{"id":"https://openalex.org/W4220659050","doi":"https://doi.org/10.1080/03081079.2022.2052062","title":"On deferred-statistical convergence of uncertain fuzzy sequences","display_name":"On deferred-statistical convergence of uncertain fuzzy sequences","publication_year":2022,"publication_date":"2022-03-31","ids":{"openalex":"https://openalex.org/W4220659050","doi":"https://doi.org/10.1080/03081079.2022.2052062"},"language":"en","primary_location":{"id":"doi:10.1080/03081079.2022.2052062","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03081079.2022.2052062","pdf_url":null,"source":{"id":"https://openalex.org/S145553572","display_name":"International Journal of General Systems","issn_l":"0308-1079","issn":["0308-1079","1026-7492","1563-5104"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of General 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/A5089807507","display_name":"L. Nayak","orcid":"https://orcid.org/0000-0003-2745-8962"},"institutions":[{"id":"https://openalex.org/I67357951","display_name":"KIIT University","ror":"https://ror.org/00k8zt527","country_code":"IN","type":"education","lineage":["https://openalex.org/I67357951"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"L. Nayak","raw_affiliation_strings":["Department of Mathematics, School of Applied Sciences, Kalinga Institute of Industrial Technology, Bhubaneswar, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, School of Applied Sciences, Kalinga Institute of Industrial Technology, Bhubaneswar, India","institution_ids":["https://openalex.org/I67357951"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019797810","display_name":"Binod Chandra Tripathy","orcid":"https://orcid.org/0000-0002-0738-652X"},"institutions":[{"id":"https://openalex.org/I72677176","display_name":"Tripura University","ror":"https://ror.org/05xqycm14","country_code":"IN","type":"education","lineage":["https://openalex.org/I72677176"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"B. C. Tripathy","raw_affiliation_strings":["Department of Mathematics, Tripura University, Agartala, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Tripura University, Agartala, India","institution_ids":["https://openalex.org/I72677176"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038442884","display_name":"P. Baliarsingh","orcid":"https://orcid.org/0000-0002-5618-0413"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"P. Baliarsingh","raw_affiliation_strings":["Institute of Mathematics and Applications, Bhubaneswar, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics and Applications, Bhubaneswar, India","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5038442884"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.5609,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.90203225,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"51","issue":"6","first_page":"631","last_page":"647"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12062","display_name":"Approximation Theory and Sequence Spaces","score":0.9998999834060669,"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/T12062","display_name":"Approximation Theory and Sequence Spaces","score":0.9998999834060669,"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9879000186920166,"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":0.9800000190734863,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.7093091011047363},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6664397716522217},{"id":"https://openalex.org/keywords/probability-theory","display_name":"Probability theory","score":0.5901274681091309},{"id":"https://openalex.org/keywords/symbolic-convergence-theory","display_name":"Symbolic convergence theory","score":0.54411381483078},{"id":"https://openalex.org/keywords/statistical-theory","display_name":"Statistical theory","score":0.5411434173583984},{"id":"https://openalex.org/keywords/convergence-of-random-variables","display_name":"Convergence of random variables","score":0.5299454927444458},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.5219059586524963},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.5184456706047058},{"id":"https://openalex.org/keywords/convergence-tests","display_name":"Convergence tests","score":0.5133968591690063},{"id":"https://openalex.org/keywords/proofs-of-convergence-of-random-variables","display_name":"Proofs of convergence of random variables","score":0.5108529925346375},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5039824843406677},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.501401424407959},{"id":"https://openalex.org/keywords/normal-convergence","display_name":"Normal convergence","score":0.4936569631099701},{"id":"https://openalex.org/keywords/mathematical-theory","display_name":"Mathematical theory","score":0.4877620339393616},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.45808708667755127},{"id":"https://openalex.org/keywords/modes-of-convergence","display_name":"Modes of convergence (annotated index)","score":0.42474332451820374},{"id":"https://openalex.org/keywords/dominated-convergence-theorem","display_name":"Dominated convergence theorem","score":0.4216978847980499},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.40572211146354675},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.283632755279541},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.25816118717193604},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.21041926741600037},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.2086799442768097},{"id":"https://openalex.org/keywords/algebra-of-random-variables","display_name":"Algebra of random variables","score":0.14142334461212158},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.14006438851356506},{"id":"https://openalex.org/keywords/topological-space","display_name":"Topological space","score":0.11148032546043396},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.096141517162323},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.07700195908546448}],"concepts":[{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.7093091011047363},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6664397716522217},{"id":"https://openalex.org/C122203268","wikidata":"https://www.wikidata.org/wiki/Q5862903","display_name":"Probability theory","level":2,"score":0.5901274681091309},{"id":"https://openalex.org/C64980692","wikidata":"https://www.wikidata.org/wiki/Q16191959","display_name":"Symbolic convergence theory","level":3,"score":0.54411381483078},{"id":"https://openalex.org/C48057537","wikidata":"https://www.wikidata.org/wiki/Q3551145","display_name":"Statistical theory","level":2,"score":0.5411434173583984},{"id":"https://openalex.org/C95763700","wikidata":"https://www.wikidata.org/wiki/Q578985","display_name":"Convergence of random variables","level":3,"score":0.5299454927444458},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.5219059586524963},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.5184456706047058},{"id":"https://openalex.org/C538505008","wikidata":"https://www.wikidata.org/wiki/Q3979448","display_name":"Convergence tests","level":4,"score":0.5133968591690063},{"id":"https://openalex.org/C206190082","wikidata":"https://www.wikidata.org/wiki/Q7250031","display_name":"Proofs of convergence of random variables","level":5,"score":0.5108529925346375},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5039824843406677},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.501401424407959},{"id":"https://openalex.org/C14928880","wikidata":"https://www.wikidata.org/wiki/Q1512559","display_name":"Normal convergence","level":4,"score":0.4936569631099701},{"id":"https://openalex.org/C2779193601","wikidata":"https://www.wikidata.org/wiki/Q20026918","display_name":"Mathematical theory","level":2,"score":0.4877620339393616},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.45808708667755127},{"id":"https://openalex.org/C48216909","wikidata":"https://www.wikidata.org/wiki/Q6889156","display_name":"Modes of convergence (annotated index)","level":5,"score":0.42474332451820374},{"id":"https://openalex.org/C38487692","wikidata":"https://www.wikidata.org/wiki/Q1067156","display_name":"Dominated convergence theorem","level":5,"score":0.4216978847980499},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.40572211146354675},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.283632755279541},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25816118717193604},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.21041926741600037},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.2086799442768097},{"id":"https://openalex.org/C89231458","wikidata":"https://www.wikidata.org/wiki/Q4723976","display_name":"Algebra of random variables","level":4,"score":0.14142334461212158},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.14006438851356506},{"id":"https://openalex.org/C81332173","wikidata":"https://www.wikidata.org/wiki/Q179899","display_name":"Topological space","level":2,"score":0.11148032546043396},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.096141517162323},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.07700195908546448},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C47776270","wikidata":"https://www.wikidata.org/wiki/Q1455249","display_name":"Topological vector space","level":3,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C174265945","wikidata":"https://www.wikidata.org/wiki/Q1142889","display_name":"Isolated point","level":4,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"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:10.1080/03081079.2022.2052062","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03081079.2022.2052062","pdf_url":null,"source":{"id":"https://openalex.org/S145553572","display_name":"International Journal of General Systems","issn_l":"0308-1079","issn":["0308-1079","1026-7492","1563-5104"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of General Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.44999998807907104,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W1965477947","https://openalex.org/W1981107087","https://openalex.org/W1982438020","https://openalex.org/W1985261949","https://openalex.org/W2013417878","https://openalex.org/W2019638248","https://openalex.org/W2032397721","https://openalex.org/W2034145661","https://openalex.org/W2034669360","https://openalex.org/W2139905755","https://openalex.org/W2150080768","https://openalex.org/W2157654536","https://openalex.org/W2159445606","https://openalex.org/W2162401762","https://openalex.org/W2170853747","https://openalex.org/W2313013207","https://openalex.org/W2314419630","https://openalex.org/W2325119673","https://openalex.org/W2742050653","https://openalex.org/W2759853430","https://openalex.org/W2792190754","https://openalex.org/W2810913094","https://openalex.org/W2942690213","https://openalex.org/W2994144801","https://openalex.org/W3175938209","https://openalex.org/W3181165084","https://openalex.org/W3181323880","https://openalex.org/W3214876111","https://openalex.org/W4206830167","https://openalex.org/W4211007335"],"related_works":["https://openalex.org/W2022177602","https://openalex.org/W2482464444","https://openalex.org/W1530855127","https://openalex.org/W2779146629","https://openalex.org/W2376926889","https://openalex.org/W2039045183","https://openalex.org/W576291453","https://openalex.org/W2373971468","https://openalex.org/W3095868147","https://openalex.org/W2276998430"],"abstract_inverted_index":{"Uncertain":[0,106],"theory":[1],"which":[2],"was":[3],"initially":[4],"introduced":[5],"by":[6,97],"Liu":[7],"[2016.":[8],"Unceratinty":[9],"Theory.":[10],"5th":[11],"ed.":[12],"Berlin:":[13],"Springer-Verlag]":[14],"is":[15],"significantly":[16],"speared":[17],"in":[18,58,60,63],"various":[19],"fields":[20],"of":[21,42,47,56,72,75,104,128,135,139,150],"engineering":[22],"and":[23,62,95,99,110,131],"scientific":[24],"computing":[25],"such":[26,52],"as":[27,53],"probability":[28],"theory,":[29,33,35,44],"statistics,":[30],"fuzzy":[31,129],"set":[32],"measure":[34,64],"summability":[36],"theories,":[37],"etc.":[38],"As":[39],"a":[40],"part":[41],"this":[43,117],"the":[45,54,67,73,86,123,126,133,136],"problems":[46],"convergence":[48,57,68,91,140,149],"with":[49,66],"different":[50],"perspectives":[51],"idea":[55],"distribution,":[59],"mean":[61],"along":[65],"uniformly":[69],"almost":[70],"surely":[71],"sequence":[74],"complex":[76],"numbers":[77,130],"have":[78,92],"been":[79,93],"studied":[80,96],"using":[81],"uncertain":[82,156],"variables.":[83],"Later":[84],"on,":[85],"results":[87,146],"analogue":[88],"to":[89,121],"statistical":[90],"generalized":[94],"Tripathy":[98],"Nath":[100],"[2017.":[101],"\u201cStatistical":[102],"Convergence":[103],"Complex":[105],"Sequences.\u201d":[107],"New":[108],"Mathematics":[109],"Natural":[111],"Computation":[112],"13":[113],"(3):":[114],"359\u2013374.].":[115],"In":[116],"paper,":[118],"we":[119],"indent":[120],"extend":[122],"investigation":[124],"for":[125,154],"sequences":[127,157],"study":[132],"uncertainty":[134],"above":[137],"ideas":[138],"via":[141],"deferred":[142],"Ces\u00e0ro":[143],"mean.":[144],"Certain":[145],"on":[147],"deferred-statistical":[148],"order":[151],"\u03b2(0<\u03b2\u2264":[152],"1)":[153],"real":[155],"are":[158],"established.":[159]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}