{"id":"https://openalex.org/W2269305055","doi":"https://doi.org/10.3390/e18010019","title":"Entropy of Fuzzy Partitions and Entropy of Fuzzy Dynamical Systems","display_name":"Entropy of Fuzzy Partitions and Entropy of Fuzzy Dynamical Systems","publication_year":2016,"publication_date":"2016-01-18","ids":{"openalex":"https://openalex.org/W2269305055","doi":"https://doi.org/10.3390/e18010019","mag":"2269305055"},"language":"en","primary_location":{"id":"doi:10.3390/e18010019","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e18010019","pdf_url":"https://www.mdpi.com/1099-4300/18/1/19/pdf?version=1453102396","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"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":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/18/1/19/pdf?version=1453102396","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020354344","display_name":"Dagmar Markechov\u00e1","orcid":null},"institutions":[{"id":"https://openalex.org/I306340464","display_name":"Constantine the Philosopher University in Nitra","ror":"https://ror.org/038dnay05","country_code":"SK","type":"education","lineage":["https://openalex.org/I306340464"]}],"countries":["SK"],"is_corresponding":true,"raw_author_name":"Dagmar Markechov\u00e1","raw_affiliation_strings":["Department of Mathematics, Faculty of Natural Sciences, Constantine the Philosopher University in Nitra, Trieda A. Hlinku 1, Nitra 949 01, Slovakia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Natural Sciences, Constantine the Philosopher University in Nitra, Trieda A. Hlinku 1, Nitra 949 01, Slovakia","institution_ids":["https://openalex.org/I306340464"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046677063","display_name":"Beloslav Rie\u010dan","orcid":null},"institutions":[{"id":"https://openalex.org/I207624831","display_name":"Slovak Academy of Sciences","ror":"https://ror.org/03h7qq074","country_code":"SK","type":"government","lineage":["https://openalex.org/I207624831"]},{"id":"https://openalex.org/I4210120676","display_name":"Mathematical Institute of the Slovak Academy of Sciences","ror":"https://ror.org/02fhy7464","country_code":"SK","type":"facility","lineage":["https://openalex.org/I207624831","https://openalex.org/I4210120676"]},{"id":"https://openalex.org/I59655833","display_name":"Matej Bel University","ror":"https://ror.org/016e5hy63","country_code":"SK","type":"education","lineage":["https://openalex.org/I59655833"]}],"countries":["SK"],"is_corresponding":false,"raw_author_name":"Beloslav Rie\u010dan","raw_affiliation_strings":["Department of Mathematics, Faculty of Natural Sciences, Matej Bel University, Tajovsk\u00e9ho 40, Bansk\u00e1 Bystrica 974 01, Slovakia","Mathematical Institute, Slovak Academy of Sciences, \u0160tef\u00e1nikova 49, Bratislava 814 73, Slovakia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Natural Sciences, Matej Bel University, Tajovsk\u00e9ho 40, Bansk\u00e1 Bystrica 974 01, Slovakia","institution_ids":["https://openalex.org/I59655833"]},{"raw_affiliation_string":"Mathematical Institute, Slovak Academy of Sciences, \u0160tef\u00e1nikova 49, Bratislava 814 73, Slovakia","institution_ids":["https://openalex.org/I207624831","https://openalex.org/I4210120676"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5020354344"],"corresponding_institution_ids":["https://openalex.org/I306340464"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":7.9716,"has_fulltext":true,"cited_by_count":30,"citation_normalized_percentile":{"value":0.97671375,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"18","issue":"1","first_page":"19","last_page":"19"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9851999878883362,"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":0.9851999878883362,"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":0.9735000133514404,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9355000257492065,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.6482987403869629},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5913658142089844},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.5015678405761719},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4637608528137207},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.4580603539943695},{"id":"https://openalex.org/keywords/defuzzification","display_name":"Defuzzification","score":0.42032748460769653},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.41605085134506226},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.3679161071777344},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.21922388672828674},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.20732486248016357},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1672581136226654},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.11803591251373291},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07540959119796753}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6482987403869629},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5913658142089844},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.5015678405761719},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4637608528137207},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.4580603539943695},{"id":"https://openalex.org/C170260401","wikidata":"https://www.wikidata.org/wiki/Q5251735","display_name":"Defuzzification","level":5,"score":0.42032748460769653},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.41605085134506226},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.3679161071777344},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21922388672828674},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.20732486248016357},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1672581136226654},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.11803591251373291},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07540959119796753}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/e18010019","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e18010019","pdf_url":"https://www.mdpi.com/1099-4300/18/1/19/pdf?version=1453102396","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"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":"Entropy","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:636ee2bf468a4ce7afcf58f9f3a39a8b","is_oa":true,"landing_page_url":"https://doaj.org/article/636ee2bf468a4ce7afcf58f9f3a39a8b","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":"Entropy, Vol 18, Iss 1, p 19 (2016)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/18/1/19/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e18010019","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"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":"Entropy; Volume 18; Issue 1; Pages: 19","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e18010019","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e18010019","pdf_url":"https://www.mdpi.com/1099-4300/18/1/19/pdf?version=1453102396","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"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":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2269305055.pdf","grobid_xml":"https://content.openalex.org/works/W2269305055.grobid-xml"},"referenced_works_count":45,"referenced_works":["https://openalex.org/W168055850","https://openalex.org/W197511200","https://openalex.org/W635510250","https://openalex.org/W1156828040","https://openalex.org/W1496462336","https://openalex.org/W1507772593","https://openalex.org/W1528458083","https://openalex.org/W1555314278","https://openalex.org/W1568586753","https://openalex.org/W1585620996","https://openalex.org/W1604825935","https://openalex.org/W1771584566","https://openalex.org/W1963902924","https://openalex.org/W1965085069","https://openalex.org/W1966467498","https://openalex.org/W1967925168","https://openalex.org/W1973195947","https://openalex.org/W1984450777","https://openalex.org/W1991949889","https://openalex.org/W1995875735","https://openalex.org/W2005067177","https://openalex.org/W2009900676","https://openalex.org/W2020547186","https://openalex.org/W2038190934","https://openalex.org/W2049285243","https://openalex.org/W2065294460","https://openalex.org/W2069222657","https://openalex.org/W2070758760","https://openalex.org/W2072781955","https://openalex.org/W2074918847","https://openalex.org/W2078867545","https://openalex.org/W2079605328","https://openalex.org/W2080412456","https://openalex.org/W2095674846","https://openalex.org/W2098093602","https://openalex.org/W2150872625","https://openalex.org/W2169144828","https://openalex.org/W2399980397","https://openalex.org/W2912565176","https://openalex.org/W2913764840","https://openalex.org/W3048150251","https://openalex.org/W4211007335","https://openalex.org/W4255646105","https://openalex.org/W4292295629","https://openalex.org/W6835479129"],"related_works":["https://openalex.org/W2773005380","https://openalex.org/W2060361571","https://openalex.org/W4388451300","https://openalex.org/W1879432897","https://openalex.org/W2256857057","https://openalex.org/W3167814444","https://openalex.org/W3176863924","https://openalex.org/W2023513928","https://openalex.org/W2182392910","https://openalex.org/W4361984403"],"abstract_inverted_index":{"In":[0],"the":[1,27,52,63],"paper":[2],"we":[3],"define":[4],"three":[5],"kinds":[6],"of":[7,9,17,26,29,36,38,62],"entropy":[8,28],"a":[10],"fuzzy":[11,18,30,39,71],"dynamical":[12,40,72],"system":[13],"using":[14],"different":[15,24,34],"entropies":[16,37,46],"partitions.":[19],"It":[20],"is":[21,68],"shown":[22],"that":[23],"definitions":[25],"partitions":[31],"lead":[32],"to":[33],"notions":[35],"systems.":[41,73],"The":[42],"relationships":[43],"between":[44],"these":[45],"are":[47,55],"studied":[48],"and":[49],"connections":[50],"with":[51],"classical":[53],"case":[54],"mentioned":[56],"as":[57],"well.":[58],"Finally,":[59],"an":[60],"analogy":[61],"Kolmogorov\u2013Sinai":[64],"Theorem":[65],"on":[66],"generators":[67],"proved":[69],"for":[70]},"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":12},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
