T1: Evolutionery Multi-Objective Design of Fuzzy Rule-Based Systems

Hisao Ishibuchi
Osaka Prefecture University, Japan

Rafael Alcala
University of Granada, Spain

Fuzzy systems are one of the most important areas in the applications of Fuzzy Set Theory. Usually it is considered a model structure in the form of fuzzy rule-based systems (FRBSs). FRBSs constitute an extension to classical rule-based systems, because they deal with "IF-THEN" rules, whose antecedents and consequents are composed of fuzzy logic statements, instead of classical ones.

Automatic design of FRBSs can be seen as an optimization or search problem. Evolutionary Algorithms (EAs) are a well-known and widely-used global search technique with the ability to explore a large search space for suitable solutions only requiring a solution evaluation mechanism. EAs provide a means to encode and evolve rule antecedents, rule consequents, antecedent aggregation operators, rule semantics, rule aggregation operators, and defuzzification methods. Typical approaches are based on the existence of only one performance objective. However there are different situations that require optimizing several objectives that often conflict among them. Beyond concrete problems presenting several performance objectives to optimize, the design of FRBSs presents itself a multi-objective nature. FRBSs should be not only accurate but also interpretable in spite of the original nature of fuzzy logic. Obtaining high degrees of interpretability and accuracy is a contradictory aim, and, in practice, one of the two properties often prevails over the other. Nevertheless, a new tendency in the fuzzy modeling scientific community that looks for a good balance between interpretability and accuracy is increasing in importance.

On account of this, the application of Evolutionary Multi-objective Optimization (EMO) to learn FRBSs with different accuracy-interpretability trade-offs is a current trend of high interest and, it shows considerable potential in the near future. EMO algorithms are one of the most active research areas in the field of evolutionary computation, due to population-based algorithms being capable of capturing a set of non-dominated solutions in a single run of the algorithm. A large number of algorithms have been proposed in the literature. Among them, NSGA-II and SPEA2 are well-known and frequently-used algorithms. In evolutionary multi-objective derivation of FRBSs, it is desirable to design evolutionary learning algorithms in which the learning mechanism itself finds an appropriate balance between interpretability and accuracy. Such an evolutionary learning algorithm should be able to handle as objectives not only an accuracy measure but also different kinds of complexity/interpretability measures. In the last few years, we observed the increase of published papers in this topic due to the high potential of EMO to design FRBSs. We can find among others:

  1. Multi-objective evolutionary rule selection.
  2. Multi-objective evolutionary RB learning.
  3. Multi-objective evolutionary tuning.
  4. Multi-objective evolutionary data mining (including fuzzy association rules, subgroup discovery ...).

This tutorial will provide attendees with: (1) basic ideas and representative algorithms of EMO; (2) a good understanding on the application of EMO algorithms to design FRBSs focusing on the main problem of finding good accuracy-interpretability trade-offs; and, (3) ideas for new research directions within the field of evolutionary multi-objective design of FRBSs.



Hisao Ishibuchi received the B.S. and M.S. degrees in precision mechanics from Kyoto University, Kyoto, Japan, in 1985 and 1987, respectively, and the Ph.D. degree from Osaka Prefecture University, Osaka, Japan, in 1992. From 1987 to 2005, he was with Department of Industrial Engineering, Osaka Prefecture University. He is currently a Professor in Department of Computer Science and Intelligent Systems, Osaka Prefecture University. His research interests include evolutionary multi-objective optimization, multi-objective memetic algorithms, genetic fuzzy systems, fuzzy classification, and fuzzy data mining.

Prof. Ishibuchi received the GECCO 2004 Best Paper Award in the genetic algorithm track, the HIS-NCEI 2006 Best Paper Award, and the 2007 JSPS Prize from Japan Society for the Promotion of Science. He is an Area Editor for the Soft Computing Journal and an Associate Editor for the IEEE Trans. on Evolutionary Computation, the IEEE Trans. on Fuzzy Systems, the IEEE Trans. on Systems, Man, and Cybernetics - Part B, the International Journal of Methaheuristics, and the IEEE Computational Intelligence Magazine. He is also the IEEE CIS Fuzzy Systems Technical Committee Chair, an Area Chair of IFSA 2009, an Area Chair of FUZZ-IEEE 2009, and the Program Chair of CEC 2010.

Rafael Alcala received the M.Sc. degree in Computer Science in 1998 and the Ph.D. degree in Computer Science in 2003, both from the University of Granada, Spain. From 1998 to 2003, he was with Department of Computer Science, University of Jaen. He is currently an Assistant Professor in the Department of Computer Science and Artificial Intelligence at the University of Granada, where he is a Member of the Soft Computing and Intelligent Information Systems Research Group. He has over 50 international publications. As edited activities, he has co-edited the IEEE Transactions on Fuzzy Systems Special Issue on ¡°Genetic Fuzzy Systems: What¡¯s next¡±.

He has worked on several research projects supported by the Spanish government and the European Union. He currently serves as member of the editorial/reviewer board of the journals: International Journal of Computational Intelligence Research, Journal of Advanced Research in Fuzzy and Uncertain Systems and Journal of Universal Computer Science. He is also a Program Co-Chair of GEFS 2010. His current research interests include multi-objective genetic algorithms and genetic fuzzy systems, especially the learning/tuning of fuzzy systems for modeling and control with a good trade-off between accuracy and interpretability, and fuzzy association rules.