{"id":"https://openalex.org/W3208033595","doi":"https://doi.org/10.1142/s1793005722500399","title":"Double-Framed Soft Set Theory Applied to Abel-Grassmann\u2019s Hypergroupoids","display_name":"Double-Framed Soft Set Theory Applied to Abel-Grassmann\u2019s Hypergroupoids","publication_year":2021,"publication_date":"2021-10-25","ids":{"openalex":"https://openalex.org/W3208033595","doi":"https://doi.org/10.1142/s1793005722500399","mag":"3208033595"},"language":"en","primary_location":{"id":"doi:10.1142/s1793005722500399","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793005722500399","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/A5102762851","display_name":"Muhammad Izhar","orcid":null},"institutions":[{"id":"https://openalex.org/I2802999120","display_name":"Government of Khyber Pakhtunkhwa","ror":"https://ror.org/04zyfmb02","country_code":"PK","type":"government","lineage":["https://openalex.org/I2802999120"]}],"countries":["PK"],"is_corresponding":true,"raw_author_name":"Muhammad Izhar","raw_affiliation_strings":["Department of Mathematics, Government College Garhi Kapura Mardan, Khyber Pakhtunkhwa Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Government College Garhi Kapura Mardan, Khyber Pakhtunkhwa Pakistan","institution_ids":["https://openalex.org/I2802999120"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100646949","display_name":"Tariq Mahmood","orcid":"https://orcid.org/0000-0002-4192-976X"},"institutions":[{"id":"https://openalex.org/I173207729","display_name":"University of Engineering and Technology Taxila","ror":"https://ror.org/03v00ka07","country_code":"PK","type":"education","lineage":["https://openalex.org/I173207729"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Tariq Mahmood","raw_affiliation_strings":["Department of Basic Sciences, University of Engineering and Technology, Taxila, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Basic Sciences, University of Engineering and Technology, Taxila, Pakistan","institution_ids":["https://openalex.org/I173207729"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080324586","display_name":"Asghar Khan","orcid":"https://orcid.org/0000-0002-6846-662X"},"institutions":[{"id":"https://openalex.org/I181063083","display_name":"Abdul Wali Khan University Mardan","ror":"https://ror.org/03b9y4e65","country_code":"PK","type":"education","lineage":["https://openalex.org/I181063083"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Asghar Khan","raw_affiliation_strings":["Department of Mathematics, Abdul Wali Khan, University Mardan, Khyber Pakhtunkhwa Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Abdul Wali Khan, University Mardan, Khyber Pakhtunkhwa Pakistan","institution_ids":["https://openalex.org/I181063083"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052791434","display_name":"Muhammad Shoaib Farooq","orcid":"https://orcid.org/0000-0003-3263-2646"},"institutions":[{"id":"https://openalex.org/I181063083","display_name":"Abdul Wali Khan University Mardan","ror":"https://ror.org/03b9y4e65","country_code":"PK","type":"education","lineage":["https://openalex.org/I181063083"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Muhammad Farooq","raw_affiliation_strings":["Department of Mathematics, Abdul Wali Khan, University Mardan, Khyber Pakhtunkhwa Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Abdul Wali Khan, University Mardan, Khyber Pakhtunkhwa Pakistan","institution_ids":["https://openalex.org/I181063083"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056996250","display_name":"Kostaq Hila","orcid":"https://orcid.org/0000-0001-6425-2619"},"institutions":[{"id":"https://openalex.org/I193184871","display_name":"Polytechnic University of Tirana","ror":"https://ror.org/05aec4025","country_code":"AL","type":"education","lineage":["https://openalex.org/I193184871"]}],"countries":["AL"],"is_corresponding":false,"raw_author_name":"Kostaq Hila","raw_affiliation_strings":["Department of Mathematical Engineering, Polytechnic University of Tirana, Tirana, Albania"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Engineering, Polytechnic University of Tirana, Tirana, Albania","institution_ids":["https://openalex.org/I193184871"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5102762851"],"corresponding_institution_ids":["https://openalex.org/I2802999120"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.18567722,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"18","issue":"03","first_page":"819","last_page":"841"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9995999932289124,"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/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9995999932289124,"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/converse","display_name":"Converse","score":0.8444938063621521},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7999083995819092},{"id":"https://openalex.org/keywords/idempotence","display_name":"Idempotence","score":0.7567727565765381},{"id":"https://openalex.org/keywords/distributed-file-system","display_name":"Distributed File System","score":0.5670122504234314},{"id":"https://openalex.org/keywords/identity","display_name":"Identity (music)","score":0.5323501229286194},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4610506594181061},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4332064688205719},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3285330533981323},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1085602343082428},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10197767615318298},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09522536396980286}],"concepts":[{"id":"https://openalex.org/C2776809875","wikidata":"https://www.wikidata.org/wiki/Q1375963","display_name":"Converse","level":2,"score":0.8444938063621521},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7999083995819092},{"id":"https://openalex.org/C172252984","wikidata":"https://www.wikidata.org/wiki/Q368988","display_name":"Idempotence","level":2,"score":0.7567727565765381},{"id":"https://openalex.org/C152043487","wikidata":"https://www.wikidata.org/wiki/Q1229600","display_name":"Distributed File System","level":2,"score":0.5670122504234314},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.5323501229286194},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4610506594181061},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4332064688205719},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3285330533981323},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1085602343082428},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10197767615318298},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09522536396980286},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s1793005722500399","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793005722500399","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:03:n:s1793005722500399","is_oa":false,"landing_page_url":"http://www.worldscientific.com/doi/abs/10.1142/S1793005722500399","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1738545251","https://openalex.org/W1748328170","https://openalex.org/W2008528778","https://openalex.org/W2044303848","https://openalex.org/W2083296236","https://openalex.org/W2129989425","https://openalex.org/W2495083845","https://openalex.org/W2597159815","https://openalex.org/W2889824763","https://openalex.org/W2950263178","https://openalex.org/W2972258955","https://openalex.org/W3023953025","https://openalex.org/W4206343787","https://openalex.org/W4240955797","https://openalex.org/W4246113444","https://openalex.org/W4255695749"],"related_works":["https://openalex.org/W2753380948","https://openalex.org/W2330050861","https://openalex.org/W2332136239","https://openalex.org/W2952544681","https://openalex.org/W2376429153","https://openalex.org/W2064847051","https://openalex.org/W2046049376","https://openalex.org/W3106133691","https://openalex.org/W3208033595","https://openalex.org/W1549646924"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"apply":[4],"the":[5,64],"concept":[6],"of":[7,33,74],"double-framed":[8,17,23],"soft":[9,18,24],"sets":[10],"to":[11,60],"Abel-Grassmann\u2019s":[12],"hypergroupoids":[13],"(AG-hypergroupoids).":[14],"We":[15,69],"define":[16],"AG-hypergroupoids":[19],"(DFS":[20],"AG-hypergroupoids)":[21],"and":[22],"left":[25,56],"(respectively,":[26,30],"right)":[27],"(briefly":[28],"DFS-left":[29,41],"DFS-right))":[31],"hyperideals":[32,76],"AG-hypergroupoids.":[34,79],"It":[35],"is":[36,43,58,66],"shown":[37],"that":[38],"an":[39,61],"idempotent":[40],"hyperideal":[42,50,53],"a":[44,47],"DFS-hyperideal.":[45],"Also":[46],"DFS":[48,52],"right":[49],"becomes":[51],"when":[54],"pure":[55],"identity":[57],"adjoined":[59],"AG-hypergroupoid,":[62],"but":[63],"converse":[65],"not":[67],"true.":[68],"also":[70],"discuss":[71],"some":[72],"properties":[73],"these":[75],"in":[77],"regular":[78]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
