{"id":"https://openalex.org/W4280493922","doi":"https://doi.org/10.1155/2022/8016096","title":"Wiener Index of Intuitionistic Fuzzy Graphs with an Application to Transport Network Flow","display_name":"Wiener Index of Intuitionistic Fuzzy Graphs with an Application to Transport Network Flow","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W4280493922","doi":"https://doi.org/10.1155/2022/8016096"},"language":"en","primary_location":{"id":"doi:10.1155/2022/8016096","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2022/8016096","pdf_url":"https://downloads.hindawi.com/journals/complexity/2022/8016096.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/complexity/2022/8016096.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016605731","display_name":"Tulat Naeem","orcid":null},"institutions":[{"id":"https://openalex.org/I195024194","display_name":"Riphah International University","ror":"https://ror.org/02kdm5630","country_code":"PK","type":"education","lineage":["https://openalex.org/I195024194"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Tulat Naeem","raw_affiliation_strings":["Department of Mathematics, Riphah Institute of Computing and Applied Sciences, Riphah International University, Lahore, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Riphah Institute of Computing and Applied Sciences, Riphah International University, Lahore, Pakistan","institution_ids":["https://openalex.org/I195024194"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066651205","display_name":"Muhammad Kamran Jamil","orcid":"https://orcid.org/0000-0001-5715-9299"},"institutions":[{"id":"https://openalex.org/I195024194","display_name":"Riphah International University","ror":"https://ror.org/02kdm5630","country_code":"PK","type":"education","lineage":["https://openalex.org/I195024194"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Muhammad Kamran Jamil","raw_affiliation_strings":["Department of Mathematics, Riphah Institute of Computing and Applied Sciences, Riphah International University, Lahore, Pakistan"],"raw_orcid":"https://orcid.org/0000-0001-5715-9299","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Riphah Institute of Computing and Applied Sciences, Riphah International University, Lahore, Pakistan","institution_ids":["https://openalex.org/I195024194"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027288343","display_name":"Khawaja Muhammad Fahd","orcid":null},"institutions":[{"id":"https://openalex.org/I201384688","display_name":"National University of Computer and Emerging Sciences","ror":"https://ror.org/003eyb898","country_code":"PK","type":"education","lineage":["https://openalex.org/I201384688"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Khawaja Muhammad Fahd","raw_affiliation_strings":["FAST School of Computing, National University of Computer and Emerging Sciences, Lahore, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"FAST School of Computing, National University of Computer and Emerging Sciences, Lahore, Pakistan","institution_ids":["https://openalex.org/I201384688"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054213342","display_name":"Abdu Alameri","orcid":"https://orcid.org/0000-0002-9920-4892"},"institutions":[{"id":"https://openalex.org/I118692353","display_name":"University of Science and Technology","ror":"https://ror.org/05bj7sh33","country_code":"YE","type":"education","lineage":["https://openalex.org/I118692353"]}],"countries":["YE"],"is_corresponding":true,"raw_author_name":"Abdu alAmeri","raw_affiliation_strings":["Department of Biomedical Engineering, Faculty of Engineering, University of Science and Technology, Sana'a, Yemen"],"raw_orcid":"https://orcid.org/0000-0002-9920-4892","affiliations":[{"raw_affiliation_string":"Department of Biomedical Engineering, Faculty of Engineering, University of Science and Technology, Sana'a, Yemen","institution_ids":["https://openalex.org/I118692353"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5054213342"],"corresponding_institution_ids":["https://openalex.org/I118692353"],"apc_list":{"value":2300,"currency":"USD","value_usd":2300},"apc_paid":{"value":2300,"currency":"USD","value_usd":2300},"fwci":0.5067,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.67138274,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":96},"biblio":{"volume":"2022","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9988999962806702,"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":0.9988999962806702,"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/T14175","display_name":"Intuitionistic Fuzzy Systems Applications","score":0.9965000152587891,"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/T11106","display_name":"Data Management and Algorithms","score":0.9933000206947327,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/index","display_name":"Index (typography)","score":0.6669316291809082},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5375250577926636},{"id":"https://openalex.org/keywords/wiener-index","display_name":"Wiener index","score":0.503070056438446},{"id":"https://openalex.org/keywords/topological-index","display_name":"Topological index","score":0.4533774256706238},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.42955484986305237},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3530029058456421},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.34249165654182434},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2568363547325134},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2376422882080078},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.18714123964309692}],"concepts":[{"id":"https://openalex.org/C2777382242","wikidata":"https://www.wikidata.org/wiki/Q6017816","display_name":"Index (typography)","level":2,"score":0.6669316291809082},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5375250577926636},{"id":"https://openalex.org/C16640446","wikidata":"https://www.wikidata.org/wiki/Q909065","display_name":"Wiener index","level":3,"score":0.503070056438446},{"id":"https://openalex.org/C159867001","wikidata":"https://www.wikidata.org/wiki/Q904942","display_name":"Topological index","level":2,"score":0.4533774256706238},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.42955484986305237},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3530029058456421},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.34249165654182434},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2568363547325134},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2376422882080078},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.18714123964309692},{"id":"https://openalex.org/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2022/8016096","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2022/8016096","pdf_url":"https://downloads.hindawi.com/journals/complexity/2022/8016096.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:complx:8016096","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/complexity/2022/8016096.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:d8d55a6db4504cb8813043e29bb81b85","is_oa":false,"landing_page_url":"https://doaj.org/article/d8d55a6db4504cb8813043e29bb81b85","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Complexity, Vol 2022 (2022)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2022/8016096","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2022/8016096","pdf_url":"https://downloads.hindawi.com/journals/complexity/2022/8016096.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4280493922.pdf","grobid_xml":"https://content.openalex.org/works/W4280493922.grobid-xml"},"referenced_works_count":53,"referenced_works":["https://openalex.org/W203133892","https://openalex.org/W217726381","https://openalex.org/W1980564456","https://openalex.org/W1980886530","https://openalex.org/W1982485306","https://openalex.org/W2006727531","https://openalex.org/W2015521547","https://openalex.org/W2024875454","https://openalex.org/W2028649872","https://openalex.org/W2043619358","https://openalex.org/W2044765840","https://openalex.org/W2045629821","https://openalex.org/W2054416947","https://openalex.org/W2069109824","https://openalex.org/W2075832447","https://openalex.org/W2079767857","https://openalex.org/W2111358144","https://openalex.org/W2124970246","https://openalex.org/W2157746846","https://openalex.org/W2188140604","https://openalex.org/W2237511067","https://openalex.org/W2273289985","https://openalex.org/W2288677372","https://openalex.org/W2318794083","https://openalex.org/W2344803877","https://openalex.org/W2489172749","https://openalex.org/W2511297325","https://openalex.org/W2557149854","https://openalex.org/W2607892130","https://openalex.org/W2754849094","https://openalex.org/W2804105936","https://openalex.org/W2808890614","https://openalex.org/W2901104715","https://openalex.org/W2909094418","https://openalex.org/W2911410219","https://openalex.org/W2936825285","https://openalex.org/W2945404912","https://openalex.org/W2997734707","https://openalex.org/W3045598505","https://openalex.org/W3046793793","https://openalex.org/W3048517893","https://openalex.org/W3096879449","https://openalex.org/W3119017826","https://openalex.org/W3123823813","https://openalex.org/W3126577646","https://openalex.org/W3196252993","https://openalex.org/W4205751110","https://openalex.org/W4211007335","https://openalex.org/W4245152641","https://openalex.org/W4292158025","https://openalex.org/W4292333025","https://openalex.org/W6686623758","https://openalex.org/W6737258704"],"related_works":["https://openalex.org/W1530753320","https://openalex.org/W2337701229","https://openalex.org/W2947875569","https://openalex.org/W2239438160","https://openalex.org/W1992064123","https://openalex.org/W2063284425","https://openalex.org/W2389441820","https://openalex.org/W1796630930","https://openalex.org/W2329275106","https://openalex.org/W2289583476"],"abstract_inverted_index":{"The":[0,80],"Wiener":[1],"index":[2,85],"is":[3,86,103],"one":[4],"of":[5,17,45,61,92,97],"the":[6,12,36,59,63,90,98],"connectivity":[7,84],"parameters":[8],"used":[9],"to":[10,34],"know":[11],"biochemical":[13],"and":[14,38,51,71,83],"physicochemical":[15],"properties":[16],"compounds":[18],"depending":[19],"upon":[20],"their":[21],"molecular":[22],"structures.":[23],"Intuitionistic":[24],"fuzzy":[25],"graphs":[26],"(IFG":[27],"s":[28,66],")":[29],"are":[30,78],"a":[31],"convenient":[32],"tool":[33],"represent":[35],"objects":[37],"relations":[39],"between":[40,82],"them":[41],"with":[42],"two":[43],"types":[44],"information":[46],"using":[47],"truth":[48],"membership":[49,53],"degree":[50],"falsity":[52],"degree.":[54],"This":[55],"research":[56],"work":[57],"presents":[58],"concept":[60],"under":[62],"structure":[64],"IFG":[65],",":[67],"I":[68,72],"F":[69,73],"trees,":[70],"cycles.":[74],"Some":[75],"bounds":[76],"on":[77],"investigated.":[79],"relationship":[81],"also":[87],"studied.":[88],"In":[89],"end":[91],"this":[93],"study,":[94],"an":[95],"application":[96],"in":[99],"transport":[100],"network":[101],"flow":[102],"proposed.":[104]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
