Some Theoretical Results of Learning Theory Based on Intuitionistic Fuzzy Random Samples
Zhiming Zhang *
College of Mathematics and Computer Science, Hebei University, Baoding 071002, Hebei Province, P. R. China.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we discuss the statistical learning theory based on intuitionistic fuzzy random sample. First of all, we introduce the definition of intuitionistic fuzzy number intuitionistic fuzzy random variables. Secondly, we give some properties of this concept. Thirdly, the definitions of intuitionistic fuzzy empirical risk functional, intuitionistic fuzzy expected risk functional, and intuitionistic fuzzy empirical risk minimization principle are presented. Finally, we prove the key theorem of intuitionistic fuzzy random sample and obtain the rate of uniform convergence of learning process based on the intuitionistic fuzzy random sample.
Keywords: Intuitionistic fuzzy numbers, intuitionistic fuzzy random variables, intuitionistic fuzzy empirical risk minimization principle, the key theorem, the bounds of the rate of convergence