{"id":"https://openalex.org/W2924780751","doi":"https://doi.org/10.1515/jisys-2017-0560","title":"Trapezoidal Linguistic Cubic Fuzzy TOPSIS Method and Application in a Group Decision Making Program","display_name":"Trapezoidal Linguistic Cubic Fuzzy TOPSIS Method and Application in a Group Decision Making Program","publication_year":2019,"publication_date":"2019-03-20","ids":{"openalex":"https://openalex.org/W2924780751","doi":"https://doi.org/10.1515/jisys-2017-0560","mag":"2924780751"},"language":"en","primary_location":{"id":"doi:10.1515/jisys-2017-0560","is_oa":true,"landing_page_url":"https://doi.org/10.1515/jisys-2017-0560","pdf_url":"https://www.degruyter.com/downloadpdf/journals/jisys/29/1/article-p1283.pdf","source":{"id":"https://openalex.org/S2764846071","display_name":"Journal of Intelligent Systems","issn_l":"0334-1860","issn":["0334-1860","2191-026X"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315148","host_organization_name":"IlmuKomputer.Com","host_organization_lineage":["https://openalex.org/P4310315148"],"host_organization_lineage_names":["IlmuKomputer.Com"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Intelligent Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.degruyter.com/downloadpdf/journals/jisys/29/1/article-p1283.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101840630","display_name":"Aliya Fahmi","orcid":"https://orcid.org/0000-0003-1049-430X"},"institutions":[{"id":"https://openalex.org/I82952536","display_name":"King Khalid University","ror":"https://ror.org/052kwzs30","country_code":"SA","type":"education","lineage":["https://openalex.org/I82952536"]},{"id":"https://openalex.org/I181063083","display_name":"Abdul Wali Khan University Mardan","ror":"https://ror.org/03b9y4e65","country_code":"PK","type":"education","lineage":["https://openalex.org/I181063083"]},{"id":"https://openalex.org/I263208278","display_name":"Hazara University","ror":"https://ror.org/018y22094","country_code":"PK","type":"education","lineage":["https://openalex.org/I263208278"]},{"id":"https://openalex.org/I4210088963","display_name":"University of Ha'il","ror":"https://ror.org/013w98a82","country_code":"SA","type":"education","lineage":["https://openalex.org/I4210088963"]}],"countries":["PK","SA"],"is_corresponding":true,"raw_author_name":"Aliya Fahmi","raw_affiliation_strings":["Department of Mathematics , Hazara University , Mansehra, Khyber Pakhtunkhwa , Pakistan , e-mail:","Department of Mathematics, University of Hail, P.O. Box 2440, Hail, Saudi Arabia","Department of Mathematics, College of Sciences, King Khalid University, Abha, Saudi Arabia","Department of Mathematics, Hazara University, Mansehra, Khyber Pakhtunkhwa, Pakistan","Department of Mathematics, Abdul Wali Khan University, Mardan, Khyber Pakhtunkhwa, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Hazara University , Mansehra, Khyber Pakhtunkhwa , Pakistan , e-mail:","institution_ids":["https://openalex.org/I263208278"]},{"raw_affiliation_string":"Department of Mathematics, University of Hail, P.O. Box 2440, Hail, Saudi Arabia","institution_ids":["https://openalex.org/I4210088963"]},{"raw_affiliation_string":"Department of Mathematics, College of Sciences, King Khalid University, Abha, Saudi Arabia","institution_ids":["https://openalex.org/I82952536"]},{"raw_affiliation_string":"Department of Mathematics, Hazara University, Mansehra, Khyber Pakhtunkhwa, Pakistan","institution_ids":["https://openalex.org/I263208278"]},{"raw_affiliation_string":"Department of Mathematics, Abdul Wali Khan University, Mardan, Khyber Pakhtunkhwa, Pakistan","institution_ids":["https://openalex.org/I181063083"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077817609","display_name":"Saleem Abdullah","orcid":"https://orcid.org/0000-0002-7474-5115"},"institutions":[{"id":"https://openalex.org/I181063083","display_name":"Abdul Wali Khan University Mardan","ror":"https://ror.org/03b9y4e65","country_code":"PK","type":"education","lineage":["https://openalex.org/I181063083"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Saleem Abdullah","raw_affiliation_strings":["Department of Mathematics , Abdul Wali Khan University , Mardan, Khyber Pakhtunkhwa , Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Abdul Wali Khan University , Mardan, Khyber Pakhtunkhwa , Pakistan","institution_ids":["https://openalex.org/I181063083"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020344801","display_name":"Fazli Amin","orcid":"https://orcid.org/0000-0001-7211-9324"},"institutions":[{"id":"https://openalex.org/I263208278","display_name":"Hazara University","ror":"https://ror.org/018y22094","country_code":"PK","type":"education","lineage":["https://openalex.org/I263208278"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Fazli Amin","raw_affiliation_strings":["Department of Mathematics , Hazara University , Mansehra, Khyber Pakhtunkhwa , Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Hazara University , Mansehra, Khyber Pakhtunkhwa , Pakistan","institution_ids":["https://openalex.org/I263208278"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033770251","display_name":"Muhammad Aslam","orcid":"https://orcid.org/0000-0002-6443-4962"},"institutions":[{"id":"https://openalex.org/I82952536","display_name":"King Khalid University","ror":"https://ror.org/052kwzs30","country_code":"SA","type":"education","lineage":["https://openalex.org/I82952536"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Muhammad Aslam","raw_affiliation_strings":["Department of Mathematics , College of Sciences, King Khalid University , Abha , Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics , College of Sciences, King Khalid University , Abha , Saudi Arabia","institution_ids":["https://openalex.org/I82952536"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078836879","display_name":"Shah Hussain","orcid":"https://orcid.org/0000-0003-4786-2938"},"institutions":[{"id":"https://openalex.org/I4210088963","display_name":"University of Ha'il","ror":"https://ror.org/013w98a82","country_code":"SA","type":"education","lineage":["https://openalex.org/I4210088963"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Shah Hussain","raw_affiliation_strings":["Department of Mathematics , University of Hail , P.O. Box 2440 , Hail , Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics , University of Hail , P.O. Box 2440 , Hail , Saudi Arabia","institution_ids":["https://openalex.org/I4210088963"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5101840630"],"corresponding_institution_ids":["https://openalex.org/I181063083","https://openalex.org/I263208278","https://openalex.org/I4210088963","https://openalex.org/I82952536"],"apc_list":{"value":1000,"currency":"EUR","value_usd":1078},"apc_paid":{"value":1000,"currency":"EUR","value_usd":1078},"fwci":3.367,"has_fulltext":true,"cited_by_count":21,"citation_normalized_percentile":{"value":0.92251742,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"29","issue":"1","first_page":"1283","last_page":"1300"},"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/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.9749000072479248,"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9567000269889832,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/topsis","display_name":"TOPSIS","score":0.7592979073524475},{"id":"https://openalex.org/keywords/ranking","display_name":"Ranking (information retrieval)","score":0.619656503200531},{"id":"https://openalex.org/keywords/group-decision-making","display_name":"Group decision-making","score":0.6033123135566711},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5691385865211487},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5676225423812866},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.542816162109375},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5393294095993042},{"id":"https://openalex.org/keywords/hamming-distance","display_name":"Hamming distance","score":0.5068855881690979},{"id":"https://openalex.org/keywords/multiple-criteria-decision-analysis","display_name":"Multiple-criteria decision analysis","score":0.466632217168808},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.40560024976730347},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3739655911922455},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2644611597061157},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2630351781845093},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.2628362774848938},{"id":"https://openalex.org/keywords/operations-research","display_name":"Operations research","score":0.2104317545890808},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.10282444953918457},{"id":"https://openalex.org/keywords/psychology","display_name":"Psychology","score":0.04888090491294861},{"id":"https://openalex.org/keywords/social-psychology","display_name":"Social psychology","score":0.048452943563461304}],"concepts":[{"id":"https://openalex.org/C51566761","wikidata":"https://www.wikidata.org/wiki/Q1235853","display_name":"TOPSIS","level":2,"score":0.7592979073524475},{"id":"https://openalex.org/C189430467","wikidata":"https://www.wikidata.org/wiki/Q7293293","display_name":"Ranking (information retrieval)","level":2,"score":0.619656503200531},{"id":"https://openalex.org/C20701700","wikidata":"https://www.wikidata.org/wiki/Q388791","display_name":"Group decision-making","level":2,"score":0.6033123135566711},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5691385865211487},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5676225423812866},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.542816162109375},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5393294095993042},{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.5068855881690979},{"id":"https://openalex.org/C11105738","wikidata":"https://www.wikidata.org/wiki/Q1895805","display_name":"Multiple-criteria decision analysis","level":2,"score":0.466632217168808},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.40560024976730347},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3739655911922455},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2644611597061157},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2630351781845093},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.2628362774848938},{"id":"https://openalex.org/C42475967","wikidata":"https://www.wikidata.org/wiki/Q194292","display_name":"Operations research","level":1,"score":0.2104317545890808},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.10282444953918457},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.04888090491294861},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.048452943563461304}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1515/jisys-2017-0560","is_oa":true,"landing_page_url":"https://doi.org/10.1515/jisys-2017-0560","pdf_url":"https://www.degruyter.com/downloadpdf/journals/jisys/29/1/article-p1283.pdf","source":{"id":"https://openalex.org/S2764846071","display_name":"Journal of Intelligent Systems","issn_l":"0334-1860","issn":["0334-1860","2191-026X"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315148","host_organization_name":"IlmuKomputer.Com","host_organization_lineage":["https://openalex.org/P4310315148"],"host_organization_lineage_names":["IlmuKomputer.Com"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Intelligent Systems","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:667a0efc3c304508bc38ee0048048e38","is_oa":true,"landing_page_url":"https://doaj.org/article/667a0efc3c304508bc38ee0048048e38","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Intelligent Systems, Vol 29, Iss 1, Pp 1283-1300 (2019)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1515/jisys-2017-0560","is_oa":true,"landing_page_url":"https://doi.org/10.1515/jisys-2017-0560","pdf_url":"https://www.degruyter.com/downloadpdf/journals/jisys/29/1/article-p1283.pdf","source":{"id":"https://openalex.org/S2764846071","display_name":"Journal of Intelligent Systems","issn_l":"0334-1860","issn":["0334-1860","2191-026X"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315148","host_organization_name":"IlmuKomputer.Com","host_organization_lineage":["https://openalex.org/P4310315148"],"host_organization_lineage_names":["IlmuKomputer.Com"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Intelligent Systems","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.8299999833106995,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2924780751.pdf","grobid_xml":"https://content.openalex.org/works/W2924780751.grobid-xml"},"referenced_works_count":48,"referenced_works":["https://openalex.org/W594625170","https://openalex.org/W908018526","https://openalex.org/W1976567794","https://openalex.org/W1979986495","https://openalex.org/W1980564456","https://openalex.org/W1981107087","https://openalex.org/W1983182219","https://openalex.org/W1992983421","https://openalex.org/W1993951664","https://openalex.org/W1996921169","https://openalex.org/W2012169861","https://openalex.org/W2029812528","https://openalex.org/W2031523830","https://openalex.org/W2035082729","https://openalex.org/W2042102899","https://openalex.org/W2059859512","https://openalex.org/W2065262720","https://openalex.org/W2065329409","https://openalex.org/W2069071173","https://openalex.org/W2091402852","https://openalex.org/W2097359812","https://openalex.org/W2106517302","https://openalex.org/W2160185911","https://openalex.org/W2213987030","https://openalex.org/W2238658759","https://openalex.org/W2437782838","https://openalex.org/W2506768821","https://openalex.org/W2522562129","https://openalex.org/W2527667439","https://openalex.org/W2573110008","https://openalex.org/W2585517110","https://openalex.org/W2586296979","https://openalex.org/W2604308625","https://openalex.org/W2739405590","https://openalex.org/W2744194414","https://openalex.org/W2761119604","https://openalex.org/W2762031059","https://openalex.org/W2762965914","https://openalex.org/W2767791375","https://openalex.org/W2767853298","https://openalex.org/W2769758921","https://openalex.org/W2773830462","https://openalex.org/W2811497295","https://openalex.org/W2826020435","https://openalex.org/W2963913463","https://openalex.org/W4211007335","https://openalex.org/W4238927122","https://openalex.org/W4247423167"],"related_works":["https://openalex.org/W2041949587","https://openalex.org/W2958553423","https://openalex.org/W3154161952","https://openalex.org/W2778781604","https://openalex.org/W4235219488","https://openalex.org/W2047025039","https://openalex.org/W1928481587","https://openalex.org/W2613305061","https://openalex.org/W2107523790","https://openalex.org/W4237248107"],"abstract_inverted_index":{"Abstract":[0],"The":[1,44],"aim":[2],"of":[3,75],"this":[4],"paper":[5],"is":[6,65],"to":[7,35,57,67],"define":[8,25],"some":[9],"new":[10,45],"operation":[11],"laws":[12],"for":[13,48],"the":[14,28,37,59,71,76],"trapezoidal":[15,29,49],"linguistic":[16,30,50],"cubic":[17,31,51],"fuzzy":[18,32,52],"number":[19],"and":[20,26,69,73],"Hamming":[21],"distance.":[22],"Furthermore,":[23],"we":[24],"use":[27],"TOPSIS":[33],"method":[34,47],"solve":[36],"multi":[38],"criteria":[39],"decision":[40],"making":[41],"(MCDM)":[42],"method.":[43,78],"ranking":[46],"numbers":[53],"(TrLCFNs)":[54],"are":[55],"used":[56],"rank":[58],"alternatives.":[60],"Finally,":[61],"an":[62],"illustrative":[63],"example":[64],"given":[66],"verify":[68],"prove":[70],"practicality":[72],"effectiveness":[74],"proposed":[77]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":1}],"updated_date":"2025-12-06T23:10:59.065948","created_date":"2025-10-10T00:00:00"}