The Key Theorem of Learning Theory Based on Sugeno Measure and Fuzzy Random Samples
Statistical Learning Theory is one of the welldeveloped theories to deal with learning problems about small samples, and it has become an important conceptual and algorithmic vehicle of machine learning. The theory is based on the concepts of probability measure and random samples. Given this, it becomes difficult to take advantage of the theory when dealing with learning problems based on Sugeno measure and fuzzy random samples which we encounter in real-world problems. It is well known that Sugeno measure and fuzzy random samples are interesting and important extensions of the concepts of probability measure and random samples, respectively. This motivates us to discuss the Statistical Learning Theory based on Sugeno measure and fuzzy random samples. Firstly, some definitions of the distribution function and the expectation of fuzzy random variables based on Sugeno measure are given, and the law of large numbers of fuzzy random variables based on Sugeno measure is proved. Secondly, the expected risk functional, the empirical risk functional and the principle of empirical risk minimization based on Sugeno measure and fuzzy random samples are introduced. Finally, the key theorem of learning theory based on Sugeno measure and fuzzy random samples is proved, which will play an important role in the systematic and comprehensive development of the Statistical Learning Theory based on Sugeno measure and fuzzy random samples.
Sugeno measure Fuzzy random variables The principle of empirical risk minimization Key theorem
Minghu Ha Chao Wang Witold Pedrycz
College of Mathematics and Computer Sciences, Hebei University,Baoding, 071002, P.R.China College of Physics Science & Technology, Hebei University,Baoding, 071002, P.R.China Department of Electrical and Computer Engineering, University of Alberta, Edmonton,T6G2V4, Canada, a
国际会议
无锡
英文
241-249
2010-09-17（万方平台首次上网日期，不代表论文的发表时间）