Neural networks (NNs) and fuzzy systems are commonly used computational intelligence techniques, each with their own merits in terms of applications. The integration of NNs and fuzzy systems, which leads to a hybrid framework known as neuro-fuzzy systems, inherits the useful properties of its constituents: the learning power of an NN and the knowledge representation of a fuzzy inference system, which makes their combination a powerful tool for machine learning. Numerous structures and models of neurofuzzy systems have been proposed and applied to real-world problems [1–5]. The fuzzy broad learning system (Fuzzy BLS) [6] is a recently proposed neuro-fuzzy model which is constructed by replacing the feature layer of a BLS [7] with Takagi-SugenoKang (TSK) fuzzy sub-systems (see Figure 1(a)). It retains the main architecture of a BLS and employs the k-means algorithm to cluster the input data to reduce computation complexity. Fuzzy BLS achieves higher accuracy in classification and regression problems compared with current state-of-the-art neuro-fuzzy models. To further investigate the performance of Fuzzy BLS, we employ fuzzy c-means to cluster the input data and determine the number of fuzzy rules as well as the centers of Gaussian membership functions. We also randomly generate centers in the input data domain to perform a comprehensive comparison between the case of using cluster methods (i.e., k-means and fuzzy c-means) and the case without clustering. The three variants of Fuzzy BLS (denoted by FBLS-KM, FBLS-FCM, and FBLS-RAND) are evaluated and compared using some popular data sets for classification. Fuzzy broad learning system. We consider a simplified version of Fuzzy BLS, which has m enhancement nodes instead of m groups of enhancement nodes (see Figure 1(a)). Given the following training data: X = (x1, . . . ,xN ) T ∈ R , and the corresponding targets Y = (y1, . . . ,yN ) T ∈ R (N is the number of samples, D represents the input dimension, and C is the output dimension), we employ n TSK fuzzy sub-systems with Ki fuzzy rules in the ith fuzzy sub-system for Fuzzy BLS, where the fuzzy rules have the following form (k = 1, 2, . . . , Ki): If x1 is Aik1· · · and xD is A i kD , then r k = ∑D t=1 a i kt xt, where A kt is a fuzzy set associated with the Gaussian membership
[1]
C. L. Philip Chen,et al.
Broad Learning System: An Effective and Efficient Incremental Learning System Without the Need for Deep Architecture
,
2018,
IEEE Transactions on Neural Networks and Learning Systems.
[2]
Pietro Ducange,et al.
A Distributed Fuzzy Associative Classifier for Big Data
,
2018,
IEEE Transactions on Cybernetics.
[3]
C. L. Philip Chen,et al.
A Fuzzy Restricted Boltzmann Machine: Novel Learning Algorithms Based on the Crisp Possibilistic Mean Value of Fuzzy Numbers
,
2018,
IEEE Transactions on Fuzzy Systems.
[4]
Shuang Feng,et al.
Fuzzy Broad Learning System: A Novel Neuro-Fuzzy Model for Regression and Classification
,
2020,
IEEE Transactions on Cybernetics.
[5]
Hwa Jen Yap,et al.
On Equivalence of FIS and ELM for Interpretable Rule-Based Knowledge Representation
,
2015,
IEEE Transactions on Neural Networks and Learning Systems.
[6]
Chih-Hung Wu,et al.
An Improved Fuzzy Extreme Learning Machine for Classification and Regression
,
2016,
2016 International Conference on Cybernetics, Robotics and Control (CRC).
[7]
Narasimhan Sundararajan,et al.
Online Sequential Fuzzy Extreme Learning Machine for Function Approximation and Classification Problems
,
2009,
IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).