{"id":"https://openalex.org/W2953160093","doi":"https://doi.org/10.3233/jifs-181941","title":"Spherical fuzzy sets and its representation of spherical fuzzy t-norms and t-conorms","display_name":"Spherical fuzzy sets and its representation of spherical fuzzy t-norms and t-conorms","publication_year":2019,"publication_date":"2019-06-11","ids":{"openalex":"https://openalex.org/W2953160093","doi":"https://doi.org/10.3233/jifs-181941","mag":"2953160093"},"language":"en","primary_location":{"id":"doi:10.3233/jifs-181941","is_oa":false,"landing_page_url":"https://doi.org/10.3233/jifs-181941","pdf_url":null,"source":{"id":"https://openalex.org/S179157397","display_name":"Journal of Intelligent & Fuzzy Systems","issn_l":"1064-1246","issn":["1064-1246","1875-8967"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Intelligent &amp; Fuzzy Systems","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/A5065100059","display_name":"Shahzaib Ashraf","orcid":"https://orcid.org/0000-0002-8616-8829"},"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":"Shahzaib Ashraf","raw_affiliation_strings":["Department of Mathematics, Abdul Wali Khan University, Mardan, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Abdul Wali Khan University, Mardan, Pakistan","institution_ids":["https://openalex.org/I181063083"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077817609","display_name":"Saleem Abdullah","orcid":"https://orcid.org/0000-0002-7474-5115"},"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":true,"raw_author_name":"Saleem Abdullah","raw_affiliation_strings":["Department of Mathematics, Abdul Wali Khan University, Mardan, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Abdul Wali Khan University, Mardan, Pakistan","institution_ids":["https://openalex.org/I181063083"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033770251","display_name":"Muhammad Aslam","orcid":"https://orcid.org/0000-0002-6443-4962"},"institutions":[{"id":"https://openalex.org/I82952536","display_name":"King Khalid University","ror":"https://ror.org/052kwzs30","country_code":"SA","type":"education","lineage":["https://openalex.org/I82952536"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Muhammad Aslam","raw_affiliation_strings":["Department of Mathematics, King Khalid University, Abha, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, King Khalid University, Abha, Saudi Arabia","institution_ids":["https://openalex.org/I82952536"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049847865","display_name":"Muhammad Qiyas","orcid":"https://orcid.org/0000-0002-5519-6130"},"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 Qiyas","raw_affiliation_strings":["Department of Mathematics, Abdul Wali Khan University, Mardan, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Abdul Wali Khan University, Mardan, Pakistan","institution_ids":["https://openalex.org/I181063083"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5077345013","display_name":"Marwan Amin Kutbi","orcid":"https://orcid.org/0000-0001-9001-7495"},"institutions":[{"id":"https://openalex.org/I185163786","display_name":"King Abdulaziz University","ror":"https://ror.org/02ma4wv74","country_code":"SA","type":"education","lineage":["https://openalex.org/I185163786"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Marwan A. Kutbi","raw_affiliation_strings":["Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia","institution_ids":["https://openalex.org/I185163786"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5077817609"],"corresponding_institution_ids":["https://openalex.org/I181063083"],"apc_list":null,"apc_paid":null,"fwci":17.7362,"has_fulltext":false,"cited_by_count":156,"citation_normalized_percentile":{"value":0.99424111,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"36","issue":"6","first_page":"6089","last_page":"6102"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9994999766349792,"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":0.9994999766349792,"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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9484000205993652,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.9326000213623047,"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/fuzzy-logic","display_name":"Fuzzy logic","score":0.6616188883781433},{"id":"https://openalex.org/keywords/fuzzy-set-operations","display_name":"Fuzzy set operations","score":0.6003553867340088},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5873662829399109},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.5713513493537903},{"id":"https://openalex.org/keywords/fuzzy-classification","display_name":"Fuzzy classification","score":0.5032767653465271},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.48594939708709717},{"id":"https://openalex.org/keywords/fuzzy-mathematics","display_name":"Fuzzy mathematics","score":0.46825844049453735},{"id":"https://openalex.org/keywords/defuzzification","display_name":"Defuzzification","score":0.44425323605537415},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.4420166313648224},{"id":"https://openalex.org/keywords/ranking","display_name":"Ranking (information retrieval)","score":0.440761923789978},{"id":"https://openalex.org/keywords/fuzzy-subalgebra","display_name":"Fuzzy subalgebra","score":0.4232231378555298},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.38529810309410095},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.3698485791683197},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.35855549573898315},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3516038656234741},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.29921436309814453}],"concepts":[{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.6616188883781433},{"id":"https://openalex.org/C148671577","wikidata":"https://www.wikidata.org/wiki/Q5511133","display_name":"Fuzzy set operations","level":4,"score":0.6003553867340088},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5873662829399109},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.5713513493537903},{"id":"https://openalex.org/C127385683","wikidata":"https://www.wikidata.org/wiki/Q1475696","display_name":"Fuzzy classification","level":4,"score":0.5032767653465271},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.48594939708709717},{"id":"https://openalex.org/C166586474","wikidata":"https://www.wikidata.org/wiki/Q5511129","display_name":"Fuzzy mathematics","level":5,"score":0.46825844049453735},{"id":"https://openalex.org/C170260401","wikidata":"https://www.wikidata.org/wiki/Q5251735","display_name":"Defuzzification","level":5,"score":0.44425323605537415},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4420166313648224},{"id":"https://openalex.org/C189430467","wikidata":"https://www.wikidata.org/wiki/Q7293293","display_name":"Ranking (information retrieval)","level":2,"score":0.440761923789978},{"id":"https://openalex.org/C115740575","wikidata":"https://www.wikidata.org/wiki/Q5511136","display_name":"Fuzzy subalgebra","level":5,"score":0.4232231378555298},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.38529810309410095},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.3698485791683197},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35855549573898315},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3516038656234741},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.29921436309814453},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3233/jifs-181941","is_oa":false,"landing_page_url":"https://doi.org/10.3233/jifs-181941","pdf_url":null,"source":{"id":"https://openalex.org/S179157397","display_name":"Journal of Intelligent & Fuzzy Systems","issn_l":"1064-1246","issn":["1064-1246","1875-8967"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Intelligent &amp; Fuzzy Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.5400000214576721}],"awards":[],"funders":[{"id":"https://openalex.org/F4320324433","display_name":"King Khalid University","ror":"https://ror.org/052kwzs30"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1505735190","https://openalex.org/W1845000206","https://openalex.org/W1980564456","https://openalex.org/W2004986935","https://openalex.org/W2013932252","https://openalex.org/W2087819648","https://openalex.org/W2131429285","https://openalex.org/W2248217189","https://openalex.org/W2385257316","https://openalex.org/W2507500447","https://openalex.org/W2624112931","https://openalex.org/W2767160721","https://openalex.org/W2815079924","https://openalex.org/W2896141939","https://openalex.org/W2897088503","https://openalex.org/W2898322660","https://openalex.org/W2901104715","https://openalex.org/W2965653711","https://openalex.org/W4211007335","https://openalex.org/W6645914205","https://openalex.org/W6766541553"],"related_works":["https://openalex.org/W2253053392","https://openalex.org/W2331106272","https://openalex.org/W1542808721","https://openalex.org/W2674573885","https://openalex.org/W3176863924","https://openalex.org/W2325893522","https://openalex.org/W2037428035","https://openalex.org/W1489009679","https://openalex.org/W2466052371","https://openalex.org/W2586653035"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"introduce":[4],"spherical":[5,44,60,64,71,78,82,98],"fuzzy":[6,16,19,23,39,61,65,72,79,83,99],"sets":[7,20],"(SFSs)":[8],"which":[9,87],"is":[10,108],"an":[11],"advanced":[12],"tool":[13],"of":[14,30,43,77,120],"the":[15,27,34,92,97,116,121],"sets,":[17],"intuitionistic":[18],"and":[21,32,47,63,74,81,118],"picture":[22,38,48],"sets.":[24,40],"We":[25],"investigate":[26],"basic":[28],"properties":[29],"SFSs":[31,36],"compare":[33],"idea":[35],"with":[37],"The":[41],"spaces":[42],"membership":[45,49],"grades":[46,50],"are":[51,67,88],"examined":[52],"by":[53],"graphically.":[54],"Some":[55],"useful":[56,89],"operation":[57],"such":[58],"as":[59,110],"t\u2019-norms":[62,80],"t\u2019-conorms":[66],"introduced.":[68],"Also":[69],"introduced":[70],"negator":[73],"some":[75],"classifications":[76],"t":[84],"\u2032":[85],"-conorms":[86],"for":[90],"development":[91],"aggregation":[93],"operator":[94],"to":[95,114],"aggregate":[96],"information.":[100],"Finally,":[101],"a":[102,111],"food":[103],"circulation":[104],"center":[105],"evaluation":[106],"problem":[107],"given":[109],"practical":[112],"application":[113],"demonstrate":[115],"usage":[117],"applicability":[119],"proposed":[122],"ranking":[123],"approach.":[124]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":13},{"year":2024,"cited_by_count":21},{"year":2023,"cited_by_count":33},{"year":2022,"cited_by_count":27},{"year":2021,"cited_by_count":32},{"year":2020,"cited_by_count":23},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-11T08:14:18.477133","created_date":"2025-10-10T00:00:00"}
