{"id":"https://openalex.org/W4229448406","doi":"https://doi.org/10.3390/axioms11050220","title":"New Fuzzy Extensions on Binomial Distribution","display_name":"New Fuzzy Extensions on Binomial Distribution","publication_year":2022,"publication_date":"2022-05-09","ids":{"openalex":"https://openalex.org/W4229448406","doi":"https://doi.org/10.3390/axioms11050220"},"language":"en","primary_location":{"id":"doi:10.3390/axioms11050220","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11050220","pdf_url":"https://www.mdpi.com/2075-1680/11/5/220/pdf?version=1652420355","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://www.mdpi.com/2075-1680/11/5/220/pdf?version=1652420355","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5081617835","display_name":"Gia Sirbiladze","orcid":"https://orcid.org/0000-0002-5279-7571"},"institutions":[{"id":"https://openalex.org/I102808428","display_name":"Tbilisi State University","ror":"https://ror.org/05fd1hd85","country_code":"GE","type":"education","lineage":["https://openalex.org/I102808428"]}],"countries":["GE"],"is_corresponding":true,"raw_author_name":"Gia Sirbiladze","raw_affiliation_strings":["Department of Computer Sciences, Faculty of Exact and Natural Sciences, Ivane Javakhishvili Tbilisi State University, University St. 13, Tbilisi 0186, Georgia"],"affiliations":[{"raw_affiliation_string":"Department of Computer Sciences, Faculty of Exact and Natural Sciences, Ivane Javakhishvili Tbilisi State University, University St. 13, Tbilisi 0186, Georgia","institution_ids":["https://openalex.org/I102808428"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005837856","display_name":"Janusz Kacprzyk","orcid":"https://orcid.org/0000-0003-4187-5877"},"institutions":[{"id":"https://openalex.org/I66083562","display_name":"Systems Research Institute","ror":"https://ror.org/0111cp837","country_code":"PL","type":"facility","lineage":["https://openalex.org/I66083562","https://openalex.org/I99542240"]},{"id":"https://openalex.org/I99542240","display_name":"Polish Academy of Sciences","ror":"https://ror.org/01dr6c206","country_code":"PL","type":"funder","lineage":["https://openalex.org/I99542240"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Janusz Kacprzyk","raw_affiliation_strings":["Intelligent Systems Laboratory, Systems Research Institute, Polish Academy of Sciences, Ul. Newelska 6, 01-447 Warsaw, Poland"],"affiliations":[{"raw_affiliation_string":"Intelligent Systems Laboratory, Systems Research Institute, Polish Academy of Sciences, Ul. Newelska 6, 01-447 Warsaw, Poland","institution_ids":["https://openalex.org/I66083562","https://openalex.org/I99542240"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010226224","display_name":"Teimuraz Manjafarashvili","orcid":null},"institutions":[{"id":"https://openalex.org/I102808428","display_name":"Tbilisi State University","ror":"https://ror.org/05fd1hd85","country_code":"GE","type":"education","lineage":["https://openalex.org/I102808428"]}],"countries":["GE"],"is_corresponding":false,"raw_author_name":"Teimuraz Manjafarashvili","raw_affiliation_strings":["Department of Computer Sciences, Faculty of Exact and Natural Sciences, Ivane Javakhishvili Tbilisi State University, University St. 13, Tbilisi 0186, Georgia"],"affiliations":[{"raw_affiliation_string":"Department of Computer Sciences, Faculty of Exact and Natural Sciences, Ivane Javakhishvili Tbilisi State University, University St. 13, Tbilisi 0186, Georgia","institution_ids":["https://openalex.org/I102808428"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084554925","display_name":"Bidzina Midodashvili","orcid":"https://orcid.org/0000-0002-5046-8766"},"institutions":[{"id":"https://openalex.org/I102808428","display_name":"Tbilisi State University","ror":"https://ror.org/05fd1hd85","country_code":"GE","type":"education","lineage":["https://openalex.org/I102808428"]}],"countries":["GE"],"is_corresponding":false,"raw_author_name":"Bidzina Midodashvili","raw_affiliation_strings":["Department of Computer Sciences, Faculty of Exact and Natural Sciences, Ivane Javakhishvili Tbilisi State University, University St. 13, Tbilisi 0186, Georgia"],"affiliations":[{"raw_affiliation_string":"Department of Computer Sciences, Faculty of Exact and Natural Sciences, Ivane Javakhishvili Tbilisi State University, University St. 13, Tbilisi 0186, Georgia","institution_ids":["https://openalex.org/I102808428"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027080458","display_name":"Bidzina Matsaberidze","orcid":null},"institutions":[{"id":"https://openalex.org/I102808428","display_name":"Tbilisi State University","ror":"https://ror.org/05fd1hd85","country_code":"GE","type":"education","lineage":["https://openalex.org/I102808428"]}],"countries":["GE"],"is_corresponding":false,"raw_author_name":"Bidzina Matsaberidze","raw_affiliation_strings":["Department of Computer Sciences, Faculty of Exact and Natural Sciences, Ivane Javakhishvili Tbilisi State University, University St. 13, Tbilisi 0186, Georgia"],"affiliations":[{"raw_affiliation_string":"Department of Computer Sciences, Faculty of Exact and Natural Sciences, Ivane Javakhishvili Tbilisi State University, University St. 13, Tbilisi 0186, Georgia","institution_ids":["https://openalex.org/I102808428"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5081617835"],"corresponding_institution_ids":["https://openalex.org/I102808428"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":2.188,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.88391082,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":98},"biblio":{"volume":"11","issue":"5","first_page":"220","last_page":"220"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9872000217437744,"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":0.9872000217437744,"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/T10050","display_name":"Multi-Criteria Decision Making","score":0.9861000180244446,"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/T13608","display_name":"Advanced Computational Techniques in Science and Engineering","score":0.9714999794960022,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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":0.7258889079093933},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.6422551870346069},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5472646355628967},{"id":"https://openalex.org/keywords/multinomial-distribution","display_name":"Multinomial distribution","score":0.4961872696876526},{"id":"https://openalex.org/keywords/negative-binomial-distribution","display_name":"Negative binomial distribution","score":0.4717959761619568},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.47164008021354675},{"id":"https://openalex.org/keywords/cumulative-distribution-function","display_name":"Cumulative distribution function","score":0.4682620167732239},{"id":"https://openalex.org/keywords/binomial-distribution","display_name":"Binomial distribution","score":0.4667912423610687},{"id":"https://openalex.org/keywords/binomial","display_name":"Binomial (polynomial)","score":0.4269311726093292},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.4236585199832916},{"id":"https://openalex.org/keywords/beta-binomial-distribution","display_name":"Beta-binomial distribution","score":0.4147224426269531},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3989903926849365},{"id":"https://openalex.org/keywords/poisson-distribution","display_name":"Poisson distribution","score":0.3608560860157013},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2906506657600403},{"id":"https://openalex.org/keywords/probability-density-function","display_name":"Probability density function","score":0.19997906684875488},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18811267614364624},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.14021950960159302}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7258889079093933},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.6422551870346069},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5472646355628967},{"id":"https://openalex.org/C192065140","wikidata":"https://www.wikidata.org/wiki/Q1147928","display_name":"Multinomial distribution","level":2,"score":0.4961872696876526},{"id":"https://openalex.org/C199335787","wikidata":"https://www.wikidata.org/wiki/Q743364","display_name":"Negative binomial distribution","level":3,"score":0.4717959761619568},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.47164008021354675},{"id":"https://openalex.org/C103784038","wikidata":"https://www.wikidata.org/wiki/Q386228","display_name":"Cumulative distribution function","level":3,"score":0.4682620167732239},{"id":"https://openalex.org/C41054675","wikidata":"https://www.wikidata.org/wiki/Q185547","display_name":"Binomial distribution","level":2,"score":0.4667912423610687},{"id":"https://openalex.org/C2781315470","wikidata":"https://www.wikidata.org/wiki/Q193623","display_name":"Binomial (polynomial)","level":2,"score":0.4269311726093292},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.4236585199832916},{"id":"https://openalex.org/C165480597","wikidata":"https://www.wikidata.org/wiki/Q307557","display_name":"Beta-binomial distribution","level":4,"score":0.4147224426269531},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3989903926849365},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.3608560860157013},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2906506657600403},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.19997906684875488},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18811267614364624},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.14021950960159302}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms11050220","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11050220","pdf_url":"https://www.mdpi.com/2075-1680/11/5/220/pdf?version=1652420355","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:e7b3e30f5e744aba90c064f631e9a3c9","is_oa":true,"landing_page_url":"https://doaj.org/article/e7b3e30f5e744aba90c064f631e9a3c9","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 11, Iss 5, p 220 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/11/5/220/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms11050220","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":"Axioms; Volume 11; Issue 5; Pages: 220","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms11050220","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11050220","pdf_url":"https://www.mdpi.com/2075-1680/11/5/220/pdf?version=1652420355","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4229448406.pdf","grobid_xml":"https://content.openalex.org/works/W4229448406.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W189623986","https://openalex.org/W196596189","https://openalex.org/W231896955","https://openalex.org/W575976088","https://openalex.org/W2014814286","https://openalex.org/W2030853345","https://openalex.org/W2038190934","https://openalex.org/W2062241359","https://openalex.org/W2086860546","https://openalex.org/W2101680584","https://openalex.org/W2118654963","https://openalex.org/W2266106419","https://openalex.org/W2478752356","https://openalex.org/W2480397040","https://openalex.org/W2510242871","https://openalex.org/W2552419662","https://openalex.org/W2946227173","https://openalex.org/W2992342299","https://openalex.org/W3200160023","https://openalex.org/W3201063394","https://openalex.org/W3207455188","https://openalex.org/W4210514196","https://openalex.org/W4240278385","https://openalex.org/W6675645705","https://openalex.org/W6802180343"],"related_works":["https://openalex.org/W1978000964","https://openalex.org/W2046711921","https://openalex.org/W2386576143","https://openalex.org/W4291340098","https://openalex.org/W2355806151","https://openalex.org/W4238009488","https://openalex.org/W1504588487","https://openalex.org/W1857611597","https://openalex.org/W3103515985","https://openalex.org/W203320791"],"abstract_inverted_index":{"The":[0,98,125,146,185,234,258,288],"use":[1],"of":[2,35,64,90,100,118,122,132,155,164,167,178,181,191,193,216,219,228,241,253,277,283,290,298,309,328,334,338,350,364,368,372,377,393,398,403],"discrete":[3],"probabilistic":[4,88],"distributions":[5,67],"is":[6,96,109,149,166,172,198,204,222,232,236,263,271,322,381,387],"relevant":[7],"to":[8,48,52,344],"many":[9],"practical":[10],"tasks,":[11],"especially":[12],"in":[13,39,361,389,408],"present-day":[14],"situations":[15],"where":[16,384],"the":[17,29,33,78,87,91,116,128,133,137,152,162,179,189,201,209,213,217,226,229,239,251,269,274,278,284,291,295,299,307,326,331,335,351,362,365,369,385,390,399,401],"data":[18],"on":[19,84,102,115,238,325],"distribution":[20,89,104,135,148,231,262,293,300,312,316,380],"are":[21,28,74,81,105,143,301,317,355,406],"insufficient":[22],"and":[23,26,44,69,107,120,136,139,171,200,245,280,294,313],"expert":[24],"knowledge":[25],"evaluations":[27],"only":[30],"instruments":[31],"for":[32,127,187,211,306],"restoration":[34],"probability":[36,190],"distributions.":[37],"However,":[38],"such":[40],"cases,":[41],"uncertainty":[42],"arises,":[43],"it":[45,108],"becomes":[46,340],"necessary":[47],"build":[49],"suitable":[50],"approaches":[51],"overcome":[53],"it.":[54],"In":[55,266],"this":[56,58,85,103,267],"direction,":[57],"paper":[59],"discusses":[60],"a":[61,156,168,175,207,242,310,314],"new":[62],"approach":[63],"fuzzy":[65,169,176,196,220,254,259,375,404],"binomial":[66,94,158,194,260,279],"(BDs)":[68],"their":[70],"extensions.":[71],"Four":[72],"cases":[73],"considered:":[75],"(1)":[76],"When":[77,161,225],"elementary":[79],"events":[80,197,256,282],"fuzzy.":[82,233],"Based":[83],"information,":[86],"corresponding":[92,202],"fuzzy-random":[93,157,243],"variable":[95],"calculated.":[97,303],"conditions":[99,113,305],"restrictions":[101],"obtained,":[106,199],"shown":[110],"that":[111],"these":[112],"depend":[114],"ratio":[117],"success":[119,183],"failure":[121,286],"membership":[123,275],"levels.":[124],"formulas":[126],"generating":[129],"function":[130],"(GF)":[131],"constructed":[134,292],"first":[138],"second":[140],"order":[141],"moments":[142],"also":[144,302,318,382],"obtained.":[145,319],"Poisson":[147,315],"calculated":[150],"as":[151,174,248,250],"limit":[153,311],"case":[154,268],"experiment.":[159],"(2)":[160],"number":[163,218],"successes":[165,221],"nature":[170],"represented":[173,272],"subset":[177],"set":[180],"possible":[182],"numbers.":[184],"formula":[186],"calculating":[188,212],"convolution":[192],"dependent":[195],"GF":[203,289],"built.":[205],"As":[206,321],"result,":[208],"scheme":[210],"mathematical":[214],"expectation":[215],"defined.":[223],"(3)":[224],"spectrum":[227,333,367],"extended":[230],"discussion":[235],"based":[237,324],"concepts":[240],"event":[244],"its":[246],"probability,":[247],"well":[249],"notion":[252],"random":[255],"independence.":[257],"upper":[261],"specifically":[264],"considered.":[265],"fuzziness":[270,386],"by":[273],"levels":[276],"non-binomial":[281],"complete":[285],"complex.":[287],"first-order":[296],"moment":[297],"Sufficient":[304],"existence":[308],"(4)":[320],"known,":[323],"analysis":[327,363],"lexical":[329],"material,":[330],"linguistic":[332,366],"statistical":[336,370],"process":[337,354,371],"word-formation":[339],"two-component":[341],"when":[342],"switching":[343],"vocabulary.":[345],"For":[346,395],"this,":[347],"two":[348],"variants":[349],"hybrid":[352],"fuzzy-probabilistic":[353],"constructed,":[356],"which":[357],"can":[358],"be":[359],"used":[360],"word-formation.":[373],"A":[374],"extension":[376],"standard":[378],"Fuchs":[379],"presented,":[383],"reflected":[388],"growing":[391],"numbers":[392],"failures.":[394],"better":[396],"representation":[397],"results,":[400],"examples":[402],"BD":[405],"illustrated":[407],"each":[409],"section.":[410]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}