A new support vector machine based on type-2 fuzzy samples

Classical support vector machine is based on the real valued random samples and established on the probability space. It is hard to deal with classification problems based on type-2 fuzzy samples established on non-probability space. The existing algorithm, type-2 fuzzy support vector machine established on generalized credibility space, transforms the classification problems based on type-2 fuzzy samples to general fuzzy optimization problems and expands the application range of traditional support vector machine. However, nonnegativeness of the decision variables of general fuzzy optimization problems is too strict to be satisfied in some practical applications. Motivated by this, the concept of expected fuzzy possibility measure is proposed. Then type-2 fuzzy support vector machine on expected fuzzy possibility space is established, and the second-order cone programming of type-2 fuzzy support vector machine on expected fuzzy possibility space is given. The results of numerical experiments show the effectiveness of the type-2 fuzzy support vector machine established on expected fuzzy possibility space.