{"id":"https://openalex.org/W2432062829","doi":"https://doi.org/10.1142/s0218488516500197","title":"Fubini-Like Theorem of Real-Valued Choquet Integrals for Set-Valued Mappings","display_name":"Fubini-Like Theorem of Real-Valued Choquet Integrals for Set-Valued Mappings","publication_year":2016,"publication_date":"2016-06-01","ids":{"openalex":"https://openalex.org/W2432062829","doi":"https://doi.org/10.1142/s0218488516500197","mag":"2432062829"},"language":"en","primary_location":{"id":"doi:10.1142/s0218488516500197","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218488516500197","pdf_url":null,"source":{"id":"https://openalex.org/S69518169","display_name":"International Journal of Uncertainty Fuzziness and Knowledge-Based Systems","issn_l":"0218-4885","issn":["0218-4885","1793-6411"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems","raw_type":"journal-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/A5074963449","display_name":"Gaofeng Zong","orcid":"https://orcid.org/0000-0002-4888-9959"},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]},{"id":"https://openalex.org/I59483232","display_name":"Shandong University of Finance and Economics","ror":"https://ror.org/02e2nnq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I59483232"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Gaofeng Zong","raw_affiliation_strings":["School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, Jinan, China","School of Mathematics, Shandong University, Jinan, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, Jinan, China","institution_ids":["https://openalex.org/I59483232"]},{"raw_affiliation_string":"School of Mathematics, Shandong University, Jinan, China","institution_ids":["https://openalex.org/I154099455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071779760","display_name":"Zengjing Chen","orcid":null},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zengjing Chen","raw_affiliation_strings":["Institute of Financial Study, Shandong University, Jinan, China","School of Mathematics, Shandong University, Jinan, China"],"affiliations":[{"raw_affiliation_string":"Institute of Financial Study, Shandong University, Jinan, China","institution_ids":["https://openalex.org/I154099455"]},{"raw_affiliation_string":"School of Mathematics, Shandong University, Jinan, China","institution_ids":["https://openalex.org/I154099455"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112861069","display_name":"Yuting Lan","orcid":null},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuting Lan","raw_affiliation_strings":["Institute of Financial Study, Shandong University, Jinan, China"],"affiliations":[{"raw_affiliation_string":"Institute of Financial Study, Shandong University, Jinan, China","institution_ids":["https://openalex.org/I154099455"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5074963449"],"corresponding_institution_ids":["https://openalex.org/I154099455","https://openalex.org/I59483232"],"apc_list":null,"apc_paid":null,"fwci":0.7181,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.76735806,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"24","issue":"03","first_page":"387","last_page":"403"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9984999895095825,"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"}},"topics":[{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9984999895095825,"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"}},{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.998199999332428,"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/T11413","display_name":"Risk and Portfolio Optimization","score":0.9973000288009644,"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/fubinis-theorem","display_name":"Fubini's theorem","score":0.9323219656944275},{"id":"https://openalex.org/keywords/choquet-integral","display_name":"Choquet integral","score":0.8167821764945984},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8044177293777466},{"id":"https://openalex.org/keywords/set-function","display_name":"Set function","score":0.6303509473800659},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5315810441970825},{"id":"https://openalex.org/keywords/choquet-theory","display_name":"Choquet theory","score":0.5294610857963562},{"id":"https://openalex.org/keywords/frame","display_name":"Frame (networking)","score":0.5172522664070129},{"id":"https://openalex.org/keywords/additive-function","display_name":"Additive function","score":0.4360297918319702},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4208255112171173},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.41259995102882385},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.35863447189331055},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1377701759338379},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12222272157669067},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09144183993339539}],"concepts":[{"id":"https://openalex.org/C55526981","wikidata":"https://www.wikidata.org/wiki/Q1149022","display_name":"Fubini's theorem","level":2,"score":0.9323219656944275},{"id":"https://openalex.org/C112799922","wikidata":"https://www.wikidata.org/wiki/Q5104911","display_name":"Choquet integral","level":3,"score":0.8167821764945984},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8044177293777466},{"id":"https://openalex.org/C15312841","wikidata":"https://www.wikidata.org/wiki/Q1657198","display_name":"Set function","level":3,"score":0.6303509473800659},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5315810441970825},{"id":"https://openalex.org/C176684429","wikidata":"https://www.wikidata.org/wiki/Q1076274","display_name":"Choquet theory","level":5,"score":0.5294610857963562},{"id":"https://openalex.org/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"score":0.5172522664070129},{"id":"https://openalex.org/C38803922","wikidata":"https://www.wikidata.org/wiki/Q95745348","display_name":"Additive function","level":2,"score":0.4360297918319702},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4208255112171173},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.41259995102882385},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.35863447189331055},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1377701759338379},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12222272157669067},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09144183993339539},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.0},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C134912446","wikidata":"https://www.wikidata.org/wiki/Q5166516","display_name":"Convex body","level":4,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218488516500197","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218488516500197","pdf_url":null,"source":{"id":"https://openalex.org/S69518169","display_name":"International Journal of Uncertainty Fuzziness and Knowledge-Based Systems","issn_l":"0218-4885","issn":["0218-4885","1793-6411"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1578430072","https://openalex.org/W1579549043","https://openalex.org/W1983602031","https://openalex.org/W1985286096","https://openalex.org/W1987030921","https://openalex.org/W1988103797","https://openalex.org/W1995271294","https://openalex.org/W2009348076","https://openalex.org/W2016334607","https://openalex.org/W2021194178","https://openalex.org/W2024412689","https://openalex.org/W2037847611","https://openalex.org/W2050520469","https://openalex.org/W2051460359","https://openalex.org/W2051842686","https://openalex.org/W2055815544","https://openalex.org/W2060935534","https://openalex.org/W2072774297","https://openalex.org/W2079891793","https://openalex.org/W2085246855","https://openalex.org/W2099727673","https://openalex.org/W2099847272","https://openalex.org/W2108060696","https://openalex.org/W2148379282","https://openalex.org/W2152088337","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W4295277097","https://openalex.org/W4320718717","https://openalex.org/W154952466","https://openalex.org/W3047472495","https://openalex.org/W3186488231","https://openalex.org/W2473075650","https://openalex.org/W1970351388","https://openalex.org/W3123542200","https://openalex.org/W2379272961","https://openalex.org/W2735486879"],"abstract_inverted_index":{"The":[0],"purpose":[1],"of":[2,11,21,41,45],"this":[3],"paper":[4],"is":[5],"to":[6,37],"establish":[7],"a":[8],"Fubini-like":[9],"theorem":[10],"real-valued":[12],"Choquet":[13,46],"integrals":[14],"for":[15],"set-valued":[16,34],"mappings":[17],"in":[18],"the":[19,28,42],"frame":[20],"capacity":[22],"theory.":[23],"To":[24],"this,":[25],"we":[26],"introduce":[27],"comonotonic":[29,43],"random":[30],"sets":[31],"and":[32],"slice-comonotonic":[33],"mappings,":[35],"which":[36],"make":[38],"good":[39],"use":[40],"additivity":[44],"integrals.":[47]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
