Abstract:
A piecewise multilinear and a piecewise linear model for fuzzy systems are introduced and their approximation capabilities investigated. Classical results on the approxim...Show MoreMetadata
Abstract:
A piecewise multilinear and a piecewise linear model for fuzzy systems are introduced and their approximation capabilities investigated. Classical results on the approximation of regular functions are improved showing that fuzzy systems may keep their semantic structure while approximating to any degree of accuracy not only sufficiently regular functions, but also their derivatives.
Published in: IEEE Transactions on Fuzzy Systems ( Volume: 6, Issue: 2, May 1998)
DOI: 10.1109/91.669022
Citations are not available for this document.
Cites in Papers - |
Cites in Papers - IEEE (46)
Select All
1.
Wen Yan, Tao Zhao, Ben Niu, Xin Wang, "Adaptive T-S Fuzzy Control for an Unknown Structure System With a Self-Adjusting Control Accuracy", IEEE Transactions on Automation Science and Engineering, vol.22, pp.944-957, 2025.
2.
Paulo A. Salgado, T-P Azevedo Perdicoúlis, "A note on the assessment of a fuzzy derivatives’ time-series predictor", 2022 IEEE 10th Jubilee International Conference on Computational Cybernetics and Cyber-Medical Systems (ICCC), pp.000377-000382, 2022.
3.
Inés del Campo, Victoria Martínez, Flavia Orosa, Javier Echanobe, Estibalitz Asua, Koldo Basterretxea, "Piecewise multi-linear fuzzy extreme learning machine for the implementation of intelligent agents", 2017 International Joint Conference on Neural Networks (IJCNN), pp.3363-3370, 2017.
4.
Vaibhav B. Joshi, Mehul S. Raval, Dhruv Gupta, Priti P. Rege, "An invertible fuzzy scheme for securing a fragile watermark", 2016 International Conference on Computing, Analytics and Security Trends (CAST), pp.517-522, 2016.
5.
Assem H. Sonbol, M. Sami Fadali, Saeed Jafarzadeh, "TSK Fuzzy Function Approximators: Design and Accuracy Analysis", IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), vol.42, no.3, pp.702-712, 2012.
6.
Inés del Campo, Koldo Basterretxea, Javier Echanobe, Guillermo Bosque, Faiyaz Doctor, "A System-on-Chip Development of a Neuro–Fuzzy Embedded Agent for Ambient-Intelligence Environments", IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), vol.42, no.2, pp.501-512, 2012.
7.
Changchun Hua, Steven X. Ding, "Decentralized Networked Control System Design Using T–S Fuzzy Approach", IEEE Transactions on Fuzzy Systems, vol.20, no.1, pp.9-21, 2012.
8.
Gang Chen, "Discussion of approximation properties of minimum inference fuzzy system", Proceedings of the 29th Chinese Control Conference, pp.2540-2546, 2010.
9.
Koldo Basterretxea, Inés del Campo, Javier Echanobe, "A semi-active suspension embedded controller in a FPGA", International Symposium on Industrial Embedded System (SIES), pp.69-78, 2010.
10.
Tomaso Poggi, Marco Storace, "Digital architectures implementing piecewise-affine functions: An overview", Proceedings of 2010 IEEE International Symposium on Circuits and Systems, pp.3304-3307, 2010.
11.
Iluminada Baturone, Santiago Sánchez-Solano, Andrés A. Gersnoviez, María Brox, "An automated design flow from linguistic models to piecewise polynomial digital circuits", Proceedings of 2010 IEEE International Symposium on Circuits and Systems, pp.3317-3320, 2010.
12.
Ernesto Araujo, Fernando P. A. Araujo, Jose C. Becceneri, Haroldo F. Campos Velho, "Particle swarm optimization with turbulence (PSOT) applied to thermal-vacuum modelling", 2009 IEEE International Conference on Fuzzy Systems, pp.344-349, 2009.
13.
Hao Ying, "Interval Type-2 Takagi-Sugeno fuzzy systems with linear rule consequent are universal approximators", NAFIPS 2009 - 2009 Annual Meeting of the North American Fuzzy Information Processing Society, pp.1-5, 2009.
14.
JosÉ Manuel AndÚjar MÁrquez, Antonio Javier BarragÁn PiÑa, Manuel Emilio GegÚndez Arias, "A General and Formal Methodology to Design Stable Nonlinear Fuzzy Control Systems", IEEE Transactions on Fuzzy Systems, vol.17, no.5, pp.1081-1091, 2009.
15.
Changchun Hua, Qing-Guo Wang, Xinping Guan, "Robust Adaptive Controller Design for Nonlinear Time-Delay Systems via T–S Fuzzy Approach", IEEE Transactions on Fuzzy Systems, vol.17, no.4, pp.901-910, 2009.
16.
InÉs del Campo, Javier Echanobe, Guillermo Bosque, JosÉ Manuel Tarela, "Efficient Hardware/Software Implementation of an Adaptive Neuro-Fuzzy System", IEEE Transactions on Fuzzy Systems, vol.16, no.3, pp.761-778, 2008.
17.
Fahit Gharibnezhad, Alireza Mohammad Shahri, "Elliptec Piezo electric motor: Modeling and control using fuzzy approaches", 2008 5th International Symposium on Mechatronics and Its Applications, pp.1-9, 2008.
18.
Hao Ying, "General interval type-2 Mamdani fuzzy systems are universal approximators", NAFIPS 2008 - 2008 Annual Meeting of the North American Fuzzy Information Processing Society, pp.1-6, 2008.
19.
Ozer Ciftcioglu, I. Sevil Sariyildiz, Michael S. Bittermann, "Building performance analysis supported by GA", 2007 IEEE Congress on Evolutionary Computation, pp.859-866, 2007.
20.
Koldo Basterretxea, Jos Manuel Tarela, Ins del Campo, Guillermo Bosque, "An Experimental Study on Nonlinear Function Computation for Neural/Fuzzy Hardware Design", IEEE Transactions on Neural Networks, vol.18, no.1, pp.266-283, 2007.
21.
Paulo Salgado, Fernando Gouveia, "Approximation of Derivatives by Fuzzy Systems", 2006 3rd International IEEE Conference Intelligent Systems, pp.237-242, 2006.
22.
P. Salgado, "Approximation of Function and its Derivatives by Fuzzy Systems", International Conference on Computational Intelligence for Modelling, Control and Automation and International Conference on Intelligent Agents, Web Technologies and Internet Commerce (CIMCA-IAWTIC'06), vol.1, pp.543-548, 2005.
23.
A. Mencattini, M. Salmeri, A. Salsano, "Sufficient conditions to impose derivative constraints on MISO Takagi-Sugeno Fuzzy logic systems", IEEE Transactions on Fuzzy Systems, vol.13, no.4, pp.454-467, 2005.
24.
Ruiyun Qi, M.A. Brdys, "Adaptive fuzzy modelling and control for discrete-time nonlinear uncertain systems", Proceedings of the 2005, American Control Conference, 2005., pp.1108-1113 vol. 2, 2005.
25.
A. Mencattini, M. Salmeri, R. Lojacono, "A novel methodology for measured data fitting", 2005 IEEE Aerospace Conference, pp.1764-1778, 2005.
26.
Feng Zheng, Qing-Guo Wang, Tong Heng Lee, "Adaptive and robust controller design for uncertain nonlinear systems via fuzzy modeling approach", IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), vol.34, no.1, pp.166-178, 2004.
27.
Yixin Chen, J.Z. Wang, "Support vector learning for fuzzy rule-based classification systems", IEEE Transactions on Fuzzy Systems, vol.11, no.6, pp.716-728, 2003.
28.
A. Sonbol, M.S. Fadali, "Improved fuzzy approximation accuracy using a linear TSK approach", Proceedings of the 2003 American Control Conference, 2003., vol.3, pp.2465-2470 vol.3, 2003.
29.
R. Boukezzoula, S. Galichet, L. Foulloy, "Fuzzy adaptive linearizing control for non-affine systems", The 12th IEEE International Conference on Fuzzy Systems, 2003. FUZZ '03., vol.1, pp.543-548 vol.1, 2003.
30.
Yixin Chen, J.Z. Wang, "Kernel machines and additive fuzzy systems: classification and function approximation", The 12th IEEE International Conference on Fuzzy Systems, 2003. FUZZ '03., vol.2, pp.789-795 vol.2, 2003.
Cites in Papers - Other Publishers (32)
1.
Ruiyun Qi, Gang Tao, Bin Jiang, Fuzzy System Identification and Adaptive Control, pp.25, 2019.
2.
Ruiyun Qi, Gang Tao, Bin Jiang, "Introduction", Fuzzy System Identification and Adaptive Control, pp.1, 2019.
3.
Abhejit Rajagopal, Vincent Radzicki, Hua Lee, Shivkumar Chandrasekaran, "Nonlinear electrocardiographic imaging using polynomial approximation networks", APL Bioengineering, vol.2, no.4, pp.046101, 2018.
4.
Chao Deng, Guang-Hong Yang, "Decentralized fault-tolerant control for a class of nonlinear large-scale systems with actuator faults", Information Sciences, vol.382-383, pp.334, 2017.
5.
G. Bosque, I. del Campo, J. Echanobe, "Fuzzy systems, neural networks and neuro-fuzzy systems: A vision on their hardware implementation and platforms over two decades", Engineering Applications of Artificial Intelligence, vol.32, pp.283, 2014.
6.
Tong Zhao, Guo-ping Lu, Yun-li Hao, Yi-min Li, "The Hybrid Adaptive Control of T-S Fuzzy System Based on Niche", Journal of Applied Mathematics, vol.2012, pp.1, 2012.
7.
Marco Storace, Tomaso Poggi, "Digital architectures realizing piecewise?linear multivariate functions: Two FPGA implementations", International Journal of Circuit Theory and Applications, vol.39, no.1, pp.1, 2011.
8.
Hoang Viet Long, "A note on the rates of uniform approximation of fuzzy systems", International Journal of Computational Intelligence Systems, vol.4, no.4, pp.712, 2011.
9.
INÉS DEL CAMPO, JAVIER ECHANOBE, KOLDO BASTERRETXEA, GUILLERMO BOSQUE, "SCALABLE ARCHITECTURE FOR HIGH-SPEED MULTIDIMENSIONAL FUZZY INFERENCE SYSTEMS", Journal of Circuits, Systems and Computers, vol.20, no.03, pp.375, 2011.
10.
Kuo-Ching Ying, Shih-Wei Lin, Zne-Jung Lee, I.-Lin Lee, "A novel function approximation based on robust fuzzy regression algorithm model and particle swarm optimization", Applied Soft Computing, vol.11, no.2, pp.1820, 2011.
11.
Chunshien Li, Tsunghan Wu, "Adaptive fuzzy approach to function approximation with PSO and RLSE", Expert Systems with Applications, vol.38, no.10, pp.13266, 2011.
12.
Zhendong Sun, "Stability of piecewise linear systems revisited", Annual Reviews in Control, vol.34, no.2, pp.221, 2010.
13.
Jie Liu, Wilson Wang, Farid Golnaraghi, Eric Kubica, "A novel fuzzy framework for nonlinear system control", Fuzzy Sets and Systems, vol.161, no.21, pp.2746, 2010.
14.
Koldo Basterretxea, Inés del Campo, Scalable Fuzzy Algorithms for Data Management and Analysis, pp.1, 2010.
15.
Leandro dos Santos Coelho, Ernesto Araujo, "Identification of the Henon chaotic map by fuzzy modeling and Nelder?Mead simplex method", Chaos, Solitons & Fractals, vol.41, no.5, pp.2762, 2009.
16.
Gang Chen, Hai-jing Wang, Fuzzy Information and Engineering Volume 2, vol.62, pp.357, 2009.
17.
Ruiyun Qi, Mietek A. Brdys, "Stable indirect adaptive control based on discrete-time T?S fuzzy model", Fuzzy Sets and Systems, vol.159, no.8, pp.900, 2008.
18.
Guillermo Bosque, Javier Echanobe, Ines del Campo, Jose M. Tarela, "Modeling and Synthesis of Computational Efficient Adaptive Neuro-Fuzzy Systems Based on Matlab", Artificial Neural Networks - ICANN 2008, vol.5164, pp.131, 2008.
19.
Yixin Chen, "Support Vector Machines and Fuzzy Systems", Soft Computing for Knowledge Discovery and Data Mining, pp.205, 2008.
20.
Paulo Salgado, Fernando Gouveia, Applications of Fuzzy Sets Theory, vol.4578, pp.61, 2007.
21.
Pablo Echevarria, M. Victoria Martínez, Javier Echanobe, Inés del Campo, Jose M. Tarela, Applications of Fuzzy Sets Theory, vol.4578, pp.245, 2007.
22.
Reda Boukezzoula, Sylvie Galichet, Laurent Foulloy, "Fuzzy Feedback Linearizing Controller and Its Equivalence With the Fuzzy Nonlinear Internal Model Control Structure", International Journal of Applied Mathematics and Computer Science, vol.17, no.2, 2007.
23.
Irina Ioannou, Gilles Mauris, Gilles Trystram, Nathalie Perrot, "Back-propagation of imprecision in a cheese ripening fuzzy model based on human sensory evaluations", Fuzzy Sets and Systems, vol.157, no.9, pp.1179, 2006.
24.
Ruiyun Qi, Mietek A. Brdys, "ADAPTIVE FUZZY T-S CONTROL BASED ON LOCAL LINEAR INTEGRAL CONTROLLERS", IFAC Proceedings Volumes, vol.39, no.14, pp.137, 2006.
25.
Giancarlo Ferrari-Trecate, Riccardo Rovatti, "Consistent Sobolev regression via fuzzy systems with overlapping concepts", Fuzzy Sets and Systems, vol.157, no.8, pp.1075, 2006.
26.
J. Echanobe, I. del Campo, J.M. Tarela, "Issues concerning the analysis and implementation of a class of fuzzy controllers", Fuzzy Sets and Systems, vol.155, no.2, pp.252, 2005.
27.
Sylvie Galichet, Reda Boukezzoula, Laurent Foulloy, "Explicit analytical formulation and exact inversion of decomposable fuzzy systems with singleton consequents", Fuzzy Sets and Systems, vol.146, no.3, pp.421, 2004.
28.
Inés Campo, Javier Echanobe, José M. Tarela, Applications and Science in Soft Computing, pp.111, 2004.
29.
Shiji Song, Cheng Wu, "Reverse triple I method of fuzzy reasoning", Science in China Series F Information Sciences, vol.45, no.5, pp.344, 2002.
30.
Giancarlo Ferrari-Trecate, Riccardo Rovatti, "Fuzzy systems with overlapping Gaussian concepts: Approximation properties in Sobolev norms", Fuzzy Sets and Systems, vol.130, no.2, pp.137, 2002.
