A Self-Evolving Interval Type-2 Fuzzy Neural Network With Online Structure and Parameter Learning

This paper proposes a self-evolving interval type-2 fuzzy neural network (SEIT2FNN) with online structure and parameter learning. The antecedent parts in each fuzzy rule of the SEIT2FNN are interval type-2 fuzzy sets and the fuzzy rules are of the Takagi-Sugeno-Kang (TSK) type. The initial rule base in the SEIT2FNN is empty, and the online clustering method is proposed to generate fuzzy rules that flexibly partition the input space. To avoid generating highly overlapping fuzzy sets in each input variable, an efficient fuzzy set reduction method is also proposed. This method independently determines whether a corresponding fuzzy set should be generated in each input variable when a new fuzzy rule is generated. For parameter learning, the consequent part parameters are tuned by the rule-ordered Kalman filter algorithm for high-accuracy learning performance. Detailed learning equations on applying the rule-ordered Kalman filter algorithm to the SEIT2FNN consequent part learning, with rules being generated online, are derived. The antecedent part parameters are learned by gradient descent algorithms. The SEIT2FNN is applied to simulations on nonlinear plant modeling, adaptive noise cancellation, and chaotic signal prediction. Comparisons with other type-1 and type-2 fuzzy systems in these examples verify the performance of the SEIT2FNN.

[1]  Hani Hagras,et al.  A hierarchical type-2 fuzzy logic control architecture for autonomous mobile robots , 2004, IEEE Transactions on Fuzzy Systems.

[2]  Nikola K. Kasabov,et al.  HyFIS: adaptive neuro-fuzzy inference systems and their application to nonlinear dynamical systems , 1999, Neural Networks.

[3]  Oscar Castillo,et al.  Intelligent control of non-linear dynamic plants using type-2 fuzzy logic and neural networks , 2002, 2002 Annual Meeting of the North American Fuzzy Information Processing Society Proceedings. NAFIPS-FLINT 2002 (Cat. No. 02TH8622).

[4]  Kim-Fung Man,et al.  Multi-objective hierarchical genetic algorithm for interpretable fuzzy rule-based knowledge extraction , 2005, Fuzzy Sets Syst..

[5]  Meng Joo Er,et al.  NARMAX time series model prediction: feedforward and recurrent fuzzy neural network approaches , 2005, Fuzzy Sets Syst..

[6]  Emil Levi,et al.  Identification of complex systems based on neural and Takagi-Sugeno fuzzy model , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[7]  Wen Yu,et al.  Nonlinear system identification with recurrent neural networks and dead-zone Kalman filter algorithm , 2007, Neurocomputing.

[8]  Luigi Di Lascio,et al.  Medical Differential Diagnosis through Type-2 Fuzzy Sets , 2005, The 14th IEEE International Conference on Fuzzy Systems, 2005. FUZZ '05..

[9]  George C. Mouzouris,et al.  A Singular-Value-QR Decomposition Based Method for Training Fuzzy Logic Systems in Uncertain Environments , 1997, J. Intell. Fuzzy Syst..

[10]  Stephen L. Chiu,et al.  Fuzzy Model Identification Based on Cluster Estimation , 1994, J. Intell. Fuzzy Syst..

[11]  Maurice Clerc,et al.  The particle swarm - explosion, stability, and convergence in a multidimensional complex space , 2002, IEEE Trans. Evol. Comput..

[12]  Chin-Teng Lin,et al.  An online self-constructing neural fuzzy inference network and its applications , 1998, IEEE Trans. Fuzzy Syst..

[13]  Chia-Feng Juang,et al.  An adaptive neural fuzzy filter and its applications , 1996, Proceedings of IEEE 5th International Fuzzy Systems.

[14]  Lei Guo.  Estimating time-varying parameters by the Kalman filter based algorithm: stability and convergence , 1990 .

[15]  Oscar Castillo,et al.  Interval Type-2 TSK Fuzzy Logic Systems Using Hybrid Learning Algorithm , 2005, The 14th IEEE International Conference on Fuzzy Systems, 2005. FUZZ '05..

[16]  Rui Pedro Paiva,et al.  Interpretability and learning in neuro-fuzzy systems , 2004, Fuzzy Sets Syst..

[17]  Jerry M. Mendel,et al.  Type-2 fuzzy sets made simple , 2002, IEEE Trans. Fuzzy Syst..

[18]  H. Ishibuchi.  Genetic fuzzy systems: evolutionary tuning and learning of fuzzy knowledge bases , 2004 .

[19]  Yu-Ching Lin,et al.  Systems identification using type-2 fuzzy neural network (type-2 FNN) systems , 2003, Proceedings 2003 IEEE International Symposium on Computational Intelligence in Robotics and Automation. Computational Intelligence in Robotics and Automation for the New Millennium (Cat. No.03EX694).

[20]  Wan-Jui Lee,et al.  A TSK-type neurofuzzy network approach to system modeling problems , 2005, IEEE Trans. Syst. Man Cybern. Part B.

[21]  Jerry M. Mendel,et al.  Equalization of nonlinear time-varying channels using type-2 fuzzy adaptive filters , 2000, IEEE Trans. Fuzzy Syst..

[22]  Jerry M. Mendel,et al.  Computing derivatives in interval type-2 fuzzy logic systems , 2004, IEEE Transactions on Fuzzy Systems.

[23]  Oscar Castillo,et al.  Adaptive noise cancellation using type-2 fuzzy logic and neural networks , 2004, 2004 IEEE International Conference on Fuzzy Systems (IEEE Cat. No.04CH37542).

[24]  H. B. Mitchell.  Pattern recognition using type-II fuzzy sets , 2005, Inf. Sci..

[25]  Satish Kumar,et al.  Subsethood-product fuzzy neural inference system (SuPFuNIS) , 2002, IEEE Trans. Neural Networks.

[26]  Rudolf Kruse,et al.  Neuro-fuzzy systems for function approximation , 1999, Fuzzy Sets Syst..

[27]  Chia-Feng Juang,et al.  Automatic construction of feedforward/recurrent fuzzy systems by clustering-aided simplex particle swarm optimization , 2007, Fuzzy Sets Syst..

[28]  J. Mendel.  Uncertain Rule-Based Fuzzy Logic Systems: Introduction and New Directions , 2001 .

[29]  Jyh-Shing Roger Jang,et al.  ANFIS: adaptive-network-based fuzzy inference system , 1993, IEEE Trans. Syst. Man Cybern..

[30]  Chin-Teng Lin,et al.  An On-Line Self-Constructing Neural Fuzzy Inference Network and Its Applications , 1998 .

[31]  Robert Ivor John,et al.  Neuro-fuzzy clustering of radiographic tibia image data using type 2 fuzzy sets , 2000, Inf. Sci..

[32]  John Yen,et al.  Simplifying fuzzy rule-based models using orthogonal transformation methods , 1999, IEEE Trans. Syst. Man Cybern. Part B.

[33]  Jerry M. Mendel,et al.  Type-2 fuzzy logic systems , 1999, IEEE Trans. Fuzzy Syst..

[34]  Marco Russo,et al.  Genetic fuzzy learning , 2000, IEEE Trans. Evol. Comput..

[35]  Carlos Andrés Peña-Reyes,et al.  Hardware architecture and FPGA implementation of a type-2 fuzzy system , 2004, GLSVLSI '04.

[36]  Francisco Herrera,et al.  Genetic Fuzzy Systems - Evolutionary Tuning and Learning of Fuzzy Knowledge Bases , 2002, Advances in Fuzzy Systems - Applications and Theory.

[37]  Yaochu Jin,et al.  Fuzzy modeling of high-dimensional systems: complexity reduction and interpretability improvement , 2000, IEEE Trans. Fuzzy Syst..

[38]  D.P. Filev,et al.  An approach to online identification of Takagi-Sugeno fuzzy models , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[39]  Meng Joo Er,et al.  Dynamic fuzzy neural networks-a novel approach to function approximation , 2000, IEEE Trans. Syst. Man Cybern. Part B.

[40]  Hani Hagras.  Comments on "Dynamical Optimal Training for Interval Type-2 Fuzzy Neural Network (T2FNN) , 2006, IEEE Trans. Syst. Man Cybern. Part B.

[41]  Jerry M. Mendel,et al.  Interval type-2 fuzzy logic systems: theory and design , 2000, IEEE Trans. Fuzzy Syst..

[42]  C.J.H. Mann.  Similarity and Compatibility in Fuzzy Set Theory – Assessment and Applications , 2002 .

[43]  Uzay Kaymak,et al.  Similarity measures in fuzzy rule base simplification , 1998, IEEE Trans. Syst. Man Cybern. Part B.

[44]  C. S. George Lee,et al.  Neural fuzzy systems: a neuro-fuzzy synergism to intelligent systems , 1996 .

[45]  Kwang Bo Cho,et al.  Radial basis function based adaptive fuzzy systems and their applications to system identification and prediction , 1996, Fuzzy Sets Syst..

[46]  Chi-Hsu Wang,et al.  Dynamical optimal training for interval type-2 fuzzy neural network (T2FNN) , 2003, SMC'03 Conference Proceedings. 2003 IEEE International Conference on Systems, Man and Cybernetics. Conference Theme - System Security and Assurance (Cat. No.03CH37483).

[47]  Jerry M. Mendel,et al.  A Vector Similarity Measure for Interval Type-2 Fuzzy Sets , 2007, 2007 IEEE International Fuzzy Systems Conference.

[48]  Nikola K. Kasabov,et al.  DENFIS: dynamic evolving neural-fuzzy inference system and its application for time-series prediction , 2002, IEEE Trans. Fuzzy Syst..

[49]  Chin-Teng Lin,et al.  An ART-based fuzzy adaptive learning control network , 1997, IEEE Trans. Fuzzy Syst..