{"id":"https://openalex.org/W4324057131","doi":"https://doi.org/10.3390/sym15030697","title":"A Detailed Study of Mathematical Rings in q-Rung Orthopair Fuzzy Framework","display_name":"A Detailed Study of Mathematical Rings in q-Rung Orthopair Fuzzy Framework","publication_year":2023,"publication_date":"2023-03-10","ids":{"openalex":"https://openalex.org/W4324057131","doi":"https://doi.org/10.3390/sym15030697"},"language":"en","primary_location":{"id":"doi:10.3390/sym15030697","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15030697","pdf_url":"https://www.mdpi.com/2073-8994/15/3/697/pdf?version=1678687061","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/15/3/697/pdf?version=1678687061","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055955473","display_name":"Asima Razzaque","orcid":"https://orcid.org/0000-0002-7579-8972"},"institutions":[{"id":"https://openalex.org/I4626487","display_name":"King Faisal University","ror":"https://ror.org/00dn43547","country_code":"SA","type":"education","lineage":["https://openalex.org/I4626487"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"Asima Razzaque","raw_affiliation_strings":["Department of Basic Sciences, Deanship of Preparatory Year, King Faisal University, Al Ahsa Hofuf 31982, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0002-7579-8972","affiliations":[{"raw_affiliation_string":"Department of Basic Sciences, Deanship of Preparatory Year, King Faisal University, Al Ahsa Hofuf 31982, Saudi Arabia","institution_ids":["https://openalex.org/I4626487"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002237072","display_name":"Abdul Razaq","orcid":"https://orcid.org/0000-0002-1898-4082"},"institutions":[{"id":"https://openalex.org/I3130814776","display_name":"University of Okara","ror":"https://ror.org/02fmg6q11","country_code":"PK","type":"education","lineage":["https://openalex.org/I3130814776"]},{"id":"https://openalex.org/I5100685","display_name":"University of Education","ror":"https://ror.org/052z7nw84","country_code":"PK","type":"education","lineage":["https://openalex.org/I5100685"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Abdul Razaq","raw_affiliation_strings":["Department of Mathematics, Division of Science and Technology, University of Education, Lahore 54770, Pakistan"],"raw_orcid":"https://orcid.org/0000-0002-1898-4082","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Division of Science and Technology, University of Education, Lahore 54770, Pakistan","institution_ids":["https://openalex.org/I3130814776","https://openalex.org/I5100685"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056160727","display_name":"Ghaliah Alhamzi","orcid":"https://orcid.org/0000-0002-9146-7145"},"institutions":[{"id":"https://openalex.org/I240666556","display_name":"Imam Mohammad ibn Saud Islamic University","ror":"https://ror.org/05gxjyb39","country_code":"SA","type":"education","lineage":["https://openalex.org/I240666556"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Ghaliah Alhamzi","raw_affiliation_strings":["Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11564, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11564, Saudi Arabia","institution_ids":["https://openalex.org/I240666556"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054194585","display_name":"Harish Garg","orcid":"https://orcid.org/0000-0001-9099-8422"},"institutions":[{"id":"https://openalex.org/I146367977","display_name":"Applied Science Private University","ror":"https://ror.org/01ah6nb52","country_code":"JO","type":"education","lineage":["https://openalex.org/I146367977"]},{"id":"https://openalex.org/I162030827","display_name":"Thapar Institute of Engineering & Technology","ror":"https://ror.org/00wdq3744","country_code":"IN","type":"education","lineage":["https://openalex.org/I162030827"]},{"id":"https://openalex.org/I3131779051","display_name":"Iraqi University","ror":"https://ror.org/01wfhkb67","country_code":"IQ","type":"education","lineage":["https://openalex.org/I3131779051"]},{"id":"https://openalex.org/I4405259362","display_name":"Islamic University of Najaf","ror":"https://ror.org/024dzaa63","country_code":"IQ","type":"education","lineage":["https://openalex.org/I4405259362"]},{"id":"https://openalex.org/I60054993","display_name":"Graphic Era University","ror":"https://ror.org/03wqgqd89","country_code":"IN","type":"education","lineage":["https://openalex.org/I60054993"]}],"countries":["IN","IQ","JO"],"is_corresponding":true,"raw_author_name":"Harish Garg","raw_affiliation_strings":["Applied Science Research Center, Applied Science Private University, Amman 11931, Jordan","College of Technical Engineering, The Islamic University, Najaf 54001, Iraq","Department of Mathematics, Graphic Era Deemed to Be University, Dehradun 248002, Uttarakhand, India","School of Mathematics, Thapar Institute of Engineering & Technology, Deemed University, Patiala 147004, Punjab, India"],"raw_orcid":"https://orcid.org/0000-0001-9099-8422","affiliations":[{"raw_affiliation_string":"Applied Science Research Center, Applied Science Private University, Amman 11931, Jordan","institution_ids":["https://openalex.org/I146367977"]},{"raw_affiliation_string":"College of Technical Engineering, The Islamic University, Najaf 54001, Iraq","institution_ids":["https://openalex.org/I3131779051","https://openalex.org/I4405259362"]},{"raw_affiliation_string":"Department of Mathematics, Graphic Era Deemed to Be University, Dehradun 248002, Uttarakhand, India","institution_ids":["https://openalex.org/I60054993"]},{"raw_affiliation_string":"School of Mathematics, Thapar Institute of Engineering & Technology, Deemed University, Patiala 147004, Punjab, India","institution_ids":["https://openalex.org/I162030827"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020843278","display_name":"Muhammad Iftikhar Faraz","orcid":"https://orcid.org/0000-0002-5761-9467"},"institutions":[{"id":"https://openalex.org/I4626487","display_name":"King Faisal University","ror":"https://ror.org/00dn43547","country_code":"SA","type":"education","lineage":["https://openalex.org/I4626487"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Muhammad Iftikhar Faraz","raw_affiliation_strings":["College of Mechanical Engineering, King Faisal University, Al-Ahsa Hofuf 31982, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mechanical Engineering, King Faisal University, Al-Ahsa Hofuf 31982, Saudi Arabia","institution_ids":["https://openalex.org/I4626487"]}]}],"institutions":[],"countries_distinct_count":5,"institutions_distinct_count":9,"corresponding_author_ids":["https://openalex.org/A5054194585","https://openalex.org/A5055955473"],"corresponding_institution_ids":["https://openalex.org/I146367977","https://openalex.org/I162030827","https://openalex.org/I3131779051","https://openalex.org/I4405259362","https://openalex.org/I4626487","https://openalex.org/I60054993"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":1.9743,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.85885289,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"15","issue":"3","first_page":"697","last_page":"697"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9984999895095825,"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":0.9984999895095825,"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/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9980999827384949,"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/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.9958999752998352,"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/homomorphism","display_name":"Homomorphism","score":0.6503774523735046},{"id":"https://openalex.org/keywords/ring","display_name":"Ring (chemistry)","score":0.5848376750946045},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5707414150238037},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5210177898406982},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.4874260723590851},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.46759718656539917},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4211379289627075},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4017460346221924},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23285076022148132}],"concepts":[{"id":"https://openalex.org/C4042151","wikidata":"https://www.wikidata.org/wiki/Q215111","display_name":"Homomorphism","level":2,"score":0.6503774523735046},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.5848376750946045},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5707414150238037},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5210177898406982},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.4874260723590851},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46759718656539917},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4211379289627075},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4017460346221924},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23285076022148132},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"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":3,"locations":[{"id":"doi:10.3390/sym15030697","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15030697","pdf_url":"https://www.mdpi.com/2073-8994/15/3/697/pdf?version=1678687061","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:8157b0c018f044d99d1116b81eefd294","is_oa":false,"landing_page_url":"https://doaj.org/article/8157b0c018f044d99d1116b81eefd294","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":"Symmetry, Vol 15, Iss 3, p 697 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/15/3/697/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym15030697","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry; Volume 15; Issue 3; Pages: 697","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym15030697","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15030697","pdf_url":"https://www.mdpi.com/2073-8994/15/3/697/pdf?version=1678687061","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4324057131.pdf"},"referenced_works_count":45,"referenced_works":["https://openalex.org/W111239304","https://openalex.org/W1543040129","https://openalex.org/W1971850040","https://openalex.org/W1972723563","https://openalex.org/W1975725196","https://openalex.org/W1980564456","https://openalex.org/W1983603730","https://openalex.org/W2004634249","https://openalex.org/W2024213525","https://openalex.org/W2034998024","https://openalex.org/W2036632353","https://openalex.org/W2044315800","https://openalex.org/W2055487540","https://openalex.org/W2069269408","https://openalex.org/W2079457935","https://openalex.org/W2091650058","https://openalex.org/W2100579677","https://openalex.org/W2514754342","https://openalex.org/W2799561996","https://openalex.org/W2805477634","https://openalex.org/W2902568446","https://openalex.org/W2912392110","https://openalex.org/W2913554400","https://openalex.org/W2913689958","https://openalex.org/W2947554262","https://openalex.org/W2990758628","https://openalex.org/W2999352603","https://openalex.org/W3033057870","https://openalex.org/W3134082691","https://openalex.org/W3135529646","https://openalex.org/W3169916055","https://openalex.org/W3190370251","https://openalex.org/W3191027913","https://openalex.org/W3200104522","https://openalex.org/W3200407878","https://openalex.org/W3201063394","https://openalex.org/W3208067371","https://openalex.org/W3216781731","https://openalex.org/W4200128973","https://openalex.org/W4229078348","https://openalex.org/W4242007632","https://openalex.org/W4288070246","https://openalex.org/W4293104829","https://openalex.org/W4311531011","https://openalex.org/W6604556291"],"related_works":["https://openalex.org/W4308159138","https://openalex.org/W4327811209","https://openalex.org/W1979798674","https://openalex.org/W3169947911","https://openalex.org/W2914794208","https://openalex.org/W3037616202","https://openalex.org/W2963079901","https://openalex.org/W390508480","https://openalex.org/W2294450783","https://openalex.org/W2375240985"],"abstract_inverted_index":{"Symmetry-related":[0],"problems":[1],"can":[2,13],"be":[3,14],"addressed":[4,75],"by":[5,77],"means":[6],"of":[7,19,38,44,53,60,66,87,114,120,132,135,149,153,161,173],"group":[8,21],"theory,":[9,24],"and":[10,48,90,104,123,168],"ring":[11,88,154],"theory":[12,59,89],"seen":[15],"as":[16],"an":[17],"extension":[18],"additive":[20],"theory.":[22,50],"Ring":[23],"a":[25,35,63,121,136,139,145,170],"significant":[26],"topic":[27],"in":[28,34,62,71,101],"abstract":[29],"algebra,":[30],"is":[31,55],"currently":[32],"active":[33],"diverse":[36],"range":[37,65],"study":[39,52],"domains":[40],"across":[41],"the":[42,58,72,78,85,91,112,130,150,159],"disciplines":[43],"mathematics,":[45],"theoretical":[46],"physics":[47],"coding":[49],"The":[51,68],"ideals":[54,99,166],"vital":[56],"to":[57],"rings":[61,103,180],"wide":[64],"ways.":[67],"uncertainties":[69],"present":[70,158],"information":[73],"are":[74],"well":[76],"q-rung":[79,96,115,146,162],"orthopair":[80,97,116,147,163],"fuzzy":[81,98,117,164],"set":[82],"(q-ROFS).":[83],"Considering":[84],"significance":[86],"q-ROFS,":[92],"this":[93],"article":[94],"defines":[95],"(q-ROFIs)":[100],"conventional":[102],"investigates":[105],"its":[106],"various":[107],"algebraic":[108,176],"features.":[109],"We":[110],"introduce":[111],"notion":[113,160],"cosets":[118],"(q-ROFCs)":[119],"q-ROFI":[122,137],"demonstrate":[124],"that,":[125],"under":[126],"certain":[127],"binary":[128],"operations,":[129],"collection":[131],"all":[133],"q-ROFCs":[134],"forms":[138],"ring.":[140],"In":[141],"addition,":[142],"we":[143,157],"provide":[144,169],"analog":[148],"fundamental":[151],"theorem":[152],"homomorphism.":[155],"Furthermore,":[156],"semi-prime":[165],"(q-ROFSPIs)":[167],"comprehensive":[171],"explanation":[172],"their":[174],"many":[175],"properties.":[177],"Finally,":[178],"regular":[179],"were":[181],"characterized":[182],"using":[183],"q-ROFIs.":[184]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
