{"id":"https://openalex.org/W2030341448","doi":"https://doi.org/10.1142/s0218488507004595","title":"MAXIMUM ENTROPY PRINCIPLE FOR FUZZY VARIABLES","display_name":"MAXIMUM ENTROPY PRINCIPLE FOR FUZZY VARIABLES","publication_year":2007,"publication_date":"2007-04-01","ids":{"openalex":"https://openalex.org/W2030341448","doi":"https://doi.org/10.1142/s0218488507004595","mag":"2030341448"},"language":"en","primary_location":{"id":"doi:10.1142/s0218488507004595","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218488507004595","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/A5100394767","display_name":"Xiang Li","orcid":"https://orcid.org/0000-0002-0761-0931"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"XIANG LI","raw_affiliation_strings":["Uncertainty Theory Laboratory, Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Uncertainty Theory Laboratory, Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022730182","display_name":"Baoding Liu","orcid":"https://orcid.org/0000-0002-3106-6761"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"BAODING LIU","raw_affiliation_strings":["Uncertainty Theory Laboratory, Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Uncertainty Theory Laboratory, Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China","institution_ids":["https://openalex.org/I99065089"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I99065089"],"apc_list":null,"apc_paid":null,"fwci":6.2197,"has_fulltext":false,"cited_by_count":53,"citation_normalized_percentile":{"value":0.9629561,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"15","issue":"supp02","first_page":"43","last_page":"52"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.996999979019165,"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":0.996999979019165,"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":0.9969000220298767,"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":0.9825000166893005,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7927324771881104},{"id":"https://openalex.org/keywords/principle-of-maximum-entropy","display_name":"Principle of maximum entropy","score":0.7310527563095093},{"id":"https://openalex.org/keywords/maximum-entropy-probability-distribution","display_name":"Maximum entropy probability distribution","score":0.6702976822853088},{"id":"https://openalex.org/keywords/maximum-entropy-spectral-estimation","display_name":"Maximum entropy spectral estimation","score":0.6564857959747314},{"id":"https://openalex.org/keywords/maximum-entropy-thermodynamics","display_name":"Maximum entropy thermodynamics","score":0.5753382444381714},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.5414992570877075},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.5361402630805969},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5196703672409058},{"id":"https://openalex.org/keywords/membership-function","display_name":"Membership function","score":0.5092350244522095},{"id":"https://openalex.org/keywords/binary-entropy-function","display_name":"Binary entropy function","score":0.502072811126709},{"id":"https://openalex.org/keywords/defuzzification","display_name":"Defuzzification","score":0.48790618777275085},{"id":"https://openalex.org/keywords/joint-entropy","display_name":"Joint entropy","score":0.4714946150779724},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44363197684288025},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4281378984451294},{"id":"https://openalex.org/keywords/type-2-fuzzy-sets-and-systems","display_name":"Type-2 fuzzy sets and systems","score":0.41908228397369385},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.4044105112552643},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.17670544981956482},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17465472221374512},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.14703723788261414},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.05493074655532837}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7927324771881104},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.7310527563095093},{"id":"https://openalex.org/C60507348","wikidata":"https://www.wikidata.org/wiki/Q6795892","display_name":"Maximum entropy probability distribution","level":3,"score":0.6702976822853088},{"id":"https://openalex.org/C89735579","wikidata":"https://www.wikidata.org/wiki/Q6795894","display_name":"Maximum entropy spectral estimation","level":3,"score":0.6564857959747314},{"id":"https://openalex.org/C49775889","wikidata":"https://www.wikidata.org/wiki/Q6795896","display_name":"Maximum entropy thermodynamics","level":4,"score":0.5753382444381714},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.5414992570877075},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5361402630805969},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5196703672409058},{"id":"https://openalex.org/C5263885","wikidata":"https://www.wikidata.org/wiki/Q1967302","display_name":"Membership function","level":4,"score":0.5092350244522095},{"id":"https://openalex.org/C44415725","wikidata":"https://www.wikidata.org/wiki/Q4913893","display_name":"Binary entropy function","level":3,"score":0.502072811126709},{"id":"https://openalex.org/C170260401","wikidata":"https://www.wikidata.org/wiki/Q5251735","display_name":"Defuzzification","level":5,"score":0.48790618777275085},{"id":"https://openalex.org/C106752470","wikidata":"https://www.wikidata.org/wiki/Q1364826","display_name":"Joint entropy","level":3,"score":0.4714946150779724},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44363197684288025},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4281378984451294},{"id":"https://openalex.org/C17350324","wikidata":"https://www.wikidata.org/wiki/Q7860605","display_name":"Type-2 fuzzy sets and systems","level":5,"score":0.41908228397369385},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.4044105112552643},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.17670544981956482},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17465472221374512},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.14703723788261414},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05493074655532837},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218488507004595","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218488507004595","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":[{"id":"https://metadata.un.org/sdg/10","score":0.46000000834465027,"display_name":"Reduced inequalities"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W4791300","https://openalex.org/W1980297452","https://openalex.org/W1987811848","https://openalex.org/W1988794238","https://openalex.org/W1991494243","https://openalex.org/W2016905747","https://openalex.org/W2019950953","https://openalex.org/W2022988502","https://openalex.org/W2029703282","https://openalex.org/W2032558547","https://openalex.org/W2040121225","https://openalex.org/W2047431606","https://openalex.org/W2087018611","https://openalex.org/W2111499159","https://openalex.org/W2128530362","https://openalex.org/W2148880811","https://openalex.org/W2170853747","https://openalex.org/W2402164117","https://openalex.org/W2615737084","https://openalex.org/W2912565176","https://openalex.org/W3136950049","https://openalex.org/W3143971390","https://openalex.org/W4211007335","https://openalex.org/W4230588984","https://openalex.org/W4249936906","https://openalex.org/W4252095604","https://openalex.org/W4254329280"],"related_works":["https://openalex.org/W2030341448","https://openalex.org/W1593029792","https://openalex.org/W2372540914","https://openalex.org/W2260486223","https://openalex.org/W3203322774","https://openalex.org/W2432811566","https://openalex.org/W2396561768","https://openalex.org/W2019499277","https://openalex.org/W2089488300","https://openalex.org/W2158823848"],"abstract_inverted_index":{"The":[0,48,62],"concept":[1],"of":[2,12,33,56,64],"fuzzy":[3,18,28],"entropy":[4,25,59],"is":[5,50,52,67],"used":[6],"to":[7,68],"provide":[8],"a":[9],"quantitative":[10],"measure":[11],"the":[13,23,35,42,53,57],"uncertainty":[14],"associated":[15],"with":[16],"every":[17],"variable.":[19],"This":[20],"paper":[21,66],"proposes":[22],"maximum":[24,46,58],"principle":[26],"for":[27],"variables,":[29],"that":[30,44],"is,":[31],"out":[32],"all":[34],"membership":[36,60],"functions":[37],"satisfying":[38],"given":[39],"constraints,":[40],"choose":[41],"one":[43],"has":[45],"entropy.":[47],"problem":[49,71],"what":[51],"specific":[54],"formulation":[55],"function.":[61],"purpose":[63],"this":[65,70],"solve":[69],"by":[72],"Euler\u2013Lagrange":[73],"equation.":[74]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":10},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":3}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}