The Fuzzy- Number Based Key Theorem of Statistical Learning Theory

Recently, many scholars are becoming interested in the study of statistical learning theory based on fuzzy field. In this paper, we redefine the definitions of fuzzy expected risk functional, fuzzy empirical risk functional and fuzzy empirical risk minimization principal based on fuzzy samples, where the two type of fuzzy risk functional are still fuzzy number. Based on the above, we give the proof of the key theorem, which plays an important role in the statistical learning theory