@Article{JICS-5-019,
author = {Zhiming Zhang, Jingfeng Tian},
title = {Structural Risk Minimization Principle Based on Complex Fuzzy Random Samples},
journal = {Journal of Information and Computing Science},
year = {2024},
volume = {5},
number = {1},
pages = {019--040},
abstract = { Statistical  Learning  Theory  is  commonly  regarded  as  a  sound  framework  within  which  we 
handle  a  variety  of  learning  problems  in  presence  of  small  size  data  samples.  It  has  become  a  rapidly 
progressing research area in machine learning. The theory is based on real random samples and as such is not 
ready to deal with the statistical learning problems involving complex fuzzy random samples, which we may 
encounter  in  real  world  scenarios.  This  paper  explores  statistical  learning  theory  based  on  complex  fuzzy 
random samples. Firstly, the definition of complex fuzzy random variable is introduced. Next the concepts 
and some properties of the mathematical expectation and independence of complex fuzzy random variables 
are provided. Secondly, the concepts of annealed entropy, growth function and VC dimension of measurable 
complex  fuzzy  set  valued  functions  are  proposed,  and  the  bounds  on  the  rate  of  uniform  convergence  of 
learning  process  based  on  complex  fuzzy  random  samples  are  constructed.  Thirdly,  on  the  basis  of  these 
bounds,  the  idea  of  the  complex  fuzzy  structural  risk  minimization  principle  is  presented.  Finally,  the 
consistency of this principle is proven and the bound on the asymptotic rate of convergence is derived. 
},
issn = {1746-7659},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/jics/22726.html}
}