{"id":"https://openalex.org/W1971539233","doi":"https://doi.org/10.3390/axioms2030390","title":"Discrete Integrals Based on Comonotonic Modularity","display_name":"Discrete Integrals Based on Comonotonic Modularity","publication_year":2013,"publication_date":"2013-07-23","ids":{"openalex":"https://openalex.org/W1971539233","doi":"https://doi.org/10.3390/axioms2030390","mag":"1971539233"},"language":"en","primary_location":{"id":"doi:10.3390/axioms2030390","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms2030390","pdf_url":"https://www.mdpi.com/2075-1680/2/3/390/pdf?version=1374570756","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/2/3/390/pdf?version=1374570756","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066732273","display_name":"Miguel Couceiro","orcid":"https://orcid.org/0000-0003-2316-7623"},"institutions":[{"id":"https://openalex.org/I56435720","display_name":"Universit\u00e9 Paris Dauphine-PSL","ror":"https://ror.org/052bz7812","country_code":"FR","type":"education","lineage":["https://openalex.org/I2746051580","https://openalex.org/I56435720"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Miguel Couceiro","raw_affiliation_strings":["Lamsade, University Paris-Dauphine, Place du Mar\u00e9chal de Lattre de Tassigny, Paris Cedex 16 F-75775, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Lamsade, University Paris-Dauphine, Place du Mar\u00e9chal de Lattre de Tassigny, Paris Cedex 16 F-75775, France","institution_ids":["https://openalex.org/I56435720"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081046253","display_name":"Jean\u2010Luc Marichal","orcid":"https://orcid.org/0000-0002-2984-6363"},"institutions":[{"id":"https://openalex.org/I186903577","display_name":"University of Luxembourg","ror":"https://ror.org/036x5ad56","country_code":"LU","type":"education","lineage":["https://openalex.org/I186903577"]}],"countries":["LU"],"is_corresponding":false,"raw_author_name":"Jean-Luc Marichal","raw_affiliation_strings":["Mathematics Research Unit, University of Luxembourg, 6 Rue Coudenhove-Kalergi, Luxembourg L-1359, Luxembourg"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Research Unit, University of Luxembourg, 6 Rue Coudenhove-Kalergi, Luxembourg L-1359, Luxembourg","institution_ids":["https://openalex.org/I186903577"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5066732273"],"corresponding_institution_ids":["https://openalex.org/I56435720"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":1.7046,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.85339194,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":96},"biblio":{"volume":"2","issue":"3","first_page":"390","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":0.9866999983787537,"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":0.9866999983787537,"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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9711999893188477,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9598000049591064,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/modular-design","display_name":"Modular design","score":0.7718233466148376},{"id":"https://openalex.org/keywords/modularity","display_name":"Modularity (biology)","score":0.769447386264801},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7153509855270386},{"id":"https://openalex.org/keywords/choquet-integral","display_name":"Choquet integral","score":0.639614462852478},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.583166241645813},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5097789168357849},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.44358205795288086},{"id":"https://openalex.org/keywords/modular-form","display_name":"Modular form","score":0.4274931252002716},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3403419256210327},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.33900779485702515},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1517305076122284},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.12949877977371216},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09132117033004761}],"concepts":[{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.7718233466148376},{"id":"https://openalex.org/C2779478453","wikidata":"https://www.wikidata.org/wiki/Q6889748","display_name":"Modularity (biology)","level":2,"score":0.769447386264801},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7153509855270386},{"id":"https://openalex.org/C112799922","wikidata":"https://www.wikidata.org/wiki/Q5104911","display_name":"Choquet integral","level":3,"score":0.639614462852478},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.583166241645813},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5097789168357849},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.44358205795288086},{"id":"https://openalex.org/C75764964","wikidata":"https://www.wikidata.org/wiki/Q870797","display_name":"Modular form","level":2,"score":0.4274931252002716},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3403419256210327},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33900779485702515},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1517305076122284},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.12949877977371216},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09132117033004761},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.3390/axioms2030390","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms2030390","pdf_url":"https://www.mdpi.com/2075-1680/2/3/390/pdf?version=1374570756","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1304.3042","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1304.3042","pdf_url":"https://arxiv.org/pdf/1304.3042","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.367.8347","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.367.8347","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mdpi.com/2075-1680/2/3/390/pdf?y=1","raw_type":"text"},{"id":"pmh:oai:HAL:hal-01090567v1","is_oa":true,"landing_page_url":"https://hal.science/hal-01090567","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, 2013, 2 (3), pp.14. ⟨10.3390/axioms2030390⟩","raw_type":"Journal articles"},{"id":"pmh:oai:basepub.dauphine.fr:123456789/16631","is_oa":false,"landing_page_url":"https://basepub.dauphine.fr/handle/123456789/16631","pdf_url":null,"source":{"id":"https://openalex.org/S4306401007","display_name":"Base Institutionnelle de Recherche de l'universit\u00e9 Paris-Dauphine (BIRD) (University Paris-Dauphine)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I102197404","host_organization_name":"Universit\u00e9 Paris-Sud","host_organization_lineage":["https://openalex.org/I102197404"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article accept\u00e9 pour publication ou publi\u00e9"},{"id":"pmh:oai:doaj.org/article:6b14e55893c24221b4effee33b98cb9c","is_oa":true,"landing_page_url":"https://doaj.org/article/6b14e55893c24221b4effee33b98cb9c","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 2, Iss 3, Pp 390-403 (2013)","raw_type":"article"},{"id":"pmh:oai:orbilu.uni.lu:10993/9475","is_oa":true,"landing_page_url":"http://www.mdpi.com/2075-1680/2/3/390","pdf_url":null,"source":{"id":"https://openalex.org/S4306401815","display_name":"Open Repository and Bibliography (University of Luxembourg)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I186903577","host_organization_name":"University of Luxembourg","host_organization_lineage":["https://openalex.org/I186903577"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, 2(3), 390-403. MDPI (2013).","raw_type":null}],"best_oa_location":{"id":"doi:10.3390/axioms2030390","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms2030390","pdf_url":"https://www.mdpi.com/2075-1680/2/3/390/pdf?version=1374570756","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G145492078","display_name":null,"funder_award_id":"F1R-MTH-PUL-12RDO2","funder_id":"https://openalex.org/F4320310700","funder_display_name":"Universit\u00e9 du Luxembourg"}],"funders":[{"id":"https://openalex.org/F4320310700","display_name":"Universit\u00e9 du Luxembourg","ror":"https://ror.org/036x5ad56"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1971539233.pdf","grobid_xml":"https://content.openalex.org/works/W1971539233.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W169692285","https://openalex.org/W1484881229","https://openalex.org/W1905771608","https://openalex.org/W2000205155","https://openalex.org/W2004483800","https://openalex.org/W2014936898","https://openalex.org/W2070401392","https://openalex.org/W2086721181","https://openalex.org/W2140103808","https://openalex.org/W2161413792","https://openalex.org/W2164275725","https://openalex.org/W2205883422","https://openalex.org/W2330548796","https://openalex.org/W2379063125","https://openalex.org/W2962707676","https://openalex.org/W2963316763","https://openalex.org/W3105285160","https://openalex.org/W4252793191","https://openalex.org/W6640011692","https://openalex.org/W6688031434"],"related_works":["https://openalex.org/W2297768894","https://openalex.org/W2378076731","https://openalex.org/W3109014690","https://openalex.org/W2122405502","https://openalex.org/W2114254072","https://openalex.org/W2127721729","https://openalex.org/W2884798239","https://openalex.org/W1531253727","https://openalex.org/W2366669483","https://openalex.org/W2333635112"],"abstract_inverted_index":{"It":[0],"is":[1],"known":[2],"that":[3,45],"several":[4],"discrete":[5,43],"integrals,":[6,12,57],"including":[7,49],"the":[8,30],"Choquet":[9,51,56],"and":[10,53],"Sugeno":[11,64],"as":[13,15,58,60],"well":[14,59],"some":[16],"of":[17,29,32,42,63],"their":[18],"generalizations,":[19],"are":[20,46],"comonotonically":[21,33,47],"modular":[22,34],"functions.":[23],"Based":[24],"on":[25],"a":[26],"recent":[27],"description":[28],"class":[31],"functions,":[35],"we":[36],"axiomatically":[37],"identify":[38],"more":[39],"general":[40],"families":[41],"integrals":[44,52],"modular,":[48],"signed":[50,55],"symmetric":[54],"natural":[61],"extensions":[62],"integrals.":[65]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}