{"id":"https://openalex.org/W4414129879","doi":"https://doi.org/10.3390/axioms14090690","title":"Max\u2013Min Transitive Closure of Randomly Generated Fuzzy Matrix: Bernoulli and Classical Probabilistic Models","display_name":"Max\u2013Min Transitive Closure of Randomly Generated Fuzzy Matrix: Bernoulli and Classical Probabilistic Models","publication_year":2025,"publication_date":"2025-09-11","ids":{"openalex":"https://openalex.org/W4414129879","doi":"https://doi.org/10.3390/axioms14090690"},"language":"en","primary_location":{"id":"doi:10.3390/axioms14090690","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14090690","pdf_url":null,"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":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/axioms14090690","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100341075","display_name":"Nan Li","orcid":"https://orcid.org/0009-0003-9255-259X"},"institutions":[{"id":"https://openalex.org/I4210101072","display_name":"Shangluo University","ror":"https://ror.org/01a56n213","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210101072"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Nan Li","raw_affiliation_strings":["School of Economics and Management, Shangluo University, Shangluo 726000, China"],"affiliations":[{"raw_affiliation_string":"School of Economics and Management, Shangluo University, Shangluo 726000, China","institution_ids":["https://openalex.org/I4210101072"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020419743","display_name":"Xianfeng Yu","orcid":null},"institutions":[{"id":"https://openalex.org/I4210101072","display_name":"Shangluo University","ror":"https://ror.org/01a56n213","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210101072"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xianfeng Yu","raw_affiliation_strings":["Engineering Research Center of Qinling Health Welfare Big Data, Universities of Shaanxi Province, Shangluo 726000, China","School of Mathematics and Computer Application, Shangluo University, Shangluo 726000, China"],"affiliations":[{"raw_affiliation_string":"Engineering Research Center of Qinling Health Welfare Big Data, Universities of Shaanxi Province, Shangluo 726000, China","institution_ids":["https://openalex.org/I4210101072"]},{"raw_affiliation_string":"School of Mathematics and Computer Application, Shangluo University, Shangluo 726000, China","institution_ids":["https://openalex.org/I4210101072"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056807499","display_name":"Wuniu Liu","orcid":"https://orcid.org/0000-0002-0220-9436"},"institutions":[{"id":"https://openalex.org/I88830068","display_name":"Shaanxi Normal University","ror":"https://ror.org/0170z8493","country_code":"CN","type":"education","lineage":["https://openalex.org/I88830068"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wuniu Liu","raw_affiliation_strings":["School of Mathematics and Statistics, Shaanxi Normal University, Xi\u2019an 710119, China","School of Mathematics and Statistics, Shaanxi Normal University, Xi'an 710119, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Shaanxi Normal University, Xi\u2019an 710119, China","institution_ids":["https://openalex.org/I88830068"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Shaanxi Normal University, Xi'an 710119, China","institution_ids":["https://openalex.org/I88830068"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5020419743"],"corresponding_institution_ids":["https://openalex.org/I4210101072"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.29930226,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"9","first_page":"690","last_page":"690"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9952999949455261,"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":0.9952999949455261,"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/T11106","display_name":"Data Management and Algorithms","score":0.9868999719619751,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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":0.9796000123023987,"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/transitive-closure","display_name":"Transitive closure","score":0.7159000039100647},{"id":"https://openalex.org/keywords/closure","display_name":"Closure (psychology)","score":0.6189000010490417},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.5985999703407288},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5568000078201294},{"id":"https://openalex.org/keywords/bernoulli-distribution","display_name":"Bernoulli distribution","score":0.5414000153541565},{"id":"https://openalex.org/keywords/fuzzy-subalgebra","display_name":"Fuzzy subalgebra","score":0.4528999924659729},{"id":"https://openalex.org/keywords/fuzzy-associative-matrix","display_name":"Fuzzy associative matrix","score":0.4341000020503998},{"id":"https://openalex.org/keywords/bernoullis-principle","display_name":"Bernoulli's principle","score":0.42570000886917114},{"id":"https://openalex.org/keywords/defuzzification","display_name":"Defuzzification","score":0.4223000109195709}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.828499972820282},{"id":"https://openalex.org/C128896722","wikidata":"https://www.wikidata.org/wiki/Q1501387","display_name":"Transitive closure","level":2,"score":0.7159000039100647},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.6189000010490417},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.5985999703407288},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5568000078201294},{"id":"https://openalex.org/C27956954","wikidata":"https://www.wikidata.org/wiki/Q391371","display_name":"Bernoulli distribution","level":3,"score":0.5414000153541565},{"id":"https://openalex.org/C115740575","wikidata":"https://www.wikidata.org/wiki/Q5511136","display_name":"Fuzzy subalgebra","level":5,"score":0.4528999924659729},{"id":"https://openalex.org/C144170203","wikidata":"https://www.wikidata.org/wiki/Q5511099","display_name":"Fuzzy associative matrix","level":5,"score":0.4341000020503998},{"id":"https://openalex.org/C152361515","wikidata":"https://www.wikidata.org/wiki/Q181328","display_name":"Bernoulli's principle","level":2,"score":0.42570000886917114},{"id":"https://openalex.org/C170260401","wikidata":"https://www.wikidata.org/wiki/Q5251735","display_name":"Defuzzification","level":5,"score":0.4223000109195709},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.41119998693466187},{"id":"https://openalex.org/C191399111","wikidata":"https://www.wikidata.org/wiki/Q64861","display_name":"Transitive relation","level":2,"score":0.40639999508857727},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.4023999869823456},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.390500009059906},{"id":"https://openalex.org/C127385683","wikidata":"https://www.wikidata.org/wiki/Q1475696","display_name":"Fuzzy classification","level":4,"score":0.3882000148296356},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3801000118255615},{"id":"https://openalex.org/C148671577","wikidata":"https://www.wikidata.org/wiki/Q5511133","display_name":"Fuzzy set operations","level":4,"score":0.37290000915527344},{"id":"https://openalex.org/C17350324","wikidata":"https://www.wikidata.org/wiki/Q7860605","display_name":"Type-2 fuzzy sets and systems","level":5,"score":0.3709000051021576},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.3571999967098236},{"id":"https://openalex.org/C100516043","wikidata":"https://www.wikidata.org/wiki/Q4455138","display_name":"Fuzzy measure theory","level":5,"score":0.35199999809265137},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33009999990463257},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.3246000111103058},{"id":"https://openalex.org/C18653775","wikidata":"https://www.wikidata.org/wiki/Q1333358","display_name":"Joint probability distribution","level":2,"score":0.29760000109672546},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.27959999442100525},{"id":"https://openalex.org/C5263885","wikidata":"https://www.wikidata.org/wiki/Q1967302","display_name":"Membership function","level":4,"score":0.26330000162124634},{"id":"https://openalex.org/C166586474","wikidata":"https://www.wikidata.org/wiki/Q5511129","display_name":"Fuzzy mathematics","level":5,"score":0.257999986410141}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms14090690","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14090690","pdf_url":null,"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:doaj.org/article:aa33b2d089d041d6856fc382f3d4bde8","is_oa":true,"landing_page_url":"https://doaj.org/article/aa33b2d089d041d6856fc382f3d4bde8","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 14, Iss 9, p 690 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms14090690","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14090690","pdf_url":null,"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":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W380795639","https://openalex.org/W1496554236","https://openalex.org/W1500256440","https://openalex.org/W2019508321","https://openalex.org/W2065835067","https://openalex.org/W2081763828","https://openalex.org/W2101193451","https://openalex.org/W4211007335","https://openalex.org/W4231268499","https://openalex.org/W4292998656","https://openalex.org/W4294811339","https://openalex.org/W4385656588","https://openalex.org/W4400275662","https://openalex.org/W4404238195"],"related_works":["https://openalex.org/W1553139688","https://openalex.org/W2371151875","https://openalex.org/W2136009070","https://openalex.org/W2362009423","https://openalex.org/W2391133415","https://openalex.org/W2012063573","https://openalex.org/W2123627450","https://openalex.org/W4230967508","https://openalex.org/W203725150","https://openalex.org/W1499233953"],"abstract_inverted_index":{"A":[0,101],"randomly":[1,40,67,92,107],"generated":[2,41,68,93,108],"fuzzy":[3,8,42,55,69,85,95,109],"matrix":[4,9,96,110],"refers":[5],"to":[6,17],"a":[7,22,27],"in":[10],"which":[11],"the":[12,18,34,51,59,63,78,83,91,106,114,121,124,129],"values":[13],"of":[14,21,38,53,62,66,90,113],"elements":[15],"belong":[16],"sample":[19],"space":[20],"[0,1]-random":[23],"variable":[24],"that":[25],"follows":[26],"certain":[28],"probability":[29,60,116],"distribution.":[30],"This":[31],"paper":[32],"studies":[33],"max\u2013min":[35],"transitive":[36,64,111,131],"closure":[37,65,98,112,132],"two-type":[39],"matrices:":[43],"Bernoulli":[44,94],"and":[45,128],"classical":[46,115],"probabilistic":[47,73],"models.":[48,74],"By":[49],"introducing":[50],"concept":[52],"superposed":[54,84],"matrices,":[56],"we":[57,76],"investigate":[58],"distribution":[61],"matrices":[70],"for":[71,82,105],"two":[72],"First,":[75],"presented":[77],"arithmetic":[79],"operation":[80],"rules":[81],"relations.":[86],"The":[87],"expected":[88],"value":[89],"transition":[97],"was":[99,118],"studied.":[100],"direct":[102,125],"calculation":[103,126,133],"method":[104,127,134],"model":[117],"provided.":[119],"Finally,":[120],"errors":[122],"between":[123],"traditional":[130],"were":[135],"compared.":[136]},"counts_by_year":[],"updated_date":"2026-03-07T16:01:11.037858","created_date":"2025-10-10T00:00:00"}