{"id":"https://openalex.org/W4308585153","doi":"https://doi.org/10.3390/e24111617","title":"The Extended Linguistic Hellwig\u2019s Methods Based on Oriented Fuzzy Numbers and Their Application to the Evaluation of Negotiation Offers","display_name":"The Extended Linguistic Hellwig\u2019s Methods Based on Oriented Fuzzy Numbers and Their Application to the Evaluation of Negotiation Offers","publication_year":2022,"publication_date":"2022-11-06","ids":{"openalex":"https://openalex.org/W4308585153","doi":"https://doi.org/10.3390/e24111617","pmid":"https://pubmed.ncbi.nlm.nih.gov/36359707"},"language":"en","primary_location":{"id":"doi:10.3390/e24111617","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24111617","pdf_url":"https://www.mdpi.com/1099-4300/24/11/1617/pdf?version=1668491862","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/24/11/1617/pdf?version=1668491862","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102998080","display_name":"Ewa Roszkowska","orcid":"https://orcid.org/0000-0003-2249-7217"},"institutions":[{"id":"https://openalex.org/I1323121030","display_name":"Bialystok University of Technology","ror":"https://ror.org/02bzfsy61","country_code":"PL","type":"education","lineage":["https://openalex.org/I1323121030"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Ewa Roszkowska","raw_affiliation_strings":["Faculty of Computer Science, Bialystok University of Technology, Wiejska 45A, 15-351 Bialystok, Poland"],"raw_orcid":"https://orcid.org/0000-0003-2249-7217","affiliations":[{"raw_affiliation_string":"Faculty of Computer Science, Bialystok University of Technology, Wiejska 45A, 15-351 Bialystok, Poland","institution_ids":["https://openalex.org/I1323121030"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040670392","display_name":"Tomasz Wachowicz","orcid":"https://orcid.org/0000-0001-9485-6667"},"institutions":[{"id":"https://openalex.org/I188922065","display_name":"University of Economics in Katowice","ror":"https://ror.org/01vxt3d40","country_code":"PL","type":"education","lineage":["https://openalex.org/I188922065"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Tomasz Wachowicz","raw_affiliation_strings":["Department of Operations Research, University of Economics in Katowice, 1 Maja 50, 40-287 Katowice, Poland"],"raw_orcid":"https://orcid.org/0000-0001-9485-6667","affiliations":[{"raw_affiliation_string":"Department of Operations Research, University of Economics in Katowice, 1 Maja 50, 40-287 Katowice, Poland","institution_ids":["https://openalex.org/I188922065"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044946988","display_name":"Marzena Filipowicz-Chomko","orcid":"https://orcid.org/0000-0003-3041-4063"},"institutions":[{"id":"https://openalex.org/I1323121030","display_name":"Bialystok University of Technology","ror":"https://ror.org/02bzfsy61","country_code":"PL","type":"education","lineage":["https://openalex.org/I1323121030"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Marzena Filipowicz-Chomko","raw_affiliation_strings":["Faculty of Computer Science, Bialystok University of Technology, Wiejska 45A, 15-351 Bialystok, Poland"],"raw_orcid":"https://orcid.org/0000-0003-3041-4063","affiliations":[{"raw_affiliation_string":"Faculty of Computer Science, Bialystok University of Technology, Wiejska 45A, 15-351 Bialystok, Poland","institution_ids":["https://openalex.org/I1323121030"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029016873","display_name":"Anna \u0141yczkowska-Han\u0107kowiak","orcid":"https://orcid.org/0000-0002-6011-7855"},"institutions":[{"id":"https://openalex.org/I4210137990","display_name":"WSB Merito University in Poznan","ror":"https://ror.org/04kz5ba43","country_code":"PL","type":"education","lineage":["https://openalex.org/I4210137990"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Anna \u0141yczkowska-Han\u0107kowiak","raw_affiliation_strings":["Institute of Economics and Finance, WSB University of Poznan, ul. Powsta\u0144c\u00f3w Wielkopolskich 5, 61-895 Poznan, Poland"],"raw_orcid":"https://orcid.org/0000-0002-6011-7855","affiliations":[{"raw_affiliation_string":"Institute of Economics and Finance, WSB University of Poznan, ul. Powsta\u0144c\u00f3w Wielkopolskich 5, 61-895 Poznan, Poland","institution_ids":["https://openalex.org/I4210137990"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5102998080"],"corresponding_institution_ids":["https://openalex.org/I1323121030"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.3512,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.82498396,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"24","issue":"11","first_page":"1617","last_page":"1617"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9998999834060669,"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9941999912261963,"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/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.9779999852180481,"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/negotiation","display_name":"Negotiation","score":0.7904835939407349},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.674952507019043},{"id":"https://openalex.org/keywords/weighting","display_name":"Weighting","score":0.6371879577636719},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6351820230484009},{"id":"https://openalex.org/keywords/preference","display_name":"Preference","score":0.5526198744773865},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.45704466104507446},{"id":"https://openalex.org/keywords/defuzzification","display_name":"Defuzzification","score":0.4395171105861664},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.4218481183052063},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.38137325644493103},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.3669778108596802},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.3396650552749634},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.32428428530693054},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.19323521852493286},{"id":"https://openalex.org/keywords/sociology","display_name":"Sociology","score":0.08352148532867432}],"concepts":[{"id":"https://openalex.org/C199776023","wikidata":"https://www.wikidata.org/wiki/Q202875","display_name":"Negotiation","level":2,"score":0.7904835939407349},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.674952507019043},{"id":"https://openalex.org/C183115368","wikidata":"https://www.wikidata.org/wiki/Q856577","display_name":"Weighting","level":2,"score":0.6371879577636719},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6351820230484009},{"id":"https://openalex.org/C2781249084","wikidata":"https://www.wikidata.org/wiki/Q908656","display_name":"Preference","level":2,"score":0.5526198744773865},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.45704466104507446},{"id":"https://openalex.org/C170260401","wikidata":"https://www.wikidata.org/wiki/Q5251735","display_name":"Defuzzification","level":5,"score":0.4395171105861664},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.4218481183052063},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.38137325644493103},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3669778108596802},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.3396650552749634},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.32428428530693054},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.19323521852493286},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.08352148532867432},{"id":"https://openalex.org/C126838900","wikidata":"https://www.wikidata.org/wiki/Q77604","display_name":"Radiology","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C36289849","wikidata":"https://www.wikidata.org/wiki/Q34749","display_name":"Social science","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/e24111617","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24111617","pdf_url":"https://www.mdpi.com/1099-4300/24/11/1617/pdf?version=1668491862","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmid:36359707","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/36359707","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:doaj.org/article:9d97413d64074481b4e75308c3f64804","is_oa":true,"landing_page_url":"https://doaj.org/article/9d97413d64074481b4e75308c3f64804","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 24, Iss 11, p 1617 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/24/11/1617/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e24111617","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy; Volume 24; Issue 11; Pages: 1617","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:9689203","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/9689203","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e24111617","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24111617","pdf_url":"https://www.mdpi.com/1099-4300/24/11/1617/pdf?version=1668491862","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.4300000071525574}],"awards":[{"id":"https://openalex.org/G7669454563","display_name":null,"funder_award_id":"WZ/WI-IIT/2/2022","funder_id":"https://openalex.org/F4320323075","funder_display_name":"Politechnika Bialostocka"}],"funders":[{"id":"https://openalex.org/F4320323075","display_name":"Politechnika Bialostocka","ror":"https://ror.org/02bzfsy61"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4308585153.pdf","grobid_xml":"https://content.openalex.org/works/W4308585153.grobid-xml"},"referenced_works_count":68,"referenced_works":["https://openalex.org/W1524771255","https://openalex.org/W1586654377","https://openalex.org/W1876381961","https://openalex.org/W1965671311","https://openalex.org/W1979565051","https://openalex.org/W1989605611","https://openalex.org/W2031428758","https://openalex.org/W2035132353","https://openalex.org/W2041210202","https://openalex.org/W2055641388","https://openalex.org/W2065109455","https://openalex.org/W2069069851","https://openalex.org/W2069071173","https://openalex.org/W2069468205","https://openalex.org/W2114291956","https://openalex.org/W2124417247","https://openalex.org/W2125843991","https://openalex.org/W2157041604","https://openalex.org/W2171235516","https://openalex.org/W2304576809","https://openalex.org/W2312663874","https://openalex.org/W2497739385","https://openalex.org/W2499828064","https://openalex.org/W2506201062","https://openalex.org/W2506768821","https://openalex.org/W2613405179","https://openalex.org/W2737908918","https://openalex.org/W2739396666","https://openalex.org/W2766770065","https://openalex.org/W2774764306","https://openalex.org/W2792277465","https://openalex.org/W2795900481","https://openalex.org/W2806957117","https://openalex.org/W2888230393","https://openalex.org/W2891127388","https://openalex.org/W2893488791","https://openalex.org/W2898935290","https://openalex.org/W2904489908","https://openalex.org/W2912392110","https://openalex.org/W2934896270","https://openalex.org/W2947073918","https://openalex.org/W2972943450","https://openalex.org/W2993500389","https://openalex.org/W2995565434","https://openalex.org/W3007547533","https://openalex.org/W3010322136","https://openalex.org/W3023183598","https://openalex.org/W3045907164","https://openalex.org/W3082304628","https://openalex.org/W3086799236","https://openalex.org/W3088097521","https://openalex.org/W3092958607","https://openalex.org/W3124219177","https://openalex.org/W3133792895","https://openalex.org/W3134531420","https://openalex.org/W3139365950","https://openalex.org/W3167262744","https://openalex.org/W3199927741","https://openalex.org/W3203993367","https://openalex.org/W3207429747","https://openalex.org/W4206237384","https://openalex.org/W4240278385","https://openalex.org/W4245152641","https://openalex.org/W4290467432","https://openalex.org/W4312768746","https://openalex.org/W6635056329","https://openalex.org/W6677088644","https://openalex.org/W6678724782"],"related_works":["https://openalex.org/W2773005380","https://openalex.org/W4388451300","https://openalex.org/W2060361571","https://openalex.org/W1879432897","https://openalex.org/W2256857057","https://openalex.org/W3167814444","https://openalex.org/W3176863924","https://openalex.org/W2023513928","https://openalex.org/W2182392910","https://openalex.org/W4361984403"],"abstract_inverted_index":{"This":[0],"study":[1],"proposes":[2],"a":[3,74,87],"novel":[4],"fuzzy":[5,50,64,152],"framework":[6],"for":[7,19,77],"eliciting":[8],"and":[9,44,62,90,108,202],"organizing":[10],"the":[11,15,20,55,78,95,115,119,132,163,173,178,181,192,200,203],"preference":[12,120],"information":[13,121],"of":[14,22,32,54,84,156,165,172,184,191],"negotiator":[16],"to":[17,40,72,93,139],"allow":[18],"evaluation":[21,31],"negotiation":[23,33,79,96,101,193],"offers.":[24],"The":[25,104,128,168],"approach":[26,61],"is":[27,102,122],"based":[28,58],"on":[29,59],"verbal":[30],"options":[34],"that":[35,131,146],"operates":[36],"with":[37,110,150],"linguistic":[38,56],"variables":[39],"handle":[41],"vague":[42],"preferences":[43],"operationalizes":[45],"them":[46],"through":[47],"oriented":[48,63,151],"trapezoidal":[49],"numbers.":[51],"Two":[52],"variants":[53],"method":[57],"Hellwig's":[60,198],"numbers":[65],"are":[66,106],"proposed,":[67],"which":[68,118],"can":[69,135],"be":[70,136,160,206],"applied":[71],"building":[73],"scoring":[75,88],"system":[76,89],"template.":[80],"Then,":[81],"an":[82,137],"example":[83],"determining":[85],"such":[86],"using":[91],"it":[92],"evaluate":[94],"offers":[97],"in":[98,117],"typical":[99],"multi-issue":[100],"shown.":[103],"results":[105],"discussed":[107],"compared":[109],"other":[111],"methods":[112,134,145],"known":[113],"from":[114,162],"literature,":[116],"organized":[123],"similarly":[124],"but":[125,154],"processed":[126],"differently.":[127],"comparison":[129],"shows":[130],"presented":[133],"alternative":[138],"Simple":[140],"Additive":[141],"Weighting":[142],"or":[143],"TOPSIS":[144],"may":[147,159,205],"also":[148],"operate":[149],"numbers,":[153],"some":[155],"their":[157],"characteristics":[158],"problematic":[161],"viewpoint":[164],"data":[166],"interpretation.":[167],"former":[169,201],"requires":[170,180],"defuzzification":[171],"global":[174],"scores":[175],"determined,":[176],"while":[177],"latter":[179,204],"compulsory":[182],"use":[183],"two":[185],"reference":[186],"points":[187],"derived":[188],"mechanically":[189],"out":[190],"space.":[194],"By":[195],"applying":[196],"modified":[197],"approaches,":[199],"easily":[207],"avoided.":[208]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":1}],"updated_date":"2026-05-08T15:41:06.802602","created_date":"2025-10-10T00:00:00"}