@conference {4222979, title = {Modeling Vague Data with Genetic Fuzzy Systems under a Combination of Crisp and Imprecise Criteria}, booktitle = {2007 IEEE Symposium on Computational Intelligence in Multi-Criteria Decision-Making}, year = {2007}, month = {April}, pages = {30-37}, abstract = {Multicriteria genetic algorithms can produce fuzzy models with a good balance between their precision and their complexity. The accuracy of a model is usually measured by the mean squared error of its residual. When vague training data is used, the residual becomes a fuzzy number, and it is needed to optimize a combination of crisp and fuzzy objectives in order to learn balanced models. In this paper, we will extend the NSGA-II algorithm to this last case, and test it over a practical problem of causal modeling in marketing. Different setups of this algorithm are compared, and it is shown that the algorithm proposed here is able to improve the generalization properties of those models obtained from the defuzzified training data.}, keywords = {Additive noise, combination, Computer science, crisp objectives, defuzzified training data, fuzzy logic, fuzzy models, fuzzy objectives, Fuzzy systems, generalisation (artificial intelligence), generalization, genetic algorithms, Genetic Fuzzy Systems, Global Positioning System, mean squared error, multicriteria genetic algorithms, Noise measurement, NSGA-II algorithm, Position measurement, Probability distribution, Stochastic resonance, Training data, vague data modeling}, doi = {10.1109/MCDM.2007.369413}, author = {L. S{\'a}nchez and I. Couso and J. Casillas} } @conference {943781, title = {A fast genetic method for inducting linguistically understandable fuzzy models}, booktitle = {Proceedings Joint 9th IFSA World Congress and 20th NAFIPS International Conference (Cat. No. 01TH8569)}, volume = {3}, year = {2001}, month = {July}, pages = {1559-1563 vol.3}, abstract = {Fuzzy rule bases can be regarded as mixtures of experts, and boosting techniques can be applied to learn them from data. In particular, provided that adequate reasoning methods are used, fuzzy models are extended additive models, thus backfitting can be applied to them. We propose to use an implementation of backfitting that uses a genetic algorithm for fitting submodels to residuals and we also show that it is both more accurate and faster than other fuzzy rule learning methods.}, keywords = {Artificial intelligence, backfitting, boosting techniques, computational linguistics, extended additive models, fast genetic method, fuzzy logic, fuzzy models, Fuzzy reasoning, fuzzy rule bases, fuzzy rule learning methods, fuzzy set theory, Fuzzy sets, genetic algorithm, genetic algorithms, inference mechanisms, learning (artificial intelligence), Learning systems, linguistically understandable fuzzy model induction, mixtures of experts, reasoning methods, residuals, submodel fitting, Training data, uncertainty handling}, doi = {10.1109/NAFIPS.2001.943781}, author = {L. S{\'a}nchez} }