Fuzzy neural networks: a survey
Fuzzy Sets and Systems
The nature of statistical learning theory
The nature of statistical learning theory
Fuzzy sets as a basis for a theory of possibility
Fuzzy Sets and Systems
Shrinking the tube: a new support vector regression algorithm
Proceedings of the 1998 conference on Advances in neural information processing systems II
Practical Applications of Fuzzy Technologies
Practical Applications of Fuzzy Technologies
Constructing the Pignistic Probability Function in a Context of Uncertainty
UAI '89 Proceedings of the Fifth Annual Conference on Uncertainty in Artificial Intelligence
Multi-dimensional Function Approximation and Regression Estimation
ICANN '02 Proceedings of the International Conference on Artificial Neural Networks
A new approach to fuzzy regression models with application to business cycle analysis
Fuzzy Sets and Systems
Fuzzy least squares support vector machines for multiclass problems
Neural Networks - 2003 Special issue: Advances in neural networks research — IJCNN'03
Support vector fuzzy regression machines
Fuzzy Sets and Systems - Theme: Learning and modeling
Evaluation for uncertain image classification and segmentation
Pattern Recognition
Pairwise classifier combination using belief functions
Pattern Recognition Letters
LIBSVM: A library for support vector machines
ACM Transactions on Intelligent Systems and Technology (TIST)
Practical uses of belief functions
UAI'99 Proceedings of the Fifteenth conference on Uncertainty in artificial intelligence
SVM multiregression for nonlinear channel estimation in multiple-input multiple-output systems
IEEE Transactions on Signal Processing
An evidence-theoretic k-NN rule with parameter optimization
IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews
A neural network classifier based on Dempster-Shafer theory
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
A learning scheme for a fuzzy k-NN rule
Pattern Recognition Letters
On the convergence of the decomposition method for support vector machines
IEEE Transactions on Neural Networks
Asymptotic convergence of an SMO algorithm without any assumptions
IEEE Transactions on Neural Networks
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Caused by many applications during the last few years, many models have been proposed to represent imprecise and uncertain data. These models are essentially based on the theory of fuzzy sets, the theory of possibilities and the theory of belief functions. These two first theories are based on the membership functions and the last one on the belief functions. Hence, it could be interesting to learn these membership and belief functions from data and then we can, for example, deduce the class for a classification task. Therefore, we propose in this paper a regression approach based on the statistical learning theory of Vapnik. The membership and belief functions have the same properties; that we take as constraints in the resolution of our convex problem in the support vector regression. The proposed approach is applied in a pattern recognition context to evaluate its efficiency. Hence, the regression of the membership functions and the regression of the belief functions give two kinds of classifiers: a fuzzy SVM and a belief SVM. From the learning data, the membership and belief functions are generated from two classical approaches given respectively by fuzzy and belief k-nearest neighbors. Therefore, we compare the proposed approach, in terms of classification results, with these two k-nearest neighbors and with support vector machines classifier.