Some Theoretical Results of Learning Theory Based on Intuitionistic Fuzzy Random Samples

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.