{"id":"https://openalex.org/W4412506334","doi":"https://doi.org/10.5391/ijfis.2025.25.2.207","title":"\u03b3-Product of Product Fuzzy Graphs","display_name":"\u03b3-Product of Product Fuzzy Graphs","publication_year":2025,"publication_date":"2025-06-30","ids":{"openalex":"https://openalex.org/W4412506334","doi":"https://doi.org/10.5391/ijfis.2025.25.2.207"},"language":"en","primary_location":{"id":"doi:10.5391/ijfis.2025.25.2.207","is_oa":true,"landing_page_url":"https://doi.org/10.5391/ijfis.2025.25.2.207","pdf_url":"https://www.ijfis.org/journal/download_pdf.php?doi=10.5391/IJFIS.2025.25.2.207","source":{"id":"https://openalex.org/S4210177700","display_name":"International Journal of Fuzzy Logic and Intelligent Systems","issn_l":"1598-2645","issn":["1598-2645","2093-744X"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4327628602","host_organization_name":"Korean Institute of Intelligent Systems","host_organization_lineage":["https://openalex.org/P4327628602"],"host_organization_lineage_names":["Korean Institute of Intelligent Systems"],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGENT SYSTEMS","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.ijfis.org/journal/download_pdf.php?doi=10.5391/IJFIS.2025.25.2.207","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087246756","display_name":"Talal Ali Al-Hawary","orcid":"https://orcid.org/0000-0002-5167-5265"},"institutions":[{"id":"https://openalex.org/I85507684","display_name":"Yarmouk University","ror":"https://ror.org/004mbaj56","country_code":"JO","type":"education","lineage":["https://openalex.org/I85507684"]}],"countries":["JO"],"is_corresponding":true,"raw_author_name":"Talal Ali Al-Hawary","raw_affiliation_strings":["Department of Mathematics, Yarmouk University, Irbid, Jordan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Yarmouk University, Irbid, Jordan","institution_ids":["https://openalex.org/I85507684"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5087246756"],"corresponding_institution_ids":["https://openalex.org/I85507684"],"apc_list":null,"apc_paid":null,"fwci":2.0726,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.87602162,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":97},"biblio":{"volume":"25","issue":"2","first_page":"207","last_page":"212"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9293000102043152,"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":0.9293000102043152,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.6648225784301758},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.48459064960479736},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4292541444301605},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.40023714303970337},{"id":"https://openalex.org/keywords/business","display_name":"Business","score":0.3246919512748718},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.14767372608184814},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06655362248420715}],"concepts":[{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.6648225784301758},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.48459064960479736},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4292541444301605},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.40023714303970337},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.3246919512748718},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.14767372608184814},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06655362248420715}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.5391/ijfis.2025.25.2.207","is_oa":true,"landing_page_url":"https://doi.org/10.5391/ijfis.2025.25.2.207","pdf_url":"https://www.ijfis.org/journal/download_pdf.php?doi=10.5391/IJFIS.2025.25.2.207","source":{"id":"https://openalex.org/S4210177700","display_name":"International Journal of Fuzzy Logic and Intelligent Systems","issn_l":"1598-2645","issn":["1598-2645","2093-744X"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4327628602","host_organization_name":"Korean Institute of Intelligent Systems","host_organization_lineage":["https://openalex.org/P4327628602"],"host_organization_lineage_names":["Korean Institute of Intelligent Systems"],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGENT SYSTEMS","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.5391/ijfis.2025.25.2.207","is_oa":true,"landing_page_url":"https://doi.org/10.5391/ijfis.2025.25.2.207","pdf_url":"https://www.ijfis.org/journal/download_pdf.php?doi=10.5391/IJFIS.2025.25.2.207","source":{"id":"https://openalex.org/S4210177700","display_name":"International Journal of Fuzzy Logic and Intelligent Systems","issn_l":"1598-2645","issn":["1598-2645","2093-744X"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4327628602","host_organization_name":"Korean Institute of Intelligent Systems","host_organization_lineage":["https://openalex.org/P4327628602"],"host_organization_lineage_names":["Korean Institute of Intelligent Systems"],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGENT SYSTEMS","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4412506334.pdf","grobid_xml":"https://content.openalex.org/works/W4412506334.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W2075832447","https://openalex.org/W4366779419","https://openalex.org/W4394884788","https://openalex.org/W4407402831","https://openalex.org/W4407423657","https://openalex.org/W4409251769","https://openalex.org/W4412506334","https://openalex.org/W6628075005"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W3022942420","https://openalex.org/W2012731963"],"abstract_inverted_index":{"Fuzzy":[0],"logic":[1],"is":[2,42,83,91,154],"used":[3],"to":[4,65,74,98,123],"address":[5],"the":[6,46,59,88,102,107,116,130,133,136,143,151],"undetermined":[7],"nature":[8],"of":[9,48,61,104,109,132,135,145],"most":[10,99],"graph-related":[11],"problems.Product":[12],"fuzzy":[13,50,55,63,111,140],"graphs":[14,51,64,112,141],"are":[15],"widely":[16],"applied":[17],"in":[18,53,96],"various":[19],"fields,":[20],"including":[21],"decision-making":[22],"theory,":[23],"computer":[24],"science,":[25],"psychology,":[26],"neurological":[27],"systems,":[28],"and":[29,70,115,118],"artificial":[30],"intelligence.In":[31],"this":[32,94],"study,":[33],"a":[34],"new":[35],"operation":[36,90],"for":[37,58,121],"product-fuzzy":[38],"graphs,":[39],"namely":[40],"\u03b3-product,":[41],"proposed.We":[43],"demonstrated":[44,128],"that":[45,87,129,150],"\u03b3product":[47],"two-product":[49,62],"results":[52],"product":[54,110,139],"graphs.Sufficient":[56],"conditions":[57,120],"\u03b3-product":[60,122,134],"be":[66,75,124],"strong":[67],"were":[68,72,126],"provided,":[69],"they":[71],"shown":[73],"complete":[76],"when":[77],"at":[78],"least":[79],"one":[80],"factor":[81],"graph":[82],"strong.Moreover,":[84],"we":[85,148],"proved":[86,149],"complement":[89],"distributive":[92],"over":[93],"product,":[95],"contrast":[97],"well-known":[100],"products.Furthermore,":[101],"concept":[103],"unbiasedness":[105],"within":[106],"class":[108],"was":[113],"explored,":[114],"necessary":[117],"sufficient":[119],"unbiased":[125,138,152],"established.We":[127],"density":[131,144],"two":[137],"equals":[142],"each":[146],"graph.Finally,":[147],"notion":[153],"retained":[155],"under":[156],"isomorphism.":[157]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}