to data compression algorithms based on granulation that are able not only to group compatible data but also to capture relationships-rules within information [3][4][5][6][7][8][9]. For instance, in [2] the authors developed a granulation mechanism that captures data relationships in the form of information granules (hyperboxes), while also emphasising process transparency.…”

“…In addition, the compatibility criterion introduced in [10] favours the creation of highly dense and compact information granules. In [6], a compatibility measure based on proximity was employed to construct a number of fuzzy logic rules which were used as the initial parameters of a Radial-Basis-Function Neural Network viewed as an Interval Type-II. The fuzzy rules were then optimised by applying an adaptive gradient descent approach.…”