{"id":"https://openalex.org/W2884751401","doi":"https://doi.org/10.1007/s00500-018-3290-y","title":"Method with horizontal fuzzy numbers for solving real fuzzy linear systems","display_name":"Method with horizontal fuzzy numbers for solving real fuzzy linear systems","publication_year":2018,"publication_date":"2018-06-09","ids":{"openalex":"https://openalex.org/W2884751401","doi":"https://doi.org/10.1007/s00500-018-3290-y","mag":"2884751401"},"language":"en","primary_location":{"id":"doi:10.1007/s00500-018-3290-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00500-018-3290-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00500-018-3290-y.pdf","source":{"id":"https://openalex.org/S65753830","display_name":"Soft Computing","issn_l":"1432-7643","issn":["1432-7643","1433-7479"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Soft Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00500-018-3290-y.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","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":true,"raw_author_name":"Marek Landowski","raw_affiliation_strings":["Department of Mathematical Methods, Maritime University of Szczecin, Waly Chrobrego 1-2, 70-500, Szczecin, Poland"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Methods, Maritime University of Szczecin, Waly Chrobrego 1-2, 70-500, Szczecin, Poland","institution_ids":["https://openalex.org/I199688382"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5024669170"],"corresponding_institution_ids":["https://openalex.org/I199688382"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":3.3188,"has_fulltext":true,"cited_by_count":23,"citation_normalized_percentile":{"value":0.93579978,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"23","issue":"12","first_page":"3921","last_page":"3933"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","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/T12135","display_name":"Fuzzy Systems and Optimization","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/T10050","display_name":"Multi-Criteria Decision Making","score":0.9969000220298767,"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/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.9818999767303467,"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/fuzzy-number","display_name":"Fuzzy number","score":0.7684499025344849},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7147942781448364},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.6367696523666382},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4313591420650482},{"id":"https://openalex.org/keywords/fuzzy-set-operations","display_name":"Fuzzy set operations","score":0.4303416311740875},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.42359867691993713},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.41902726888656616},{"id":"https://openalex.org/keywords/defuzzification","display_name":"Defuzzification","score":0.4157506227493286},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.39166927337646484},{"id":"https://openalex.org/keywords/fuzzy-control-system","display_name":"Fuzzy control system","score":0.3703959584236145},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.3601555824279785},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33796340227127075},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23825165629386902},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12515899538993835},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08712401986122131}],"concepts":[{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.7684499025344849},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7147942781448364},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.6367696523666382},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4313591420650482},{"id":"https://openalex.org/C148671577","wikidata":"https://www.wikidata.org/wiki/Q5511133","display_name":"Fuzzy set operations","level":4,"score":0.4303416311740875},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.42359867691993713},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41902726888656616},{"id":"https://openalex.org/C170260401","wikidata":"https://www.wikidata.org/wiki/Q5251735","display_name":"Defuzzification","level":5,"score":0.4157506227493286},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.39166927337646484},{"id":"https://openalex.org/C195975749","wikidata":"https://www.wikidata.org/wiki/Q1475705","display_name":"Fuzzy control system","level":3,"score":0.3703959584236145},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.3601555824279785},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33796340227127075},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23825165629386902},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12515899538993835},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08712401986122131},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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:10.1007/s00500-018-3290-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00500-018-3290-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00500-018-3290-y.pdf","source":{"id":"https://openalex.org/S65753830","display_name":"Soft Computing","issn_l":"1432-7643","issn":["1432-7643","1433-7479"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Soft Computing","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s00500-018-3290-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00500-018-3290-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00500-018-3290-y.pdf","source":{"id":"https://openalex.org/S65753830","display_name":"Soft Computing","issn_l":"1432-7643","issn":["1432-7643","1433-7479"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Soft Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2884751401.pdf","grobid_xml":"https://content.openalex.org/works/W2884751401.grobid-xml"},"referenced_works_count":35,"referenced_works":["https://openalex.org/W13926841","https://openalex.org/W90286923","https://openalex.org/W301079972","https://openalex.org/W1504704583","https://openalex.org/W1537731705","https://openalex.org/W1595992588","https://openalex.org/W1787190784","https://openalex.org/W1975593923","https://openalex.org/W1991563226","https://openalex.org/W2007698389","https://openalex.org/W2036102558","https://openalex.org/W2039311731","https://openalex.org/W2049785322","https://openalex.org/W2058445758","https://openalex.org/W2065397160","https://openalex.org/W2067426927","https://openalex.org/W2069069851","https://openalex.org/W2085062656","https://openalex.org/W2092092154","https://openalex.org/W2095292012","https://openalex.org/W2106745885","https://openalex.org/W2116039853","https://openalex.org/W2149911411","https://openalex.org/W2165094119","https://openalex.org/W2170112393","https://openalex.org/W2182008307","https://openalex.org/W2533997743","https://openalex.org/W2537158661","https://openalex.org/W2563209315","https://openalex.org/W2585824213","https://openalex.org/W2756505297","https://openalex.org/W2883827036","https://openalex.org/W2911454810","https://openalex.org/W4231523620","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2184441312","https://openalex.org/W4388451300","https://openalex.org/W4242970302","https://openalex.org/W2571050636","https://openalex.org/W2060361571","https://openalex.org/W1975005191","https://openalex.org/W3176863924","https://openalex.org/W1485268022","https://openalex.org/W2382615100","https://openalex.org/W4361984403"],"abstract_inverted_index":{"The":[0,64,88,113,143,160,195],"paper":[1,53],"presents":[2,54],"a":[3,29,33,39,154,169,177,199,203,208],"method":[4,150,197],"for":[5],"solving":[6],"real":[7],"fuzzy":[8,18,30,41,68,85,96,102,118,125,188],"systems":[9,104],"of":[10,16,38,57,66,101,110,124,131,140,163,171,176,211],"linear":[11,71,86,97,103,126,189],"equations":[12],"with":[13,43,70,80,107,116,151,207],"the":[14,23,36,52,55,78,95,108,129,137,141,149,187],"usage":[15,65],"horizontal":[17,40,67,117],"numbers":[19,69,119],"(HFNs).":[20],"Based":[21],"on":[22,61],"multidimensional":[24,92,156],"RDM":[25],"interval":[26],"arithmetic":[27],"and":[28,46,72,93],"number":[31,42],"in":[32,77],"parametric":[34],"form,":[35],"definition":[37],"nonlinear":[44,73],"left":[45],"right":[47],"borders":[48,74],"was":[49,75],"given.":[50],"Additionally,":[51],"properties":[56],"basic":[58],"algebraic":[59],"operations":[60],"these":[62,218],"numbers.":[63],"illustrated":[76],"examples":[79,145],"$$n":[81],"\\times":[82],"n":[83],"$$":[84],"systems.":[87,98],"obtained":[89,115],"results":[90,109,130,162],"are":[91,167,191],"satisfy":[94,136,186],"Calculated":[99],"solutions":[100],"were":[105],"compared":[106],"other":[111,213],"methods.":[112],"solution":[114,157,179,205],"satisfies":[120],"any":[121],"equivalent":[122,138],"form":[123],"system,":[127],"whereas":[128],"existing":[132],"methods":[133,214],"do":[134,184,215],"not":[135,185,216],"forms":[139],"system.":[142],"presented":[144],"also":[146],"show":[147],"that":[148,183],"HFN":[152],"delivers":[153],"full":[155,178],"(direct":[158],"solution).":[159],"analyzed":[161],"standard":[164],"methods,":[165],"which":[166],"only":[168],"part":[170],"span":[172],"(indicator,":[173],"indirect":[174],"solution)":[175],"and/or":[180],"include":[181],"values":[182],"systems,":[190],"underestimated":[192],"or":[193],"overestimated.":[194],"proposed":[196],"gives":[198],"possibility":[200],"to":[201],"obtain":[202],"crisp":[204,209],"together":[206],"system":[210],"equations;":[212],"possess":[217],"properties.":[219]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
