{"id":"https://openalex.org/W2107638599","doi":"https://doi.org/10.1109/fuzz-ieee.2012.6251341","title":"Why bernstein polynomials are better: Fuzzy-inspired justification","display_name":"Why bernstein polynomials are better: Fuzzy-inspired justification","publication_year":2012,"publication_date":"2012-06-01","ids":{"openalex":"https://openalex.org/W2107638599","doi":"https://doi.org/10.1109/fuzz-ieee.2012.6251341","mag":"2107638599"},"language":"en","primary_location":{"id":"doi:10.1109/fuzz-ieee.2012.6251341","is_oa":false,"landing_page_url":"https://doi.org/10.1109/fuzz-ieee.2012.6251341","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 IEEE International Conference on Fuzzy Systems","raw_type":"proceedings-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/A5088212349","display_name":"Jaime Nava","orcid":"https://orcid.org/0009-0008-7572-0543"},"institutions":[{"id":"https://openalex.org/I164936912","display_name":"The University of Texas at El Paso","ror":"https://ror.org/04d5vba33","country_code":"US","type":"education","lineage":["https://openalex.org/I164936912"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jaime Nava","raw_affiliation_strings":["Department of Computer Science, University of Texas, El Paso, El Paso, TX, USA","Department of Computer Science, University of Texas at El Paso, 500 W. University, 79968, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Texas, El Paso, El Paso, TX, USA","institution_ids":["https://openalex.org/I164936912"]},{"raw_affiliation_string":"Department of Computer Science, University of Texas at El Paso, 500 W. University, 79968, USA","institution_ids":["https://openalex.org/I164936912"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075920182","display_name":"Olga Kosheleva","orcid":"https://orcid.org/0000-0003-2587-4209"},"institutions":[{"id":"https://openalex.org/I164936912","display_name":"The University of Texas at El Paso","ror":"https://ror.org/04d5vba33","country_code":"US","type":"education","lineage":["https://openalex.org/I164936912"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Olga Kosheleva","raw_affiliation_strings":["Department of Teacher Education, University of Texas, El Paso, El Paso, TX, USA","Department of Computer Science, University of Texas at El Paso, 500 W. University, 79968, USA"],"affiliations":[{"raw_affiliation_string":"Department of Teacher Education, University of Texas, El Paso, El Paso, TX, USA","institution_ids":["https://openalex.org/I164936912"]},{"raw_affiliation_string":"Department of Computer Science, University of Texas at El Paso, 500 W. University, 79968, USA","institution_ids":["https://openalex.org/I164936912"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061275811","display_name":"\u0412\u043b\u0430\u0434\u0438\u043a \u041a\u0440\u0435\u0439\u043d\u043e\u0432\u0438\u0447","orcid":"https://orcid.org/0000-0002-1244-1650"},"institutions":[{"id":"https://openalex.org/I164936912","display_name":"The University of Texas at El Paso","ror":"https://ror.org/04d5vba33","country_code":"US","type":"education","lineage":["https://openalex.org/I164936912"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Vladik Kreinovich","raw_affiliation_strings":["Department of Computer Science, University of Texas, El Paso, El Paso, TX, USA","Department of Teacher Education, University of Texas at El Paso, 500 W. University, 79968, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Texas, El Paso, El Paso, TX, USA","institution_ids":["https://openalex.org/I164936912"]},{"raw_affiliation_string":"Department of Teacher Education, University of Texas at El Paso, 500 W. University, 79968, USA","institution_ids":["https://openalex.org/I164936912"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5088212349"],"corresponding_institution_ids":["https://openalex.org/I164936912"],"apc_list":null,"apc_paid":null,"fwci":0.4281,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.72955268,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"6"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9851999878883362,"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"}},"topics":[{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9851999878883362,"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/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.9805999994277954,"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/T14351","display_name":"Statistical and Computational Modeling","score":0.9711999893188477,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/monomial","display_name":"Monomial","score":0.8105021715164185},{"id":"https://openalex.org/keywords/bernstein-polynomial","display_name":"Bernstein polynomial","score":0.691149115562439},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.6681200265884399},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6369465589523315},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5759835243225098},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4745926558971405},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4388866424560547},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.37578925490379333},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.2451794445514679},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07614555954933167}],"concepts":[{"id":"https://openalex.org/C11252640","wikidata":"https://www.wikidata.org/wiki/Q243723","display_name":"Monomial","level":2,"score":0.8105021715164185},{"id":"https://openalex.org/C34179328","wikidata":"https://www.wikidata.org/wiki/Q826841","display_name":"Bernstein polynomial","level":2,"score":0.691149115562439},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.6681200265884399},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6369465589523315},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5759835243225098},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4745926558971405},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4388866424560547},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.37578925490379333},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2451794445514679},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07614555954933167},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/fuzz-ieee.2012.6251341","is_oa":false,"landing_page_url":"https://doi.org/10.1109/fuzz-ieee.2012.6251341","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 IEEE International Conference on Fuzzy Systems","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320332161","display_name":"National Institutes of Health","ror":"https://ror.org/01cwqze88"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W126362881","https://openalex.org/W379203212","https://openalex.org/W1481101934","https://openalex.org/W1496785083","https://openalex.org/W1507872748","https://openalex.org/W1596669356","https://openalex.org/W2026110825","https://openalex.org/W2057066113","https://openalex.org/W2182997761","https://openalex.org/W2183518023","https://openalex.org/W2206012437","https://openalex.org/W2496338429","https://openalex.org/W2912565176","https://openalex.org/W4211007335","https://openalex.org/W4242608229","https://openalex.org/W4300917724","https://openalex.org/W6686285128"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2399505800","https://openalex.org/W2018253224","https://openalex.org/W333749553","https://openalex.org/W1966623661","https://openalex.org/W1578479275","https://openalex.org/W91521151","https://openalex.org/W2200996039","https://openalex.org/W2361696322","https://openalex.org/W2043650433"],"abstract_inverted_index":{"It":[0,47],"is":[1,56],"well":[2],"known":[3],"that":[4,50],"an":[5,16],"arbitrary":[6],"continuous":[7],"function":[8,36],"on":[9,15],"a":[10,29,33,64,74,98,126],"bounded":[11],"set":[12],"-":[13,20,67,80,87],"e.g.,":[14,68],"interval":[17],"[a;":[18],"b]":[19],"can":[21,122],"be,":[22],"with":[23],"any":[24],"given":[25],"accuracy,":[26],"approximated":[27],"by":[28,32],"polynomial":[30,35,62,66],"or":[31],"piece-wise":[34],"(spline).":[37],"Usually,":[38],"polynomials":[39,105],"are":[40,106],"described":[41],"as":[42,63],"linear":[43,75,111],"combinations":[44,112],"of":[45,71,77,102,113],"monomials.":[46],"turns":[48],"out":[49],"in":[51],"many":[52],"computational":[53],"problems,":[54],"it":[55],"more":[57,108],"efficient":[58,109],"to":[59],"represent":[60],"each":[61],"Bernstein":[65,104],"for":[69],"functions":[70],"one":[72],"variable,":[73],"combination":[76],"terms":[78],"(x":[79],"a)":[81],"<sup":[82,89],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[83,90],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">k</sup>":[84],"\u00b7":[85],"(b":[86],"x)":[88],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n-k</sup>":[91],".":[92],"In":[93],"this":[94,119],"paper,":[95],"we":[96,116],"provide":[97],"simple":[99],"fuzzy-based":[100],"explanation":[101,121],"why":[103],"often":[107],"than":[110],"monomials,":[114],"and":[115],"show":[117],"how":[118],"informal":[120],"be":[123],"transformed":[124],"into":[125],"precise":[127],"mathematical":[128],"explanation.":[129]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
