The Key Theorem of Statistical Learning Theory with Fuzzy Samples

The key theorem of statistical learning theory provides a theoretical basis for the applied research of support vector machine etc., so it is one of the most important theorems in learning theory. By combining fuzzy set with statistical learning theory, the key theorem of learning theory is generalized. We replace random samples with fuzzy samples. Fuzzy empirical risk minimization principle is proposed. And the key theorem of statistical learning theory with fuzzy samples is proven.