{"id":"https://openalex.org/W3183213683","doi":"https://doi.org/10.1155/2021/8295997","title":"Investigating the Short\u2010Circuit Problem Using the Planarity Index of Complex q\u2010Rung Orthopair Fuzzy Planar Graphs","display_name":"Investigating the Short\u2010Circuit Problem Using the Planarity Index of Complex q\u2010Rung Orthopair Fuzzy Planar Graphs","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3183213683","doi":"https://doi.org/10.1155/2021/8295997","mag":"3183213683"},"language":"en","primary_location":{"id":"doi:10.1155/2021/8295997","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2021/8295997","pdf_url":"https://downloads.hindawi.com/journals/complexity/2021/8295997.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/2021/8295997.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044393587","display_name":"Abrar Hussain","orcid":"https://orcid.org/0000-0003-2289-7464"},"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":"Abrar Hussain","raw_affiliation_strings":["Department of Mathematics, Riphah Institute of Computing & Applied Sciences (RICAS), Riphah International University (Lahore Campus), 54000 Lahore, Pakistan"],"raw_orcid":"https://orcid.org/0000-0003-2289-7464","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Riphah Institute of Computing & Applied Sciences (RICAS), Riphah International University (Lahore Campus), 54000 Lahore, Pakistan","institution_ids":["https://openalex.org/I195024194"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015615046","display_name":"Ahmed Alsanad","orcid":"https://orcid.org/0000-0003-1702-8643"},"institutions":[{"id":"https://openalex.org/I28022161","display_name":"King Saud University","ror":"https://ror.org/02f81g417","country_code":"SA","type":"education","lineage":["https://openalex.org/I28022161"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"Ahmed Alsanad","raw_affiliation_strings":["STC's Artificial Intelligence Chair, Department of Information Systems, College of Computer and Information Sciences, King Saud University, Riyadh 11543, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0003-1702-8643","affiliations":[{"raw_affiliation_string":"STC's Artificial Intelligence Chair, Department of Information Systems, College of Computer and Information Sciences, King Saud University, Riyadh 11543, Saudi Arabia","institution_ids":["https://openalex.org/I28022161"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037136946","display_name":"Kifayat Ullah","orcid":"https://orcid.org/0000-0002-1438-6413"},"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":true,"raw_author_name":"Kifayat Ullah","raw_affiliation_strings":["Department of Mathematics, Riphah Institute of Computing & Applied Sciences (RICAS), Riphah International University (Lahore Campus), 54000 Lahore, Pakistan"],"raw_orcid":"https://orcid.org/0000-0002-1438-6413","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Riphah Institute of Computing & Applied Sciences (RICAS), Riphah International University (Lahore Campus), 54000 Lahore, Pakistan","institution_ids":["https://openalex.org/I195024194"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100740852","display_name":"Zeeshan Ali","orcid":"https://orcid.org/0000-0001-5878-714X"},"institutions":[{"id":"https://openalex.org/I121243025","display_name":"International Islamic University, Islamabad","ror":"https://ror.org/047w75g40","country_code":"PK","type":"education","lineage":["https://openalex.org/I121243025"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Zeeshan Ali","raw_affiliation_strings":["Department of Mathematics & Statistics, International Islamic University Islamabad, Islamabad 44000, Pakistan"],"raw_orcid":"https://orcid.org/0000-0001-5878-714X","affiliations":[{"raw_affiliation_string":"Department of Mathematics & Statistics, International Islamic University Islamabad, Islamabad 44000, Pakistan","institution_ids":["https://openalex.org/I121243025"]}]},{"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 & Applied Sciences (RICAS), Riphah International University (Lahore Campus), 54000 Lahore, Pakistan"],"raw_orcid":"https://orcid.org/0000-0001-5715-9299","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Riphah Institute of Computing & Applied Sciences (RICAS), Riphah International University (Lahore Campus), 54000 Lahore, Pakistan","institution_ids":["https://openalex.org/I195024194"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080469264","display_name":"Mogeeb A. A. Mosleh","orcid":"https://orcid.org/0000-0001-5094-5561"},"institutions":[{"id":"https://openalex.org/I36197038","display_name":"Taiz University","ror":"https://ror.org/03jwcxq96","country_code":"YE","type":"education","lineage":["https://openalex.org/I36197038"]}],"countries":["YE"],"is_corresponding":true,"raw_author_name":"Mogeeb A. A. Mosleh","raw_affiliation_strings":["Faculty of Engineering and Information Technology, Taiz University, Taiz 6803, Yemen"],"raw_orcid":"https://orcid.org/0000-0001-5094-5561","affiliations":[{"raw_affiliation_string":"Faculty of Engineering and Information Technology, Taiz University, Taiz 6803, Yemen","institution_ids":["https://openalex.org/I36197038"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5015615046","https://openalex.org/A5037136946","https://openalex.org/A5080469264"],"corresponding_institution_ids":["https://openalex.org/I195024194","https://openalex.org/I28022161","https://openalex.org/I36197038"],"apc_list":{"value":2300,"currency":"USD","value_usd":2300},"apc_paid":{"value":2300,"currency":"USD","value_usd":2300},"fwci":1.97,"has_fulltext":true,"cited_by_count":13,"citation_normalized_percentile":{"value":0.86366386,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"2021","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":0.9944999814033508,"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":0.9944999814033508,"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/T13601","display_name":"Urban Transport Systems Analysis","score":0.9835000038146973,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12546","display_name":"Smart Parking Systems Research","score":0.9801999926567078,"subfield":{"id":"https://openalex.org/subfields/2215","display_name":"Building and Construction"},"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/planarity-testing","display_name":"Planarity testing","score":0.9264389872550964},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.7172502279281616},{"id":"https://openalex.org/keywords/index","display_name":"Index (typography)","score":0.6212804317474365},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.6090594530105591},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5123003721237183},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.4538730978965759},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.38942772150039673},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3494694232940674},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.34641197323799133},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.26645588874816895},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.19416165351867676},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.16347017884254456},{"id":"https://openalex.org/keywords/world-wide-web","display_name":"World Wide Web","score":0.06064984202384949},{"id":"https://openalex.org/keywords/computer-graphics","display_name":"Computer graphics (images)","score":0.04511752724647522}],"concepts":[{"id":"https://openalex.org/C68260962","wikidata":"https://www.wikidata.org/wiki/Q7200967","display_name":"Planarity testing","level":2,"score":0.9264389872550964},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.7172502279281616},{"id":"https://openalex.org/C2777382242","wikidata":"https://www.wikidata.org/wiki/Q6017816","display_name":"Index (typography)","level":2,"score":0.6212804317474365},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.6090594530105591},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5123003721237183},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.4538730978965759},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.38942772150039673},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3494694232940674},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.34641197323799133},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.26645588874816895},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.19416165351867676},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.16347017884254456},{"id":"https://openalex.org/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","level":1,"score":0.06064984202384949},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.04511752724647522}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2021/8295997","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2021/8295997","pdf_url":"https://downloads.hindawi.com/journals/complexity/2021/8295997.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:8295997","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/complexity/2021/8295997.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:4722b99c6cec4a5f8a82c461bfce5d36","is_oa":true,"landing_page_url":"https://doaj.org/article/4722b99c6cec4a5f8a82c461bfce5d36","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":"Complexity, Vol 2021 (2021)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2021/8295997","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2021/8295997","pdf_url":"https://downloads.hindawi.com/journals/complexity/2021/8295997.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":[{"id":"https://openalex.org/F4320321145","display_name":"King Saud University","ror":"https://ror.org/02f81g417"},{"id":"https://openalex.org/F4320335726","display_name":"Deanship of Scientific Research, King Saud University","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3183213683.pdf","grobid_xml":"https://content.openalex.org/works/W3183213683.grobid-xml"},"referenced_works_count":43,"referenced_works":["https://openalex.org/W1934277439","https://openalex.org/W1980345052","https://openalex.org/W1980564456","https://openalex.org/W1990733953","https://openalex.org/W2012575173","https://openalex.org/W2050147082","https://openalex.org/W2090187739","https://openalex.org/W2097403045","https://openalex.org/W2156662032","https://openalex.org/W2489172749","https://openalex.org/W2514754342","https://openalex.org/W2746747652","https://openalex.org/W2789682920","https://openalex.org/W2796547704","https://openalex.org/W2804105936","https://openalex.org/W2808872784","https://openalex.org/W2884892695","https://openalex.org/W2888642366","https://openalex.org/W2903072333","https://openalex.org/W2907615575","https://openalex.org/W2909875538","https://openalex.org/W2910635668","https://openalex.org/W2921569211","https://openalex.org/W2938214891","https://openalex.org/W2945404912","https://openalex.org/W2949657163","https://openalex.org/W2962753525","https://openalex.org/W2965503710","https://openalex.org/W2973775716","https://openalex.org/W2974202854","https://openalex.org/W2995299237","https://openalex.org/W3007573849","https://openalex.org/W3009028655","https://openalex.org/W3015234892","https://openalex.org/W3016114082","https://openalex.org/W3036877760","https://openalex.org/W3041484731","https://openalex.org/W3119370318","https://openalex.org/W3121924295","https://openalex.org/W3166981717","https://openalex.org/W3195155516","https://openalex.org/W4211007335","https://openalex.org/W4255242363"],"related_works":["https://openalex.org/W1510038041","https://openalex.org/W2373079339","https://openalex.org/W2108284102","https://openalex.org/W3047848516","https://openalex.org/W4287691299","https://openalex.org/W183093845","https://openalex.org/W4297837089","https://openalex.org/W2959817076","https://openalex.org/W3134933682","https://openalex.org/W2964235359"],"abstract_inverted_index":{"Planar":[0],"graphs":[1,29,92],"play":[2],"an":[3,192],"effective":[4],"role":[5],"in":[6,49,55,62,74,206],"many":[7],"practical":[8],"applications":[9],"where":[10,191],"the":[11,22,34,46,50,68,75,89,105,114,132,165,174,188,204,211,215],"crossing":[12,183,205],"of":[13,52,57,71,77,107,113,124,134,151,176,187,210],"edges":[14,37],"becomes":[15],"problematic.":[16],"This":[17],"paper":[18],"aims":[19],"to":[20,81,164,182],"investigate":[21],"complex":[23,41,58,90,94,135,140,196],"q\u2010rung":[24],"orthopair":[25],"fuzzy":[26,85],"(CQROF)":[27,198],"planar":[28],"(CQROFPGs).":[30],"In":[31],"a":[32,65,122],"CQROFPG,":[33],"nodes":[35],"and":[36,83,98,109,118,126,139,145,154,160,167,220],"are":[38,169,218],"based":[39,194],"on":[40,195],"QROF":[42,72,91,95,136,141,197],"information":[43,73,199],"that":[44,179],"represents":[45],"uncertain":[47,78],"knowledge":[48,79],"range":[51],"unit":[53],"circles":[54],"terms":[56,100],"numbers.":[59],"The":[60],"motivation":[61],"discussing":[63],"such":[64],"topic":[66],"is":[67,116,157,184,200,224],"wide":[69],"flexibility":[70],"expression":[76],"compared":[80],"intuitionistic":[82],"Pythagorean":[84],"settings.":[86],"We":[87,129],"discussed":[88,185],"(CQROFGs),":[93],"multigraphs":[96],"(CQROFMGs),":[97],"related":[99],"followed":[101,120],"by":[102,121],"examples.":[103,172],"Furthermore,":[104,173],"notion":[106,133],"strength":[108],"planarity":[110],"index":[111],"(PI)":[112],"CQROFPGs":[115],"defined":[117,131],"exemplified":[119,146],"study":[123,150,190,213,217,223],"strong":[125],"weak":[127,155],"edges.":[128],"further":[130],"face":[137],"(CQROFF)":[138],"dual":[142],"graph":[143],"(CQROFDG)":[144],"these":[147],"concepts.":[148],"A":[149],"isomorphism,":[152,156],"coweak":[153],"set":[158],"up,":[159],"some":[161,221],"results":[162,180],"relating":[163],"CQROFPG":[166],"isomorphisms":[168],"explored":[170],"using":[171],"problem":[175],"short":[177],"circuits":[178],"due":[181],"because":[186],"proposed":[189],"algorithm":[193],"presented":[201],"for":[202],"reducing":[203],"networks.":[207],"Some":[208],"advantages":[209],"projected":[212],"over":[214],"previous":[216],"observed,":[219],"future":[222],"predicted.":[225]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":4}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}