{"id":"https://openalex.org/W3087798822","doi":"https://doi.org/10.1109/access.2020.3025974","title":"Complex Vague Graphs and Their Application in Decision-Making Problems","display_name":"Complex Vague Graphs and Their Application in Decision-Making Problems","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3087798822","doi":"https://doi.org/10.1109/access.2020.3025974","mag":"3087798822"},"language":"en","primary_location":{"id":"doi:10.1109/access.2020.3025974","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2020.3025974","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8948470/09203801.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://ieeexplore.ieee.org/ielx7/6287639/8948470/09203801.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101978937","display_name":"Shouzhen Zeng","orcid":"https://orcid.org/0000-0002-3604-0843"},"institutions":[{"id":"https://openalex.org/I109935558","display_name":"Ningbo University","ror":"https://ror.org/03et85d35","country_code":"CN","type":"education","lineage":["https://openalex.org/I109935558"]},{"id":"https://openalex.org/I75059550","display_name":"Zhejiang Gongshang University","ror":"https://ror.org/0569mkk41","country_code":"CN","type":"education","lineage":["https://openalex.org/I75059550"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Shouzhen Zeng","raw_affiliation_strings":["College of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou, China","School of Business, Ningbo University, Ningbo, China"],"raw_orcid":"https://orcid.org/0000-0002-3604-0843","affiliations":[{"raw_affiliation_string":"College of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou, China","institution_ids":["https://openalex.org/I75059550"]},{"raw_affiliation_string":"School of Business, Ningbo University, Ningbo, China","institution_ids":["https://openalex.org/I109935558"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101518078","display_name":"Muhammad Shoaib","orcid":"https://orcid.org/0000-0001-8715-0738"},"institutions":[{"id":"https://openalex.org/I172780181","display_name":"University of the Punjab","ror":"https://ror.org/011maz450","country_code":"PK","type":"education","lineage":["https://openalex.org/I172780181"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Muhammad Shoaib","raw_affiliation_strings":["University of the Punjab, Lahore, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of the Punjab, Lahore, Pakistan","institution_ids":["https://openalex.org/I172780181"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058791499","display_name":"Shahbaz Ali","orcid":"https://orcid.org/0000-0002-5998-0053"},"institutions":[{"id":"https://openalex.org/I4210102737","display_name":"Khwaja Fareed University of Engineering and Information Technology","ror":"https://ror.org/0161dyt30","country_code":"PK","type":"education","lineage":["https://openalex.org/I4210102737"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Shahbaz Ali","raw_affiliation_strings":["Khwaja Fareed University of Engineering and Information Technology, Rahim Yar Khan, Pakistan"],"raw_orcid":"https://orcid.org/0000-0002-5998-0053","affiliations":[{"raw_affiliation_string":"Khwaja Fareed University of Engineering and Information Technology, Rahim Yar Khan, Pakistan","institution_ids":["https://openalex.org/I4210102737"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101835957","display_name":"Qamar Abbas","orcid":"https://orcid.org/0009-0009-9625-1894"},"institutions":[{"id":"https://openalex.org/I12469534","display_name":"Quaid-i-Azam University","ror":"https://ror.org/04s9hft57","country_code":"PK","type":"education","lineage":["https://openalex.org/I12469534"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Qamar Abbas","raw_affiliation_strings":["Quaid-I-Azam University, Islamabad, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Quaid-I-Azam University, Islamabad, Pakistan","institution_ids":["https://openalex.org/I12469534"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067699390","display_name":"Muhammad Shahzad Nadeem","orcid":null},"institutions":[{"id":"https://openalex.org/I12469534","display_name":"Quaid-i-Azam University","ror":"https://ror.org/04s9hft57","country_code":"PK","type":"education","lineage":["https://openalex.org/I12469534"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Muhammad Shahzad Nadeem","raw_affiliation_strings":["Quaid-I-Azam University, Islamabad, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Quaid-I-Azam University, Islamabad, Pakistan","institution_ids":["https://openalex.org/I12469534"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5101978937"],"corresponding_institution_ids":["https://openalex.org/I109935558","https://openalex.org/I75059550"],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":2.2301,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.88815545,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"8","issue":null,"first_page":"174094","last_page":"174104"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9739000201225281,"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":0.9739000201225281,"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/T12709","display_name":"Optimization and Mathematical Programming","score":0.9300000071525574,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/cartesian-product","display_name":"Cartesian product","score":0.681162416934967},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6360903978347778},{"id":"https://openalex.org/keywords/comparability","display_name":"Comparability","score":0.5495787858963013},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4690905809402466},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4479828476905823},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.4291665256023407},{"id":"https://openalex.org/keywords/graph-product","display_name":"Graph product","score":0.41906625032424927},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.41509681940078735},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3717612028121948},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3231969475746155},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.1271635890007019},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.09054723381996155}],"concepts":[{"id":"https://openalex.org/C65236422","wikidata":"https://www.wikidata.org/wiki/Q173740","display_name":"Cartesian product","level":2,"score":0.681162416934967},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6360903978347778},{"id":"https://openalex.org/C197947376","wikidata":"https://www.wikidata.org/wiki/Q5155608","display_name":"Comparability","level":2,"score":0.5495787858963013},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4690905809402466},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4479828476905823},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.4291665256023407},{"id":"https://openalex.org/C68103157","wikidata":"https://www.wikidata.org/wiki/Q569347","display_name":"Graph product","level":5,"score":0.41906625032424927},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.41509681940078735},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3717612028121948},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3231969475746155},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.1271635890007019},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.09054723381996155},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/access.2020.3025974","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2020.3025974","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8948470/09203801.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:ea606524b31c4b41b93d4e57b4a84ea2","is_oa":true,"landing_page_url":"https://doaj.org/article/ea606524b31c4b41b93d4e57b4a84ea2","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":"IEEE Access, Vol 8, Pp 174094-174104 (2020)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2020.3025974","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2020.3025974","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8948470/09203801.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.7799999713897705,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G3413499438","display_name":null,"funder_award_id":"18BTJ027","funder_id":"https://openalex.org/F4320327557","funder_display_name":"National Office for Philosophy and Social Sciences"}],"funders":[{"id":"https://openalex.org/F4320327557","display_name":"National Office for Philosophy and Social Sciences","ror":"https://ror.org/04m0ms912"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3087798822.pdf","grobid_xml":"https://content.openalex.org/works/W3087798822.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W59607384","https://openalex.org/W1601092472","https://openalex.org/W1981232799","https://openalex.org/W2007083456","https://openalex.org/W2008228846","https://openalex.org/W2044765840","https://openalex.org/W2050147082","https://openalex.org/W2184523047","https://openalex.org/W2291770014","https://openalex.org/W2324729946","https://openalex.org/W2342368241","https://openalex.org/W2346847115","https://openalex.org/W2418004530","https://openalex.org/W2490481354","https://openalex.org/W2561241420","https://openalex.org/W2782590944","https://openalex.org/W2789811370","https://openalex.org/W2803124099","https://openalex.org/W2898322660","https://openalex.org/W2905416607","https://openalex.org/W2912565176","https://openalex.org/W2921596575","https://openalex.org/W2940495357","https://openalex.org/W2970222247","https://openalex.org/W2988347501","https://openalex.org/W2999519596","https://openalex.org/W3012546479","https://openalex.org/W3045598505","https://openalex.org/W3080199361","https://openalex.org/W4211007335","https://openalex.org/W6686010921"],"related_works":["https://openalex.org/W4366733366","https://openalex.org/W2998748068","https://openalex.org/W3137798114","https://openalex.org/W2294807589","https://openalex.org/W4378087371","https://openalex.org/W2364608040","https://openalex.org/W1983442375","https://openalex.org/W3184080960","https://openalex.org/W3190844188","https://openalex.org/W2230314777"],"abstract_inverted_index":{"Fuzzy":[0],"graph":[1],"models":[2],"are":[3,24,100],"found":[4],"everywhere":[5],"in":[6,15,54,145],"natural":[7],"and":[8,18,30,64,115,128],"human":[9],"made":[10],"structures,":[11],"including":[12],"process":[13],"dynamics":[14],"biological,":[16],"physical":[17],"social":[19],"systems.":[20],"Since":[21],"real-life":[22],"problems":[23,43],"often":[25],"uncertain":[26],"due":[27],"to":[28,40,66,71,90,113],"inconsistent":[29],"indeterminate":[31],"information,":[32],"it":[33],"is":[34,52,81,112],"very":[35],"hard":[36],"for":[37],"an":[38],"expert":[39],"model":[41,51],"those":[42],"using":[44],"a":[45,78,82],"fuzzy":[46],"graph.":[47],"A":[48],"complex":[49,103,132,142],"vague":[50,73,104,133,143],"useful":[53],"the":[55,67,72,91,117],"field":[56],"of":[57,85,108,131,141],"mathematics":[58],"which":[59,99],"gives":[60],"more":[61],"precision,":[62],"comparability":[63],"flexibility":[65],"system":[68],"as":[69],"compared":[70],"model.":[74],"In":[75],"these":[76],"years,":[77],"mathematical":[79,93],"approach":[80,84],"generalized":[83],"blending":[86],"different":[87],"aspects.":[88],"According":[89],"above":[92],"approach,":[94],"we":[95,138],"investigate":[96],"strong":[97,124],"techniques":[98],"based":[101],"on":[102],"graphs.":[105],"The":[106],"purpose":[107],"this":[109],"research":[110],"study":[111],"present":[114,139],"explore":[116],"key":[118],"properties":[119],"including:":[120],"Cartesian":[121],"products,":[122],"composition,":[123],"product,":[125],"semi-strong":[126],"product":[127,130],"direct":[129],"graphs":[134,144],"with":[135],"examples.":[136],"Finally,":[137],"application":[140],"decision-making":[146],"problems.":[147]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":2}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
