Title :
The Fuzzy- Number Based Key Theorem of Statistical Learning Theory
Author :
Tian, Jing ; Ha, Ming-Hu ; Li, Jun-Hua ; Tian, Da-Zeng
Author_Institution :
Coll. of Quality & Tech. Supervision, Hebei Univ., Baoding
Abstract :
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
Keywords :
fuzzy set theory; learning (artificial intelligence); minimisation; number theory; statistical analysis; fuzzy empirical risk functional principal; fuzzy empirical risk minimization principal; fuzzy expected risk functional principal; fuzzy number; fuzzy sample; statistical learning theory; Convergence; Cybernetics; Educational institutions; Fuzzy sets; Machine learning; Physics computing; Risk management; Statistical learning; Statistics; TV; Fuzzy empirical risk functional; Fuzzy empirical risk minimization principal; Fuzzy expected risk functional; Key theorem;
Conference_Titel :
Machine Learning and Cybernetics, 2006 International Conference on
Conference_Location :
Dalian, China
Print_ISBN :
1-4244-0061-9
DOI :
10.1109/ICMLC.2006.258536
