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

fYear

2006

fDate

13-16 Aug. 2006

Firstpage

3475

Lastpage

3479

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;

fLanguage

English

Publisher

ieee

Conference_Titel

Machine Learning and Cybernetics, 2006 International Conference on

Conference_Location

Dalian, China

Print_ISBN

1-4244-0061-9

Type

conf

DOI

10.1109/ICMLC.2006.258536

Filename

4028672