{"id":"https://openalex.org/W2914190805","doi":"https://doi.org/10.1109/tfuzz.2019.2896849","title":"Strong Laws of Large Numbers for IVM-Events","display_name":"Strong Laws of Large Numbers for IVM-Events","publication_year":2019,"publication_date":"2019-02-01","ids":{"openalex":"https://openalex.org/W2914190805","doi":"https://doi.org/10.1109/tfuzz.2019.2896849","mag":"2914190805"},"language":"en","primary_location":{"id":"doi:10.1109/tfuzz.2019.2896849","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tfuzz.2019.2896849","pdf_url":null,"source":{"id":"https://openalex.org/S134177497","display_name":"IEEE Transactions on Fuzzy Systems","issn_l":"1063-6706","issn":["1063-6706","1941-0034"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Fuzzy 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/A5027801521","display_name":"Piotr Nowak","orcid":"https://orcid.org/0000-0002-9325-4493"},"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":"government","lineage":["https://openalex.org/I99542240"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Piotr Nowak","raw_affiliation_strings":["Polish Academy of Sciences, Systems Research Institute, Warsaw, Poland"],"raw_orcid":"https://orcid.org/0000-0002-9325-4493","affiliations":[{"raw_affiliation_string":"Polish Academy of Sciences, Systems Research Institute, Warsaw, Poland","institution_ids":["https://openalex.org/I66083562","https://openalex.org/I99542240"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023109012","display_name":"Olgierd Hryniewicz","orcid":"https://orcid.org/0000-0001-9877-508X"},"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":"government","lineage":["https://openalex.org/I99542240"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Olgierd Hryniewicz","raw_affiliation_strings":["Polish Academy of Sciences, Systems Research Institute, Warsaw, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Polish Academy of Sciences, Systems Research Institute, Warsaw, Poland","institution_ids":["https://openalex.org/I66083562","https://openalex.org/I99542240"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5027801521"],"corresponding_institution_ids":["https://openalex.org/I66083562","https://openalex.org/I99542240"],"apc_list":null,"apc_paid":null,"fwci":0.7999,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.74066827,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"27","issue":"12","first_page":"2293","last_page":"2301"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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":0.9976000189781189,"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":0.7063627243041992},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.6978970766067505},{"id":"https://openalex.org/keywords/probability-theory","display_name":"Probability theory","score":0.6921646595001221},{"id":"https://openalex.org/keywords/independent-and-identically-distributed-random-variables","display_name":"Independent and identically distributed random variables","score":0.6455767154693604},{"id":"https://openalex.org/keywords/algebra-of-random-variables","display_name":"Algebra of random variables","score":0.6210241317749023},{"id":"https://openalex.org/keywords/independence","display_name":"Independence (probability theory)","score":0.6179159879684448},{"id":"https://openalex.org/keywords/probability-measure","display_name":"Probability measure","score":0.5805085897445679},{"id":"https://openalex.org/keywords/observable","display_name":"Observable","score":0.5705463290214539},{"id":"https://openalex.org/keywords/law-of-large-numbers","display_name":"Law of large numbers","score":0.5696630477905273},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.4917042851448059},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.4839904308319092},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.47284796833992004},{"id":"https://openalex.org/keywords/probability-and-statistics","display_name":"Probability and statistics","score":0.431461364030838},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.36303848028182983},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3432350754737854},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2343539595603943},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.14215755462646484},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11763641238212585},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08361583948135376}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7063627243041992},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.6978970766067505},{"id":"https://openalex.org/C122203268","wikidata":"https://www.wikidata.org/wiki/Q5862903","display_name":"Probability theory","level":2,"score":0.6921646595001221},{"id":"https://openalex.org/C141513077","wikidata":"https://www.wikidata.org/wiki/Q378542","display_name":"Independent and identically distributed random variables","level":3,"score":0.6455767154693604},{"id":"https://openalex.org/C89231458","wikidata":"https://www.wikidata.org/wiki/Q4723976","display_name":"Algebra of random variables","level":4,"score":0.6210241317749023},{"id":"https://openalex.org/C35651441","wikidata":"https://www.wikidata.org/wiki/Q625303","display_name":"Independence (probability theory)","level":2,"score":0.6179159879684448},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.5805085897445679},{"id":"https://openalex.org/C32848918","wikidata":"https://www.wikidata.org/wiki/Q845789","display_name":"Observable","level":2,"score":0.5705463290214539},{"id":"https://openalex.org/C185767445","wikidata":"https://www.wikidata.org/wiki/Q207952","display_name":"Law of large numbers","level":3,"score":0.5696630477905273},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.4917042851448059},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.4839904308319092},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.47284796833992004},{"id":"https://openalex.org/C43596424","wikidata":"https://www.wikidata.org/wiki/Q98124957","display_name":"Probability and statistics","level":2,"score":0.431461364030838},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.36303848028182983},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3432350754737854},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2343539595603943},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.14215755462646484},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11763641238212585},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08361583948135376},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","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":1,"locations":[{"id":"doi:10.1109/tfuzz.2019.2896849","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tfuzz.2019.2896849","pdf_url":null,"source":{"id":"https://openalex.org/S134177497","display_name":"IEEE Transactions on Fuzzy Systems","issn_l":"1063-6706","issn":["1063-6706","1941-0034"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Fuzzy Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.7900000214576721,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W57087909","https://openalex.org/W106223561","https://openalex.org/W197511200","https://openalex.org/W1566552629","https://openalex.org/W1771584566","https://openalex.org/W1830630300","https://openalex.org/W1980147176","https://openalex.org/W1984496682","https://openalex.org/W2000599793","https://openalex.org/W2006090261","https://openalex.org/W2034048215","https://openalex.org/W2036635144","https://openalex.org/W2047723833","https://openalex.org/W2083508884","https://openalex.org/W2084418735","https://openalex.org/W2087819218","https://openalex.org/W2127195516","https://openalex.org/W2326103725","https://openalex.org/W2389299280","https://openalex.org/W2399648260","https://openalex.org/W2498839538","https://openalex.org/W2735878874","https://openalex.org/W2796291475","https://openalex.org/W3100361384","https://openalex.org/W4210409578","https://openalex.org/W4250169989","https://openalex.org/W6602278268","https://openalex.org/W6638609171"],"related_works":["https://openalex.org/W2508350231","https://openalex.org/W4253907417","https://openalex.org/W2963248475","https://openalex.org/W2064793276","https://openalex.org/W3037024381","https://openalex.org/W2390642752","https://openalex.org/W2616312727","https://openalex.org/W4251427866","https://openalex.org/W344980251","https://openalex.org/W2031285341"],"abstract_inverted_index":{"Nonstandard":[0],"probability":[1,23,42,60],"theories":[2],"have":[3,81,123],"been":[4,82,124],"developed":[5],"for":[6,73,102,120],"modeling":[7],"random":[8,47,109,141],"systems":[9],"in":[10,135,143],"complex":[11,145],"spaces,":[12],"such":[13],"as,":[14],"quantum":[15],"systems.":[16],"One":[17],"of":[18,28,39,54,69,75,98,114,139],"these":[19,58],"theories,":[20,61],"the":[21,26,37,40,45,52,66,96,99,103,136],"MV-algebraic":[22],"theory,":[24],"involves":[25],"notions":[27],"state":[29],"and":[30,44,77,117],"observable,":[31],"which":[32],"were":[33],"introduced":[34],"by":[35,106],"abstracting":[36],"properties":[38],"Kolmogorovian":[41],"measure":[43],"classical":[46],"variable,":[48],"as":[49,51],"well":[50],"notion":[53],"independence.":[55],"Although":[56],"within":[57,126],"nonstandard":[59],"many":[62],"important":[63],"theorems,":[64],"including":[65],"strong":[67],"law":[68],"large":[70],"numbers":[71],"(SLLN)":[72],"sequences":[74],"independent":[76,121],"identically":[78],"distributed":[79],"observables,":[80],"considered,":[83],"some":[84],"practical":[85],"applications":[86],"require":[87],"their":[88],"further":[89],"development.":[90],"This":[91],"paper":[92],"is":[93],"devoted":[94],"to":[95],"development":[97],"IVM-probability":[100],"theory":[101],"data":[104],"described":[105],"interval-valued":[107],"fuzzy":[108],"sets":[110],"(IVM-events).":[111],"The":[112],"generalizations":[113],"Marcinkiewicz-Zygmund":[115],"SLLN":[116,119],"Brunk-Prokhorov":[118],"IVM-events":[122],"proved":[125],"this":[127],"new":[128,133],"theory.":[129],"Our":[130],"results":[131],"open":[132],"possibilities":[134],"theoretical":[137],"analysis":[138],"imprecise":[140],"events":[142],"more":[144],"spaces.":[146]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}