Abstract
Abstract System modeling with fuzzy rule-based systems (FRBSs), i.e. fuzzy modeling (FM), usually comes with two contradictory requirements in the obtained model: the interpretability, capability to express the behavior of the real system in an understandable way, and the accuracy, capability to faithfully represent the real system. While linguistic FM (mainly developed by linguistic FRBSs) is focused on the interpretability, precise FM (mainly developed by Takagi-Sugeno-Kang FRBSs) is focused on the accuracy. Since both criteria are of vital importance in system modeling, the balance between them has started to pay attention in the fuzzy community in the last few years.
The chapter analyzes mechanisms to find this balance by improving the interpretability in linguistic FM: selecting input variables, reducing the fuzzy rule set, using more descriptive expressions, or performing linguistic approximation; and in precise FM: reducing the fuzzy rule set, reducing the number of fuzzy sets, or exploiting the local description of the rules.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
R. Alcalá, J. Casillas, O. Cordon, and F. Herrera. Building fuzzy graphs: features and taxonomy of learning for non-grid-oriented fuzzy rule-based systems. To appear in Journal of Intelligent and Fuzzy Systems. Draft version available at http://decsai.ugr.es/~casillas/.
R. Babuška. Fuzzy modeling for control. Kluwer Academic, Norwell, MA, USA, 1998.
R. Babuška, H. Bersini, D.A. Linkens, D. Nauck, G. Tselentis, and O. Wolkenhauer. Future prospects for fuzzy systems and technology. ERUDIT Newsletter Vol. 6, No. 1 . Aachen, Germany, 2000. Available at http://www.erudit.de/erudit/newsletters/news_61/page5.htm.
A. Bastian. How to handle the flexibility of linguistic variables with applications. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2(4):463–484, 1994.
M. Bikdash. A highly interpretable form of Sugeno inference systems. IEEE Transactions on Fuzzy Systems, 7(4686–696, 1999.
P. Carmona, J.L. Castro, and J.M. Zurita. Learning maximal structure fuzzy rules with exceptions. In Proceedings of the 2nd International Conference in Fuzzy Logic and Technology, pages 113–117, Leicester, UK, 2001.
B. Carse, T.C. Fogarty, and A. Munro. Evolving fuzzy rule based controllers using genetic algorithms. Fuzzy Sets and Systems, 80:273–294, 1996.
J. Casillas, O. Cordon, M.J. del Jesus, and F. Herrera. Genetic feature selection in a fuzzy rule-based classification system learning process for high dimensional problems. Information Sciences, 136(1–4):169–191, 2001.
J. Casillas, O. Cordon, and F. Herrera. Can linguistic modeling be as accurate as fuzzy modeling without losing its description to a high degree? Technical Report #DECSAI-00–01–20, Department of Computer Science and Artificial Intelligence, University of Granada, Granada, Spain, 2000. Available at http://decsai.ugr.es/~casillas/.
J.L. Castro, J.J. Castro-Schez, and J.M. Zurita. Learning maximal structure rules in fuzzy logic for knowledge acquisition in expert systems. Fuzzy Sets and Systems, 101(3):331–342, 1999.
J.L. Castro, C.J. Mantas, and J.M. BenÃtez. Interpretation of artificial neural networks by means of fuzzy rules. IEEE Transactions on Neural Networks, 13(1):101–116, 2002.
Z. Chi, H. Yan, and T. Pham. Fuzzy algorithms with application to image processing and pattern recognition. World Scientific, Singapore, 1996.
W.E. Combs and J.E. Andrews. Combinatorial rule explosion eliminated by a fuzzy rule configuration. IEEE Transactions on Fuzzy Systems, 6(1):1–11, 1998.
M.G. Cooper and J.J. Vidal. Genetic design of fuzzy controllers: the cart and jointed pole problem. In Proceedings of the 3rd IEEE International Conference on Fuzzy Systems, pages 1332–1337, Piscataway, NJ, USA, 1994.
O. Cordón and F. Herrera. A three-stage evolutionary process for learning descriptive and approximate fuzzy logic controller knowledge bases from examples. International Journal of Approximate Reasoning, 17(4):369–407, 1997.
O. Cordón and F. Herrera. A proposal for improving the accuracy of linguistic modeling. IEEE Transactions on Fuzzy Systems, 8(3):335–344, 2000.
D. Driankov, H. Hellendoorn, and M. Reinfrank. An introduction to fuzzy control. Springer-Verlag, Heidelberg, Germany, 1993.
A. Dvořák. On linguistic approximation in the frame of fuzzy logic deduction. Soft Computing, 3(2):111–116, 1999.
F. Eshragh and E.H. Mamdani. A general approach to linguistic approximation. In E.H. Mamdani and B.R. Gaines, editors, Fuzzy Reasoning and its Applications, pages 169–187. Academic Press, London, UK, 1981.
A. Fiordaliso. Autostructuration of fuzzy systems by rules sensitivity analysis. Fuzzy Sets and Systems, 118(2):281–296, 2001.
A. Fiordaliso. A constrained Takagi-Sugeno fuzzy system that allows for better interpretation and analysis. Fuzzy Sets and Systems, 118(2):307–318, 2001.
B. Fritzke. Incremental neuro-fuzzy systems. In B. Bosacchi, J.C. Bezdek, and D.B. Fogel, editors, Proceedings of the International Society for Optical Engineering: Applications of Soft Computing, volume 3165, pages 86–97, 1997.
A.F. Gómez-Skarmeta and F. Jiménez. Fuzzy modeling with hybrid systems. Fuzzy Sets and Systems, 104(2):199–208, 1999.
A. Gonzá and R. Pérez. Completeness and consistency conditions for learning fuzzy rules. Fuzzy Sets and Systems, 96(1):37–51, 1998.
A. Gonzá and R. Pérez. SLAVE: a genetic learning system based on an iterative approach. IEEE Transactions on Fuzzy Systems, 7(2):176–191, 1999.
A. González and R. Pérez. Selection of relevant features in a fuzzy genetic learning algorithm. IEEE Transactions on Systems, Man, and CyberneticsPart B: Cybernetics, 31(3):417–425, 2001.
S. Guillaume. Designing fuzzy inference systems from data: an interpretabilityoriented review. IEEE Transactions on Fuzzy Systems, 9(3):426–443, 2001.
K.M. Hangos, editor. Special issue on grey box modelling, volume 9(6) of International Journal of Adaptive Control and Signal Processing. John Wiley & Sons, New York, NY, USA, 1995.
F. Herrera, M. Lozano, and J.L. Verdegay. A learning process for fuzzy control rules using genetic algorithms. Fuzzy Sets and Systems, 100:143–158, 1998.
T.-P. Hong and J.-B. Chen. Finding relevant attributes and membership functions. Fuzzy Sets and Systems, 103(3):389–404, 1999.
T.-P. Hong and C.-Y. Lee. Effect of merging order on performance of fuzzy induction. Intelligent Data Analysis, 3(2):139–151, 1999.
H. Ishibuchi, T. Murata, and I.B. Türkşen. Single-objective and two-objective genetic algorithms for selecting linguistic rules for pattern classification problems. Fuzzy Sets and Systems, 89(2):135–150, 1997.
H. Ishibuchi, K. Nozaki, N. Yamamoto, and H. Tanaka. Selecting fuzzy if-then rules for classification problems using genetic algorithms. IEEE Transactions on Fuzzy Systems, 3(3):260–270, 1995.
Y. Jin. Fuzzy modeling of high-dimensional systems: complexity reduction and interpretability improvement. IEEE Transactions on Fuzzy Systems, 8(2):212–221, 2000.
A. Klose, A. Nurnberger, and D. Nauck. Some approaches to improve the interpretability of neuro-fuzzy classifiers. In Proceedings of the 6th European Congress on Intelligent Techniques and Soft Computing, pages 629–633, Aachen, Germany, 1998.
L. Koczy. Fuzzy if ... then rule models and their transformation one another. IEEE Transactions on Systems, Man, and Cybernetics, 26(5):621–637, 1996.
A. Krone and H. Kiendl. Automatic generation of positive and negative rules for two-way fuzzy controllers. In Proceedings of the Second European Congress on Intelligent Techniques and Soft Computing, volume 1, pages 438–447, Aachen, Germany, 1994. Verlag Mainz.
A. Krone, P. Krause, and T. Slawinski. A new rule reduction method for finding interpretable and small rule bases in high dimensional search spaces. In Proceedings of the 9th IEEE International Conference on Fuzzy Systems, pages 693–699, San Antonio, TX, USA, 2000.
A. Krone and H. Taeger. Data-based fuzzy rule test for fuzzy modelling. Fuzzy Sets and Systems, 123(3):343–358, 2001.
H.-M. Lee, C.-M. Chen, J.-M. Chen, and Y.-L. Jou. An efficient fuzzy classifier with feature selection based on fuzzy entropy. IEEE Transactions on Systems, Man, and Cybernetics-PartB:Cybernetics, 31(3):426–432, 2001.
P. Lindskog. Fuzzy identification from a grey box modeling point of view. In H. Hellendoorn and D. Driankov, editors, Fuzzy model identification, pages 3–50. Springer-Verlag, Heidelberg, Germany, 1997.
L. Magdalena. Adapting the gain of an FLC with genetic algorithms. International Journal of Approximate Reasoning, 17(4):327–349, 1997.
L. Magdalena and F. Monasterio-Huelin. A fuzzy logic controller with learning through the evolution of its knowledge base. International Journal of Approximate Reasoning, 16(3):335–358, 1997.
E.H. Mamdani. Applications of fuzzy algorithms for control a simple dynamic plant. Proceedings of the IEE121, 12:1585–1588, 1974.
E.H. Mamdani and S. Assilian. An experiment in linguistic systhesis with fuzzy logic controller. International Journal of Man-Machine Studies, 7:1–13, 1975.
J.G. MarÃn-Blázquez, Q. Shen, and A.F. Gómez-Skarmeta. From approximative to descriptive models. In Proceedings of the 9th IEEE International Conference on Fuzzy Systems, pages 829–834, San Antonio, TX, USA, 2000.
P.A. Mastorocostas, J.B. Theocharis, and V.S. Petridis. A constrained orthogonal least-squares method for generating TSK fuzzy models: application to short-term load forecasting. Fuzzy Sets and Systems, 118(2):215–233, 2001.
C.C. Mouzouris and J.M. Mendel. A singular-value-QR decomposition based method for training fuzzy logic systems in uncertain environments. Journal of Intelligent and Fuzzy Systems, 5:367–374, 1997.
W. Pedrycz, editor. Fuzzy modelling: paradigms and practice. Kluwer Academic, Norwell, MA, USA, 1996.
A. Riid and E. Rüstern. Interpretability versus adaptability in fuzzy systems. Proceedings of the Estonian Academy of Sciences. Engineering, 49(2):76–95, 2000.
H. Roubos and M. Setnes. Compact and transparent fuzzy models and classifiers through iterative complexity reduction. IEEE Transactions on Fuzzy Systems, 9(4):516–524, 2001.
M. Setnes, R. Babuška, U. Kaymak, and H.R. van Nauta Lemke. Similarity measures in fuzzy rule base simplification. IEEE Transactions on Systems, Man, and Cybernetics-Part B: Cybernetics, 28(3):376–386, 1998.
M. Setnes, R. Babuška, and H.B. Verbruggen. Complexity reduction in fuzzy modeling. Mathematics and Computers in Simulation, 46(5–6):509–518, 1998.
M. Setnes, R. Babuška, and H.B. Verbruggen. Rule-based modeling: precision and transparency. IEEE Transactions on Systems, Man, and Cybernetics-Part C: Applications and Reviews, 28(1):165–169, 1998.
M. Setnes and H. Hellendoorn. Orthogonal transforms for ordering and reduction of fuzzy rules. In Proceedings of the 9th IEEE International Conference on Fuzzy Systems, pages 700–705, San Antonio, TX, USA, 2000.
M. Setnes and H. Roubos. GA-fuzzy modeling and classification: complexity and performance. IEEE Transactions on Fuzzy Systems, 8(5):509–522, 2000.
L.I.U. Shi-Rong and Y.U. Jin-Shou. Model construction optimization for a class of fuzzy models. Chinese Journal of Computers, 24(2):164–172, 2001.
R. Silipo and M. Berthold. Discriminative power of input features in a fuzzy model. In D. Hand, J. Kok, and M. Berthold, editors, Advances in Intelligent Data Analysis (IDA-99), volume LNCS 1642, pages 87–98. Springer-Verlag, Heidelberg, Germany, 1999.
R. Silipo and M. Berthold. Input features’ impact on fuzzy decision processes. IEEE Transactions on Systems, Man, and Cybernetics-Part B: Cybernetics, 30(6):821–834, 2000.
T. Söderström and P. Stoica. System identification. Prentice Hall, Engleweed Cliffs, NJ, USA, 1989.
T. Sudkamp, J. Knapp, and A. Knapp. Refine and merge: generating small bases from training data. In Proceedings of the 9th IFSA World Congress and the 20th NAFIPS International Conference, pages 197–202, Vancouver, Canada, 2001.
M. Sugeno and G.T. Kang. Structure identification of fuzzy model. Fuzzy Sets and Systems, 28:15–33, 1988.
M. Sugeno and T. Yasukawa. A fuzzy-logic-based approach to qualitative modeling. IEEE Transactions on Fuzzy Systems, 1(1):7–31, 1993.
T. Takagi and M. Sugeno. Fuzzy identification of systems and its application to modeling and control. IEEE Transactions on Systems, Man, and Cybernetics, 15:116–132, 1985.
J. Valente de Oliveira. Semantic constraints for membership function optimization. IEEE Transactions on Systems, Man, and Cybernetics—Part A: Systems and Humans, 29(1):128–138, 1999.
L.-X. Wang and J.M. Mendel. Fuzzy basis functions, universal approximation, and orthogonal least squares learning. IEEE Transactions on Neural Networks, 3:807–814, 1992.
X. Wang and J. Hong. Learning optimization in simplifying fuzzy rules. Fuzzy Sets and Systems, 106(3):349–356, 1999.
N. Xiong and L. Litz. Fuzzy modeling based on premise optimization. In Proceedings of the 9th IEEE International Conference on Fuzzy Systems, pages 859–864, San Antonio, TX, USA, 2000.
Y. Yam, P. Baranyi, and C.-T. Yang. Reduction of fuzzy rule base via singular value decomposition. IEEE Transactions on Fuzzy Systems, 7(2):120–132, 1999.
J. Yen and L. Wang. An SVD-based fuzzy model reduction strategy. In Proceedings of the 5th IEEE International Conference on Fuzzy Systems, pages 835–841, New Orleans, LA, USA, 1996.
J. Yen and L. Wang. Application of statistical information criteria for optimal fuzzy model construction. IEEE Transactions on Fuzzy Systems, 6(3):362–372, 1998.
J. Yen and L. Wang. Simplifying fuzzy rule-based models using orthogonal transformation methods. IEEE Transactions on Systems, Man, and Cybernetics—Part B: Cybernetics, 29(1):13–24, 1999.
J. Yen, L. Wang, and C.W. Gillespie. Improving the interpretability of TSK fuzzy models by combining global learning and local learning. IEEE Transactions on Fuzzy Systems, 6(4):530–537, 1998.
W. Yu and Z. Bien. Design of fuzzy logic controller with inconsistent rule base. Journal of Intelligent and Fuzzy Systems, 2:147–159, 1994.
L.A. Zadeh. Outline of a new approach to the analysis of complex systems and desision processes. IEEE Transactions on Systems, Man, and Cybernetics, 3:28–44, 1973.
L.A. Zadeh. The concept of a linguistic variable and its application to approximate reasoning. Parts I, II and III. Information Science, 8, 9:199–249, 1975.
L.A. Zadeh. The concept of a linguistic variable and its application to approximate reasoning. Parts I, II and III. Information Science, 8, 9:301–357, 1975.
L.A. Zadeh. The concept of a linguistic variable and its application to approximate reasoning. Parts I, II and III. Information Science, 8, 9:43–80, 1975.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Casillas, J., Cordón, O., Herrera, F., Magdalena, L. (2003). Interpretability Improvements to Find the Balance Interpretability-Accuracy in Fuzzy Modeling: An Overview. In: Casillas, J., Cordón, O., Herrera, F., Magdalena, L. (eds) Interpretability Issues in Fuzzy Modeling. Studies in Fuzziness and Soft Computing, vol 128. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-37057-4_1
Download citation
DOI: https://doi.org/10.1007/978-3-540-37057-4_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-05702-1
Online ISBN: 978-3-540-37057-4
eBook Packages: Springer Book Archive