{"id":"https://openalex.org/W2735486879","doi":"https://doi.org/10.1142/s0218488517500246","title":"Comonotonic Random Sets and Its Additivity of Choquet Integrals","display_name":"Comonotonic Random Sets and Its Additivity of Choquet Integrals","publication_year":2017,"publication_date":"2017-07-14","ids":{"openalex":"https://openalex.org/W2735486879","doi":"https://doi.org/10.1142/s0218488517500246","mag":"2735486879"},"language":"en","primary_location":{"id":"doi:10.1142/s0218488517500246","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218488517500246","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":["Department of Mathematics, Shandong University, Jinan 250100, China","School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, Jinan 250002, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shandong University, Jinan 250100, China","institution_ids":["https://openalex.org/I154099455"]},{"raw_affiliation_string":"School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, Jinan 250002, China","institution_ids":["https://openalex.org/I59483232"]}]},{"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":["Department of Mathematics, Shandong University, Jinan 250100, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shandong University, Jinan 250100, China","institution_ids":["https://openalex.org/I154099455"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109370176","display_name":"Faisal Shahzad","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":"Faisal Shahzad","raw_affiliation_strings":["Department of Mathematics, Shandong University, Jinan 250100, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shandong University, Jinan 250100, 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":0.4664,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.67462487,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"25","issue":"04","first_page":"557","last_page":"571"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9997000098228455,"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":0.9997000098228455,"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/T10050","display_name":"Multi-Criteria Decision Making","score":0.9987999796867371,"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/T11413","display_name":"Risk and Portfolio Optimization","score":0.993399977684021,"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/choquet-integral","display_name":"Choquet integral","score":0.9187833070755005},{"id":"https://openalex.org/keywords/additive-function","display_name":"Additive function","score":0.891187310218811},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7756620645523071},{"id":"https://openalex.org/keywords/set-function","display_name":"Set function","score":0.5230754017829895},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.5172737240791321},{"id":"https://openalex.org/keywords/choquet-theory","display_name":"Choquet theory","score":0.46551015973091125},{"id":"https://openalex.org/keywords/homogeneity","display_name":"Homogeneity (statistics)","score":0.45537906885147095},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4023485481739044},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35580092668533325},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3457176685333252},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1357632577419281},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11625552177429199},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11521938443183899},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10054132342338562},{"id":"https://openalex.org/keywords/subderivative","display_name":"Subderivative","score":0.06627762317657471}],"concepts":[{"id":"https://openalex.org/C112799922","wikidata":"https://www.wikidata.org/wiki/Q5104911","display_name":"Choquet integral","level":3,"score":0.9187833070755005},{"id":"https://openalex.org/C38803922","wikidata":"https://www.wikidata.org/wiki/Q95745348","display_name":"Additive function","level":2,"score":0.891187310218811},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7756620645523071},{"id":"https://openalex.org/C15312841","wikidata":"https://www.wikidata.org/wiki/Q1657198","display_name":"Set function","level":3,"score":0.5230754017829895},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.5172737240791321},{"id":"https://openalex.org/C176684429","wikidata":"https://www.wikidata.org/wiki/Q1076274","display_name":"Choquet theory","level":5,"score":0.46551015973091125},{"id":"https://openalex.org/C142259097","wikidata":"https://www.wikidata.org/wiki/Q5891314","display_name":"Homogeneity (statistics)","level":2,"score":0.45537906885147095},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4023485481739044},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35580092668533325},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3457176685333252},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1357632577419281},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11625552177429199},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11521938443183899},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10054132342338562},{"id":"https://openalex.org/C200661725","wikidata":"https://www.wikidata.org/wiki/Q289500","display_name":"Subderivative","level":4,"score":0.06627762317657471},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"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/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218488517500246","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218488517500246","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":[{"display_name":"Reduced inequalities","score":0.75,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1967229060","https://openalex.org/W1986407372","https://openalex.org/W2010882790","https://openalex.org/W2020154669","https://openalex.org/W2021244475","https://openalex.org/W2037847611","https://openalex.org/W2053561951","https://openalex.org/W2077431745","https://openalex.org/W2085648025","https://openalex.org/W2092851543","https://openalex.org/W2093747547","https://openalex.org/W2158988058","https://openalex.org/W2432062829"],"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":{"In":[0],"this":[1,55],"paper,":[2],"we":[3,28],"propose":[4],"a":[5,14],"concept":[6],"of":[7,9,21,23,33,35,41,54,57],"comonotonicity":[8,22,34],"random":[10,25,36,46,62],"sets,":[11],"which":[12],"is":[13],"set":[15,47,63],"inclusion":[16],"relation":[17],"and":[18,38],"generalized":[19],"notion":[20],"real-valued":[24,42,58],"variables.":[26],"Then":[27],"study":[29],"some":[30,51],"elementary":[31],"properties":[32,53],"sets":[37],"comonotonic":[39,69],"additivity":[40],"Choquet":[43,59],"integral":[44,60],"for":[45,61,71],"mappings.":[48],"After":[49],"this,":[50],"other":[52],"kind":[56],"mappings":[64],"are":[65],"characterized":[66],"by":[67],"the":[68],"additivity,":[70],"instance,":[72],"translation":[73],"invariance,":[74],"sup-norm":[75],"continuous,":[76],"positive":[77],"homogeneity.":[78]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}