A Multi-Objective Genetic Approach to Concurrently Learn Partition Granularity and Rule Bases of Mamdani Fuzzy Systems

In this paper we propose a multi-objective genetic algorithm to generate Mamdani fuzzy rule-based systems with optimal trade-offs between complexity and accuracy. The main novelty of the algorithm is that both rule base and granularity of the uniform partitions defined on the input and output variables are learned concurrently. To this aim, we exploit a chromosome composed of two parts, which codify the numbers of fuzzy sets for each linguistic variable and the rule base, respectively. Rule bases defined on partitions with different granularity are handled by using an appropriate mapping strategy. The algorithm has been tested on a real word regression problem showing very promising results.

[1]  Francisco Herrera,et al.  COR: a methodology to improve ad hoc data-driven linguistic rule learning methods by inducing cooperation among rules , 2002, IEEE Trans. Syst. Man Cybern. Part B.

[2]  Hisao Ishibuchi,et al.  Selecting fuzzy if-then rules for classification problems using genetic algorithms , 1995, IEEE Trans. Fuzzy Syst..

[3]  M. Lozano,et al.  MOGUL: A methodology to obtain genetic fuzzy rule‐based systems under the iterative rule learning approach , 1999 .

[4]  Francisco Herrera,et al.  Generating the knowledge base of a fuzzy rule-based system by the genetic learning of the data base , 2001, IEEE Trans. Fuzzy Syst..

[5]  Jerry M. Mendel,et al.  Generating fuzzy rules by learning from examples , 1992, IEEE Trans. Syst. Man Cybern..

[6]  Hisao Ishibuchi,et al.  Analysis of interpretability-accuracy tradeoff of fuzzy systems by multiobjective fuzzy genetics-based machine learning , 2007, Int. J. Approx. Reason..

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

[8]  Antonio González Muñoz,et al.  SLAVE: a genetic learning system based on an iterative approach , 1999, IEEE Trans. Fuzzy Syst..

[9]  Beatrice Lazzerini,et al.  A Pareto-based multi-objective evolutionary approach to the identification of Mamdani fuzzy systems , 2007, Soft Comput..

[10]  Francisco Herrera,et al.  Solving Electrical Distribution Problems Using Hybrid Evolutionary Data Analysis Techniques , 2004, Applied Intelligence.

[11]  E. H. Mamdani,et al.  An Experiment in Linguistic Synthesis with a Fuzzy Logic Controller , 1999, Int. J. Man Mach. Stud..

[12]  Francisco Herrera,et al.  Analysis and guidelines to obtain a good uniform fuzzy partition granularity for fuzzy rule-based systems using simulated annealing , 2000, Int. J. Approx. Reason..

[13]  Jesús Alcalá-Fdez,et al.  Genetic learning of accurate and compact fuzzy rule based systems based on the 2-tuples linguistic representation , 2007, Int. J. Approx. Reason..

[14]  Hisao Ishibuchi,et al.  Multiobjective Genetic Fuzzy Systems: Review and Future Research Directions , 2007, 2007 IEEE International Fuzzy Systems Conference.

[15]  Francisco Herrera,et al.  Genetic fuzzy systems: taxonomy, current research trends and prospects , 2008, Evol. Intell..