{"id":"https://openalex.org/W2756505297","doi":"https://doi.org/10.1515/amcs-2017-0041","title":"Is an interval the right result of arithmetic operations on intervals?","display_name":"Is an interval the right result of arithmetic operations on intervals?","publication_year":2017,"publication_date":"2017-09-01","ids":{"openalex":"https://openalex.org/W2756505297","doi":"https://doi.org/10.1515/amcs-2017-0041","mag":"2756505297"},"language":"en","primary_location":{"id":"doi:10.1515/amcs-2017-0041","is_oa":true,"landing_page_url":"https://doi.org/10.1515/amcs-2017-0041","pdf_url":"https://content.sciendo.com/downloadpdf/journals/amcs/27/3/article-p575.pdf","source":{"id":"https://openalex.org/S117679522","display_name":"International Journal of Applied Mathematics and Computer Science","issn_l":"1641-876X","issn":["1641-876X","2083-8492"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Applied Mathematics and Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://content.sciendo.com/downloadpdf/journals/amcs/27/3/article-p575.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5027869481","display_name":"Andrzej Piegat","orcid":"https://orcid.org/0000-0001-6487-2818"},"institutions":[{"id":"https://openalex.org/I155313962","display_name":"West Pomeranian University of Technology","ror":"https://ror.org/0596m7f19","country_code":"PL","type":"education","lineage":["https://openalex.org/I155313962"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Andrzej Piegat","raw_affiliation_strings":["Faculty of Computer Science , West Pomeranian University of Technology , \u017bo\u0142nierska 49, 71-210 Szczecin , Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Computer Science , West Pomeranian University of Technology , \u017bo\u0142nierska 49, 71-210 Szczecin , Poland","institution_ids":["https://openalex.org/I155313962"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024669170","display_name":"Marek Landowski","orcid":"https://orcid.org/0000-0002-2246-1700"},"institutions":[{"id":"https://openalex.org/I199688382","display_name":"Maritime University of Szczecin","ror":"https://ror.org/02sj9tq04","country_code":"PL","type":"education","lineage":["https://openalex.org/I199688382"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Marek Landowski","raw_affiliation_strings":["Department of Mathematical Methods , Maritime University of Szczecin , Wa\u0142y Chrobrego 1\u20132, 70-500 Szczecin , Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Methods , Maritime University of Szczecin , Wa\u0142y Chrobrego 1\u20132, 70-500 Szczecin , Poland","institution_ids":["https://openalex.org/I199688382"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5027869481"],"corresponding_institution_ids":["https://openalex.org/I155313962"],"apc_list":{"value":4080,"currency":"PLN","value_usd":1100},"apc_paid":{"value":4080,"currency":"PLN","value_usd":1100},"fwci":4.3038,"has_fulltext":true,"cited_by_count":32,"citation_normalized_percentile":{"value":0.95156684,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"27","issue":"3","first_page":"575","last_page":"590"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9991999864578247,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9991999864578247,"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":0.9772999882698059,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9610000252723694,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"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/arithmetic","display_name":"Arithmetic","score":0.8838641047477722},{"id":"https://openalex.org/keywords/interval-arithmetic","display_name":"Interval arithmetic","score":0.8561691045761108},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.7211448550224304},{"id":"https://openalex.org/keywords/affine-arithmetic","display_name":"Affine arithmetic","score":0.646573543548584},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6261190176010132},{"id":"https://openalex.org/keywords/saturation-arithmetic","display_name":"Saturation arithmetic","score":0.544322669506073},{"id":"https://openalex.org/keywords/second-order-arithmetic","display_name":"Second-order arithmetic","score":0.5031816363334656},{"id":"https://openalex.org/keywords/arbitrary-precision-arithmetic","display_name":"Arbitrary-precision arithmetic","score":0.49607500433921814},{"id":"https://openalex.org/keywords/arithmetic-circuit-complexity","display_name":"Arithmetic circuit complexity","score":0.4535865783691406},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.29232102632522583},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.10753616690635681},{"id":"https://openalex.org/keywords/peano-axioms","display_name":"Peano axioms","score":0.10475683212280273},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.07742860913276672}],"concepts":[{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.8838641047477722},{"id":"https://openalex.org/C191252586","wikidata":"https://www.wikidata.org/wiki/Q1671453","display_name":"Interval arithmetic","level":3,"score":0.8561691045761108},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.7211448550224304},{"id":"https://openalex.org/C167315692","wikidata":"https://www.wikidata.org/wiki/Q3622729","display_name":"Affine arithmetic","level":3,"score":0.646573543548584},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6261190176010132},{"id":"https://openalex.org/C182775192","wikidata":"https://www.wikidata.org/wiki/Q913725","display_name":"Saturation arithmetic","level":3,"score":0.544322669506073},{"id":"https://openalex.org/C65148605","wikidata":"https://www.wikidata.org/wiki/Q7442973","display_name":"Second-order arithmetic","level":3,"score":0.5031816363334656},{"id":"https://openalex.org/C83581934","wikidata":"https://www.wikidata.org/wiki/Q527381","display_name":"Arbitrary-precision arithmetic","level":2,"score":0.49607500433921814},{"id":"https://openalex.org/C155920423","wikidata":"https://www.wikidata.org/wiki/Q4791120","display_name":"Arithmetic circuit complexity","level":3,"score":0.4535865783691406},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.29232102632522583},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.10753616690635681},{"id":"https://openalex.org/C97489613","wikidata":"https://www.wikidata.org/wiki/Q842755","display_name":"Peano axioms","level":2,"score":0.10475683212280273},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.07742860913276672},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.0},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1515/amcs-2017-0041","is_oa":true,"landing_page_url":"https://doi.org/10.1515/amcs-2017-0041","pdf_url":"https://content.sciendo.com/downloadpdf/journals/amcs/27/3/article-p575.pdf","source":{"id":"https://openalex.org/S117679522","display_name":"International Journal of Applied Mathematics and Computer Science","issn_l":"1641-876X","issn":["1641-876X","2083-8492"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Applied Mathematics and Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:8405effd33184edb8ebf28e73d76d80e","is_oa":false,"landing_page_url":"https://doaj.org/article/8405effd33184edb8ebf28e73d76d80e","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Applied Mathematics and Computer Science, Vol 27, Iss 3, Pp 575-590 (2017)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1515/amcs-2017-0041","is_oa":true,"landing_page_url":"https://doi.org/10.1515/amcs-2017-0041","pdf_url":"https://content.sciendo.com/downloadpdf/journals/amcs/27/3/article-p575.pdf","source":{"id":"https://openalex.org/S117679522","display_name":"International Journal of Applied Mathematics and Computer Science","issn_l":"1641-876X","issn":["1641-876X","2083-8492"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Applied Mathematics and Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2756505297.pdf","grobid_xml":"https://content.openalex.org/works/W2756505297.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W90286923","https://openalex.org/W101462505","https://openalex.org/W1483874187","https://openalex.org/W1490729186","https://openalex.org/W1507872748","https://openalex.org/W1531645310","https://openalex.org/W1575879412","https://openalex.org/W1583295953","https://openalex.org/W1605470283","https://openalex.org/W1915967525","https://openalex.org/W1964408286","https://openalex.org/W2013124077","https://openalex.org/W2015136438","https://openalex.org/W2030626585","https://openalex.org/W2058445758","https://openalex.org/W2066949249","https://openalex.org/W2095098951","https://openalex.org/W2131798279","https://openalex.org/W2160780842","https://openalex.org/W2340298398","https://openalex.org/W2403711553","https://openalex.org/W2404002348","https://openalex.org/W2520343034","https://openalex.org/W2563209315","https://openalex.org/W2746410388","https://openalex.org/W4230919050"],"related_works":["https://openalex.org/W2349168892","https://openalex.org/W2073476805","https://openalex.org/W2181927644","https://openalex.org/W2078971842","https://openalex.org/W2568181300","https://openalex.org/W1531645310","https://openalex.org/W2118036253","https://openalex.org/W2131798279","https://openalex.org/W1577151476","https://openalex.org/W1995106605"],"abstract_inverted_index":{"Abstract":[0],"For":[1],"many":[2],"scientists":[3],"interval":[4,67,116,154,181],"arithmetic":[5,21,38,68,106,155,170],"(IA,":[6],"I":[7],"arithmetic)":[8],"seems":[9,133],"to":[10,48,76,157,168],"be":[11,148],"easy":[12],"and":[13,42,51,172],"simple.":[14],"However,":[15,114],"this":[16,37],"is":[17,22,25,80,98,110,117,140],"not":[18,64,118],"true.":[19,141],"Interval":[20],"complicated.":[23],"This":[24,131],"confirmed":[26],"by":[27,150],"the":[28,58,62,87,91,95,99,102,115,129,151,177],"fact":[29],"that,":[30],"for":[31,90],"years,":[32],"new,":[33],"alternative":[34],"versions":[35,46],"of":[36,53,57,66,72,94,105,128,153,180],"have":[39],"been":[40],"created":[41],"published.":[43],"These":[44],"new":[45],"tried":[47],"remove":[49],"shortcomings":[50,93],"weaknesses":[52],"previously":[54],"proposed":[55,178],"options":[56],"arithmetic,":[59,74],"which":[60],"decreased":[61],"prestige":[63],"only":[65,123],"itself,":[69],"but":[70,122,135],"also":[71,111],"fuzzy":[73],"which,":[75],"a":[77,119,124,160],"great":[78,163],"extent,":[79],"based":[81],"on":[82,108],"it.":[83],"In":[84],"our":[85],"opinion,":[86],"main":[88],"reason":[89],"observed":[92],"present":[96],"IA":[97],"assumption":[100],"that":[101,138],"direct":[103,120],"result":[104,121,152],"operations":[107,156,171],"intervals":[109],"an":[112],"interval.":[113],"simplified":[125],"representative":[126],"(indicator)":[127],"result.":[130],"hypothesis":[132],"surprising,":[134],"investigations":[136],"prove":[137],"it":[139,159],"The":[142],"paper":[143],"shows":[144],"what":[145],"conditions":[146],"should":[147],"satisfied":[149],"call":[158],"\u201cresult\u201d,":[161],"how":[162,167],"its":[164],"dimensionality":[165],"is,":[166],"perform":[169],"solve":[173],"equations.":[174],"Examples":[175],"illustrate":[176],"method":[179],"computations.":[182]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":10},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
