Fuzzy Sets and Systems
Connectives and quantifiers in fuzzy sets
Fuzzy Sets and Systems - Special memorial volume on foundations of fuzzy reasoning
Fuzzy complex analysis I: differentiation
Fuzzy Sets and Systems
Fuzzy limit theory of fuzzy complex numbers
Fuzzy Sets and Systems
Fuzzy complex analysis II: integration
Fuzzy Sets and Systems
The nature of statistical learning theory
The nature of statistical learning theory
On the formalization of fuzzy random variables
Information Sciences: an International Journal - Fuzzy random variables
Generalized Lebesgue integrals of fuzzy complex valued functions
Fuzzy Sets and Systems - Mathematics
Motion Estimation Using Statistical Learning Theory
IEEE Transactions on Pattern Analysis and Machine Intelligence
Comparison between error correcting output codes and fuzzy support vector machines
Pattern Recognition Letters - Special issue: Artificial neural networks in pattern recognition
Credit scoring with a data mining approach based on support vector machines
Expert Systems with Applications: An International Journal
Feature selection for the SVM: An application to hypertension diagnosis
Expert Systems with Applications: An International Journal
Extraction of fuzzy rules from support vector machines
Fuzzy Sets and Systems
Support vector interval regression machine for crisp input and output data
Fuzzy Sets and Systems
A new fuzzy support vector machine to evaluate credit risk
IEEE Transactions on Fuzzy Systems
An overview of statistical learning theory
IEEE Transactions on Neural Networks
IEEE Transactions on Neural Networks
IEEE Transactions on Fuzzy Systems
The key theorem of learning theory based on Sugeno measure and fuzzy random samples
LSMS/ICSEE'10 Proceedings of the 2010 international conference on Life system modeling and simulation and intelligent computing, and 2010 international conference on Intelligent computing for sustainable energy and environment: Part II
Hi-index | 0.20 |
Statistical learning theory based on real-valued random samples has been regarded as one of the influential developments for small samples statistical estimation and learning. The key theorem of learning theory and the bounds on the rate of convergence of learning process are the most important theoretical fundamentals of the statistical learning theory. In this paper, we discuss a statistical learning theory based on fuzzy complex random samples. Firstly, the definition of fuzzy complex numbers is introduced and the fuzzy complex random variables along with their numeric characteristic are investigated. Secondly, we carry out further research focused on a special type of fuzzy complex number, namely rectangular fuzzy complex number and establish some properties and develop important theorems. We also prove the strong law of large numbers based on fuzzy complex random variables. Thirdly, the definitions of the fuzzy complex expected risk functional, the fuzzy complex empirical risk functional, the fuzzy complex empirical risk minimization principle and the consistency are provided and discussed. Finally, the key theorem of learning theory and the bounds on the rate of convergence of learning process based on fuzzy complex random samples are discussed.