{"id":"https://openalex.org/W4233827051","doi":"https://doi.org/10.1142/s0218488500000460","title":"ENTROPY OF DISCRETE FUZZY MEASURES","display_name":"ENTROPY OF DISCRETE FUZZY MEASURES","publication_year":2000,"publication_date":"2000-12-01","ids":{"openalex":"https://openalex.org/W4233827051","doi":"https://doi.org/10.1142/s0218488500000460"},"language":"en","primary_location":{"id":"doi:10.1142/s0218488500000460","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218488500000460","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":true,"oa_status":"green","oa_url":"https://orbilu.uni.lu/handle/10993/1772","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5081046253","display_name":"Jean\u2010Luc Marichal","orcid":"https://orcid.org/0000-0002-2984-6363"},"institutions":[{"id":"https://openalex.org/I157674565","display_name":"University of Li\u00e8ge","ror":"https://ror.org/00afp2z80","country_code":"BE","type":"education","lineage":["https://openalex.org/I157674565"]}],"countries":["BE"],"is_corresponding":true,"raw_author_name":"JEAN-LUC MARICHAL","raw_affiliation_strings":["Institute of Mathematics, University of Li\u00e8ge, Grande Traverse 12 \u2013 B37, Sart Tilman, B-4000 Li\u00e8ge, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, University of Li\u00e8ge, Grande Traverse 12 \u2013 B37, Sart Tilman, B-4000 Li\u00e8ge, Belgium","institution_ids":["https://openalex.org/I157674565"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5052285082","display_name":"Marc Roubens","orcid":null},"institutions":[{"id":"https://openalex.org/I157674565","display_name":"University of Li\u00e8ge","ror":"https://ror.org/00afp2z80","country_code":"BE","type":"education","lineage":["https://openalex.org/I157674565"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"MARC ROUBENS","raw_affiliation_strings":["Institute of Mathematics, University of Li\u00e8ge, Grande Traverse 12 \u2013 B37, Sart Tilman, B-4000 Li\u00e8ge, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, University of Li\u00e8ge, Grande Traverse 12 \u2013 B37, Sart Tilman, B-4000 Li\u00e8ge, Belgium","institution_ids":["https://openalex.org/I157674565"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5081046253"],"corresponding_institution_ids":["https://openalex.org/I157674565"],"apc_list":null,"apc_paid":null,"fwci":1.0039,"has_fulltext":false,"cited_by_count":36,"citation_normalized_percentile":{"value":0.82479443,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"08","issue":"06","first_page":"625","last_page":"640"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"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"}},"topics":[{"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/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.9950000047683716,"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.994700014591217,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7309224605560303},{"id":"https://openalex.org/keywords/ordinal-scale","display_name":"Ordinal Scale","score":0.628051221370697},{"id":"https://openalex.org/keywords/fuzzy-measure-theory","display_name":"Fuzzy measure theory","score":0.6144663095474243},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.6098219156265259},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.6087576150894165},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.5072914958000183},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.48345860838890076},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.4569630026817322},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.29198238253593445},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.2643442749977112},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2443128228187561},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.20703056454658508}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7309224605560303},{"id":"https://openalex.org/C2909711754","wikidata":"https://www.wikidata.org/wiki/Q7100785","display_name":"Ordinal Scale","level":2,"score":0.628051221370697},{"id":"https://openalex.org/C100516043","wikidata":"https://www.wikidata.org/wiki/Q4455138","display_name":"Fuzzy measure theory","level":5,"score":0.6144663095474243},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.6098219156265259},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.6087576150894165},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.5072914958000183},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.48345860838890076},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.4569630026817322},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.29198238253593445},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.2643442749977112},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2443128228187561},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.20703056454658508},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218488500000460","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218488500000460","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"},{"id":"pmh:oai:orbilu.uni.lu:10993/1772","is_oa":true,"landing_page_url":"https://orbilu.uni.lu/handle/10993/1772","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 8 (6), 625-640 (2000-12)","raw_type":"peer reviewed"}],"best_oa_location":{"id":"pmh:oai:orbilu.uni.lu:10993/1772","is_oa":true,"landing_page_url":"https://orbilu.uni.lu/handle/10993/1772","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 8 (6), 625-640 (2000-12)","raw_type":"peer reviewed"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1979639955","https://openalex.org/W1995875735","https://openalex.org/W2017449401","https://openalex.org/W2036234778","https://openalex.org/W2060907774","https://openalex.org/W2064962332","https://openalex.org/W2082601569","https://openalex.org/W2092851543","https://openalex.org/W2109897830","https://openalex.org/W2110301906","https://openalex.org/W2143899001","https://openalex.org/W2402164117"],"related_works":["https://openalex.org/W2401752011","https://openalex.org/W2390411038","https://openalex.org/W2152639368","https://openalex.org/W2952939953","https://openalex.org/W2392451206","https://openalex.org/W1514480137","https://openalex.org/W2353670105","https://openalex.org/W2168741781","https://openalex.org/W2060486654","https://openalex.org/W2371225479"],"abstract_inverted_index":{"The":[0],"concept":[1],"of":[2,4,37,62,82],"entropy":[3,61],"a":[5,29,42,57,69],"discrete":[6],"fuzzy":[7,65,70],"measure":[8,71],"has":[9],"been":[10],"recently":[11],"introduced":[12],"in":[13,24,34,75,79],"two":[14,47],"different":[15],"ways.":[16],"A":[17],"first":[18],"definition":[19,58],"was":[20],"proposed":[21],"by":[22,32],"Marichal":[23],"the":[25,35,60,80],"aggregation":[26],"framework,":[27],"and":[28,49],"second":[30],"one":[31],"Yager":[33],"framework":[36],"uncertain":[38],"variables.":[39],"We":[40,54],"present":[41],"comparative":[43],"study":[44],"between":[45],"these":[46],"proposals":[48],"point":[50],"out":[51],"their":[52],"properties.":[53],"also":[55],"propose":[56],"for":[59],"an":[63,76],"ordinal":[64,77],"measure,":[66],"that":[67],"is,":[68],"taking":[72],"its":[73],"values":[74],"scale":[78],"sense":[81],"measurement":[83],"theory.":[84]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":11}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
