{"id":"https://openalex.org/W3176662943","doi":"https://doi.org/10.1142/s1793005722500107","title":"Beta Products of Fuzzy Graphs with Application in Cryptography","display_name":"Beta Products of Fuzzy Graphs with Application in Cryptography","publication_year":2021,"publication_date":"2021-06-17","ids":{"openalex":"https://openalex.org/W3176662943","doi":"https://doi.org/10.1142/s1793005722500107","mag":"3176662943"},"language":"en","primary_location":{"id":"doi:10.1142/s1793005722500107","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793005722500107","pdf_url":null,"source":{"id":"https://openalex.org/S135331755","display_name":"New Mathematics and Natural Computation","issn_l":"1793-0057","issn":["1793-0057","1793-7027"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"New Mathematics and Natural Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5072356626","display_name":"R. A. Borzooei","orcid":"https://orcid.org/0000-0001-7538-7885"},"institutions":[{"id":"https://openalex.org/I48379061","display_name":"Shahid Beheshti University","ror":"https://ror.org/0091vmj44","country_code":"IR","type":"education","lineage":["https://openalex.org/I48379061"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"R. A. Borzooei","raw_affiliation_strings":["Department of Mathematics, Shahid Beheshti University, G. C., Tehran, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shahid Beheshti University, G. C., Tehran, Iran","institution_ids":["https://openalex.org/I48379061"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003004244","display_name":"B. Sheikh Hoseini","orcid":null},"institutions":[{"id":"https://openalex.org/I48379061","display_name":"Shahid Beheshti University","ror":"https://ror.org/0091vmj44","country_code":"IR","type":"education","lineage":["https://openalex.org/I48379061"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"B. Sheikh Hoseini","raw_affiliation_strings":["Department of Mathematics, Shahid Beheshti University, G. C., Tehran, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shahid Beheshti University, G. C., Tehran, Iran","institution_ids":["https://openalex.org/I48379061"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089205317","display_name":"Young Bae Jun","orcid":"https://orcid.org/0000-0002-0181-8969"},"institutions":[{"id":"https://openalex.org/I189442560","display_name":"Gyeongsang National University","ror":"https://ror.org/00saywf64","country_code":"KR","type":"education","lineage":["https://openalex.org/I189442560"]},{"id":"https://openalex.org/I48379061","display_name":"Shahid Beheshti University","ror":"https://ror.org/0091vmj44","country_code":"IR","type":"education","lineage":["https://openalex.org/I48379061"]}],"countries":["IR","KR"],"is_corresponding":false,"raw_author_name":"Y. B. Jun","raw_affiliation_strings":["Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea","Department of Mathematics, Shahid Beheshti University, G. C., Tehran, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea","institution_ids":["https://openalex.org/I189442560"]},{"raw_affiliation_string":"Department of Mathematics, Shahid Beheshti University, G. C., Tehran, Iran","institution_ids":["https://openalex.org/I48379061"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.10350647,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"18","issue":"01","first_page":"177","last_page":"194"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9373999834060669,"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":0.9373999834060669,"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/T13062","display_name":"Cognitive Computing and Networks","score":0.9240000247955322,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/complement","display_name":"Complement (music)","score":0.6406617164611816},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5974867939949036},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.5728909969329834},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5418949127197266},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.496277391910553},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4808143377304077},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4553457200527191},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.4543851613998413},{"id":"https://openalex.org/keywords/relation","display_name":"Relation (database)","score":0.4522666037082672},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44348815083503723},{"id":"https://openalex.org/keywords/beta","display_name":"BETA (programming language)","score":0.4295429587364197},{"id":"https://openalex.org/keywords/graph-product","display_name":"Graph product","score":0.42475077509880066},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.415315181016922},{"id":"https://openalex.org/keywords/object","display_name":"Object (grammar)","score":0.41283273696899414},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.3143773078918457},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.272164523601532},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.25027433037757874},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.24790367484092712},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.23314547538757324},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.13021063804626465}],"concepts":[{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.6406617164611816},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5974867939949036},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.5728909969329834},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5418949127197266},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.496277391910553},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4808143377304077},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4553457200527191},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.4543851613998413},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.4522666037082672},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44348815083503723},{"id":"https://openalex.org/C2776174256","wikidata":"https://www.wikidata.org/wiki/Q830842","display_name":"BETA (programming language)","level":2,"score":0.4295429587364197},{"id":"https://openalex.org/C68103157","wikidata":"https://www.wikidata.org/wiki/Q569347","display_name":"Graph product","level":5,"score":0.42475077509880066},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.415315181016922},{"id":"https://openalex.org/C2781238097","wikidata":"https://www.wikidata.org/wiki/Q175026","display_name":"Object (grammar)","level":2,"score":0.41283273696899414},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.3143773078918457},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.272164523601532},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.25027433037757874},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.24790367484092712},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.23314547538757324},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.13021063804626465},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C127716648","wikidata":"https://www.wikidata.org/wiki/Q104053","display_name":"Phenotype","level":3,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C188082640","wikidata":"https://www.wikidata.org/wiki/Q1780899","display_name":"Complementation","level":4,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s1793005722500107","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793005722500107","pdf_url":null,"source":{"id":"https://openalex.org/S135331755","display_name":"New Mathematics and Natural Computation","issn_l":"1793-0057","issn":["1793-0057","1793-7027"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"New Mathematics and Natural Computation","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:wsi:nmncxx:v:18:y:2022:i:01:n:s1793005722500107","is_oa":false,"landing_page_url":"http://www.worldscientific.com/doi/abs/10.1142/S1793005722500107","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1601092472","https://openalex.org/W1917557083","https://openalex.org/W2019529630","https://openalex.org/W2085238338","https://openalex.org/W2291770014","https://openalex.org/W2296563105","https://openalex.org/W2337721806","https://openalex.org/W2489172749","https://openalex.org/W2502697445","https://openalex.org/W2514450050","https://openalex.org/W3045598505","https://openalex.org/W3190616568","https://openalex.org/W4211007335","https://openalex.org/W4234428270","https://openalex.org/W4235644068","https://openalex.org/W4240330936","https://openalex.org/W4285088909"],"related_works":["https://openalex.org/W2382566571","https://openalex.org/W2349321798","https://openalex.org/W2366686860","https://openalex.org/W2350859087","https://openalex.org/W1486684451","https://openalex.org/W4361273540","https://openalex.org/W2099285375","https://openalex.org/W2801459815","https://openalex.org/W4361984403","https://openalex.org/W4317826560"],"abstract_inverted_index":{"Fuzzy":[0],"graph":[1,32],"theory":[2],"is":[3,94],"finding":[4],"an":[5,88],"increasing":[6],"number":[7],"of":[8,18,28,53,56,59,65,70,74,103],"application":[9,89],"in":[10,21],"modeling":[11],"real":[12],"time":[13],"systems":[14],"where":[15],"the":[16,22,42,51,86,99],"level":[17],"information":[19],"inherent":[20],"system":[23],"varies":[24],"with":[25,90],"different":[26],"levels":[27],"precision.":[29],"Special":[30],"fuzzy":[31,39,61,76,104],"can":[33],"be":[34,97],"obtained":[35],"from":[36],"two":[37,60,75],"given":[38],"graphs":[40,77],"using":[41,98],"operations":[43],"beta":[44,57],"products.":[45],"In":[46],"this":[47],"paper,":[48],"we":[49],"introduce":[50],"notions":[52],"some":[54],"kinds":[55],"product":[58],"graphs.":[62,105],"The":[63],"concept":[64],"strong,":[66],"regular":[67],"and":[68,78],"complement":[69],"[Formula:":[71,100],"see":[72,101],"text]-product":[73,102],"relation":[79],"between":[80],"them":[81],"are":[82],"also":[83],"obtained.":[84],"At":[85],"end,":[87],"a":[91],"cryptographic":[92],"object":[93],"said":[95],"to":[96]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
