{"id":"https://openalex.org/W2165559044","doi":"https://doi.org/10.1109/icmlc.2011.6016929","title":"The key theorem of learning theory based on hybrid variable","display_name":"The key theorem of learning theory based on hybrid variable","publication_year":2011,"publication_date":"2011-07-01","ids":{"openalex":"https://openalex.org/W2165559044","doi":"https://doi.org/10.1109/icmlc.2011.6016929","mag":"2165559044"},"language":"en","primary_location":{"id":"doi:10.1109/icmlc.2011.6016929","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icmlc.2011.6016929","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2011 International Conference on Machine Learning and Cybernetics","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057951804","display_name":"Xiaojing Sun","orcid":"https://orcid.org/0000-0002-3777-6270"},"institutions":[{"id":"https://openalex.org/I43337087","display_name":"Hebei University","ror":"https://ror.org/01p884a79","country_code":"CN","type":"education","lineage":["https://openalex.org/I43337087"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xiao-Jing Sun","raw_affiliation_strings":["College of Mathematics and Computer Sciences, Hebei University, Baoding, China"],"affiliations":[{"raw_affiliation_string":"College of Mathematics and Computer Sciences, Hebei University, Baoding, China","institution_ids":["https://openalex.org/I43337087"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100698386","display_name":"Chao Wang","orcid":"https://orcid.org/0000-0002-6423-0732"},"institutions":[{"id":"https://openalex.org/I43337087","display_name":"Hebei University","ror":"https://ror.org/01p884a79","country_code":"CN","type":"education","lineage":["https://openalex.org/I43337087"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chao Wang","raw_affiliation_strings":["College of Physics Science & Technology, Hebei University, Baoding, China"],"affiliations":[{"raw_affiliation_string":"College of Physics Science & Technology, Hebei University, Baoding, China","institution_ids":["https://openalex.org/I43337087"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103221923","display_name":"Ming-Hu Ha","orcid":"https://orcid.org/0000-0002-7043-4811"},"institutions":[{"id":"https://openalex.org/I43337087","display_name":"Hebei University","ror":"https://ror.org/01p884a79","country_code":"CN","type":"education","lineage":["https://openalex.org/I43337087"]},{"id":"https://openalex.org/I106079672","display_name":"Hebei University of Engineering","ror":"https://ror.org/036h65h05","country_code":"CN","type":"education","lineage":["https://openalex.org/I106079672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ming-Hu Ha","raw_affiliation_strings":["College of Mathematics and Computer Sciences, Hebei University, Baoding, China","College of Science, Hebei University of Engineering, Handan, China"],"affiliations":[{"raw_affiliation_string":"College of Mathematics and Computer Sciences, Hebei University, Baoding, China","institution_ids":["https://openalex.org/I43337087"]},{"raw_affiliation_string":"College of Science, Hebei University of Engineering, Handan, China","institution_ids":["https://openalex.org/I106079672"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102133395","display_name":"Da-Zeng Tian","orcid":null},"institutions":[{"id":"https://openalex.org/I43337087","display_name":"Hebei University","ror":"https://ror.org/01p884a79","country_code":"CN","type":"education","lineage":["https://openalex.org/I43337087"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Da-Zeng Tian","raw_affiliation_strings":["College of Physics Science & Technology, Hebei University, Baoding, China"],"affiliations":[{"raw_affiliation_string":"College of Physics Science & Technology, Hebei University, Baoding, China","institution_ids":["https://openalex.org/I43337087"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5057951804"],"corresponding_institution_ids":["https://openalex.org/I43337087"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.16733267,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"46","issue":null,"first_page":"1141","last_page":"1145"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.9865999817848206,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9818999767303467,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.6108976602554321},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.5965033769607544},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4863934814929962},{"id":"https://openalex.org/keywords/hybrid-system","display_name":"Hybrid system","score":0.48590531945228577},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.47410494089126587},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4550803601741791},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3675100803375244},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.34002768993377686},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.1923026740550995},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1038634181022644}],"concepts":[{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.6108976602554321},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.5965033769607544},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4863934814929962},{"id":"https://openalex.org/C50897621","wikidata":"https://www.wikidata.org/wiki/Q2665508","display_name":"Hybrid system","level":2,"score":0.48590531945228577},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47410494089126587},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4550803601741791},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3675100803375244},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.34002768993377686},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.1923026740550995},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1038634181022644},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/icmlc.2011.6016929","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icmlc.2011.6016929","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2011 International Conference on Machine Learning and Cybernetics","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.6499999761581421}],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322163","display_name":"Natural Science Foundation of Hebei Province","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1555051949","https://openalex.org/W1557693965","https://openalex.org/W1970505073","https://openalex.org/W1987811848","https://openalex.org/W1997564656","https://openalex.org/W2039112049","https://openalex.org/W2071978572","https://openalex.org/W2093040750","https://openalex.org/W2141643076","https://openalex.org/W2148603752","https://openalex.org/W2156909104","https://openalex.org/W2575608801","https://openalex.org/W2912189486","https://openalex.org/W4234521054","https://openalex.org/W6758671891","https://openalex.org/W7071374342","https://openalex.org/W7071544572"],"related_works":["https://openalex.org/W2140798747","https://openalex.org/W2948169060","https://openalex.org/W2730112582","https://openalex.org/W2110696645","https://openalex.org/W2358580169","https://openalex.org/W2111347279","https://openalex.org/W2487211728","https://openalex.org/W2378096925","https://openalex.org/W2348031209","https://openalex.org/W830369380"],"abstract_inverted_index":{"The":[0,22],"definitions":[1],"of":[2,25,41],"hybrid":[3,7,12,30,46],"empirical":[4,13],"risk":[5,9,14],"functional,":[6],"excepted":[8],"functional":[10],"and":[11],"minimization":[15],"principle":[16],"in":[17,32,48],"chance":[18,33,49],"space":[19,34,50],"are":[20],"proposed;":[21],"Khintchine":[23],"law":[24],"large":[26],"numbers":[27],"based":[28,44],"on":[29,45],"variable":[31,47],"is":[35,51],"proved;":[36],"And":[37],"the":[38],"key":[39],"theorem":[40],"learning":[42],"theory":[43],"proved.":[52]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}