Rule Base Reduction and Genetic Tuning of Fuzzy Systems Based on the Linguistic 3-tuples Representation

Recently, a new linguistic rule representation model was presented to perform a genetic lateral tuning of membership functions. It is based on the linguistic 2-tuples representation model, that allows the symbolic translation of a label considering an unique parameter. It involves a reduction of the search space that eases the derivation of optimal models. This work presents a new symbolic representation with three values (s, α, β), respectively representing a label, the lateral displacement and the amplitude variation of the support of this label. Based on this new representation we propose a new method for fine tuning of membership functions that is combined with a rule base reduction method in order to extract the most useful tuned rules. This approach makes use of a modified inference system that consider non-covered inputs in order to improve the final fuzzymodel generalization ability, specially in highly non-linear problems with noise points. Additionally, we analyze the proposed approach showing its behavior in two real-world applications. Supported by the Spanish Ministry of Science and Technology under Projects TIC-2002-04036-C05-01 and TIN-2005-08386-C05-01. R. Alcalá (B) · J. Alcalá-Fdez · M. J. Gacto · F. Herrera Department of Computer Science and Artificial Intelligence, University of Granada, 18071 Granada, Spain e-mail: [email protected] J. Alcalá-Fdez e-mail: [email protected] M. J. Gacto e-mail: [email protected] F. Herrera e-mail: [email protected]