Abstract
Fuzzy modelling research has traditionally focused on certain types of fuzzy rules. However, the use of alternative rule models could improve the ability of fuzzy systems to represent a specific problem. In this proposal, an extended fuzzy rule model, that can include relations between variables in the antecedent of rules is presented. Furthermore, a learning algorithm based on the iterative genetic approach which is able to represent the knowledge using this model is proposed as well. On the other hand, potential relations among initial variables imply an exponential growth in the feasible rule search space. Consequently, two filters for detecting relevant potential relations are added to the learning algorithm. These filters allows to decrease the search space complexity and increase the algorithm efficiency. Finally, we also present an experimental study to demonstrate the benefits of using fuzzy relational rules.
Article PDF
Avoid common mistakes on your manuscript.
References
E.H. Mamdani, S. Assilian, “An experiment in linguistic synthesis with fuzzy logic controller,” International Journal of Man-Machine Studies, 7, 1–13 (1975).
T. Takagi, M. Sugeno, “Fuzzy identification of systems and its application to modeling and control,” IEEE Transactions on Systems, Man and Cybernetics, 15, 116–132 (1985).
E. Aguirre, A. González, Raúl Pérez, “An inductive approach for learning fuzzy relational rules,” Proceedings Third EUSFLAT 2003 Conference, 88–93 (2003).
A. E. Gaweda, J.M. Zurada, “Data-driven linguistic modeling using relational fuzzy rules,” IEEE Transactions of Fuzzy Systems, vol 11, no. 1, 121–134 (2003).
R.R. Yager, “The representation of fuzzy relational production rules,” Journal of Applied Intelligence, 1, 35–42 (1991).
A. González, R. Pérez,”Completeness and consistency conditions for learning fuzzy rules,”. Fuzzy Sets and Systems, 96, 37–51 (1998).
Y. Caises, E. Leyva, A. González, R. Pérez, “A Genetic Learning of Fuzzy Relational Rules,” Proceedings of the IWCCI 2010, EEE World Conference on Computational Intelligence- FUZZ-IEEE, 207–214 (2010).
A. González, R. Pérez,”Improving the genetic algorithm of SLAVE,” Mathware and Soft Computing, 16, 59–70 (2009).
R.R. Yager, D. P. Filev, “Relational partitioning of fuzzy rules,” Fuzzy Sets and Systems, 80, 57–69 (1996).
T. Mitchell, “Machine Learning,” Ed. MacGraw-Hill (1997).
Michalski R.S., “Understanding the nature of learning,” Machine Learning: An artificial intelligence approach (Vol II). San Mateo, CA: Morgan Kaufmann, 1986.
A. González, R. Pérez, “An analysis of the scalability of an embedded feature selection model for classification problems,” Proceedings of the Information Processing and Management of Uncertainty on Knowledge-Based Systems IPMU 2006, 1949–1956 (2006).
A. González, R. Pérez, “Selection of Relevant Features in a Fuzzy Genetic Learning Algorithm”. IEEE Transactions on System, Man, and Cybernetics Part B, vol. 31 (3), 417–425 (2001).
S. Kullback, “Information Theory and Statistics,” Gloucester, Mass, 1978.
L. Wehenkel, “On uncertainty measures used for decision tree induction,” Proc. of IPMU’96, 413–418 (1996).
A. Asuncion, D.J. Newman, “UCI Machine Learning Repository” [http://www.ics.uci.edu/mlearn/MLRepository.html]. Irvine, CA: University of California, School of Information and Computer Science, 2007.
A. González, R. Pérez, “SLAVE: to genetic learning system based on an iterative approach,” IEEE Transaction on Fuzzy System, vol. 27 (2), pp. 176–19, 1999.
O. Dunn,”Multiple Comparisons among means,” Journal of the American Statistical Association, 1961.
I.H. Witten and E. Frank, “Data mining: practical machine learning tools and techniques, “ Morgan Kaufmann, San Francisco, 2nd edition (2005).
J. Demsar,”Statistical comparisons of classifiers over multiple data sets,” Journal of Machine Learning Research, 7, 1–30 (2006).
M. Friedman, The use of ranks to avoid the assumption of normality implicit in the analysis of variance, Journal of the American Statistical Association, vol. 32, no. 200, (1937).
Quinlan J.R., “C4.5 Program for Machine Learning,” Morgan Kaufmann (1993).
D.W. Aha, D.F Kibler and M.K. Albert, “Instance-based learning algorithms. Machine Learning”, 6, 37–66 (1991).
G.H. John and P. Langley, “Estimating continuous distributions in bayesian classifiers,” 11th Conference on Uncertainty in Artificial Intelligence, Morgan Kaufmann, 338–345 (1995).
E. Frank and I.H. Witten, “Generating accurate rule sets without global optimization,” Proceedings of the 15th International Conference on Machine Learning, Morgan Kaufmann, 144–151 (1998).
J. Platt, “Fast training of support vector machines using sequential minimal optimization,” Advances in Kernel Methods - Support Vector Machine. MIT Press (1998).
J. Alcalá et al, KEEL: “A Software Tool to Assess Evolutionary Algorithms to Data Mining Problems,” Soft Computing 13, 307–318 (2009).
H. Ishibuchi et al, “Performance evaluation of fuzzy classifier systems for multidimensional pattern classification problems,” IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics 29 (5), 601–618 (1999).
L. Sánchez, I. Couso, I., “Combining GP Operators With SA Search To Evolve Fuzzy Rule Based Classifiers,” Information Sciences 136 (1–4), 175–192 (2001).
J. Otero, L. Sánchez, “Induction of descriptive fuzzy classifiers with the Logitboost algorithm,” Soft Computing 10 (9), 825–835 (2006).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
This is an open access article distributed under the CC BY-NC license (https://doi.org/creativecommons.org/licenses/by-nc/4.0/).
About this article
Cite this article
González, A., Pérez, R., Caises, Y. et al. An Efficient Inductive Genetic Learning Algorithm for Fuzzy Relational Rules. Int J Comput Intell Syst 5, 212–230 (2012). https://doi.org/10.1080/18756891.2012.685265
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1080/18756891.2012.685265