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SLT based on random samples formed in probability space is considered, at present, as one of the fundamental theories about small samples statistical learning. It has become a novel and important field of machine learning, along with other concepts and architectures such as neural networks. However, the theory hardly handles statistical learning problems for samples that involve random set samples.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Design\/methodology\/approach<\/jats:title><jats:p>Being motivated by some applications, in this paper a SLT is developed based on random set samples. First, a certain law of large numbers for random sets is proved. Second, the definitions of the distribution function and the expectation of random sets are introduced, and the concepts of the expected risk functional and the empirical risk functional are discussed. A notion of the strict consistency of the principle of empirical risk minimization is presented.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Findings<\/jats:title><jats:p>The paper formulates and proves the key theorem and presents the bounds on the rate of uniform convergence of learning theory based on random sets in set\u2010valued probability space, which become cornerstones of the theoretical fundamentals of the SLT for random set samples.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Originality\/value<\/jats:title><jats:p>The paper provides a studied analysis of some theoretical results of learning theory.<\/jats:p><\/jats:sec>","DOI":"10.1108\/03684920910944867","type":"journal-article","created":{"date-parts":[[2009,5,30]],"date-time":"2009-05-30T07:11:04Z","timestamp":1243667464000},"page":"635-657","source":"Crossref","is-referenced-by-count":8,"title":["Some theoretical results of learning theory based on random sets in set\u2010valued probability space"],"prefix":"10.1108","volume":"38","author":[{"given":"Minghu","family":"Ha","sequence":"first","affiliation":[]},{"given":"Witold","family":"Pedrycz","sequence":"additional","affiliation":[]},{"given":"Jiqiang","family":"Chen","sequence":"additional","affiliation":[]},{"given":"Lifang","family":"Zheng","sequence":"additional","affiliation":[]}],"member":"140","reference":[{"key":"key2022021020024517900_b5","doi-asserted-by":"crossref","unstructured":"Artstein, Z. 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