{"id":"https://openalex.org/W4313472543","doi":"https://doi.org/10.3390/sym15010085","title":"Multi-Criteria Decision-Making Method Based on Complex t-Spherical Fuzzy Aczel\u2013Alsina Aggregation Operators and Their Application","display_name":"Multi-Criteria Decision-Making Method Based on Complex t-Spherical Fuzzy Aczel\u2013Alsina Aggregation Operators and Their Application","publication_year":2022,"publication_date":"2022-12-28","ids":{"openalex":"https://openalex.org/W4313472543","doi":"https://doi.org/10.3390/sym15010085"},"language":"en","primary_location":{"id":"doi:10.3390/sym15010085","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15010085","pdf_url":"https://www.mdpi.com/2073-8994/15/1/85/pdf?version=1672965350","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/2073-8994/15/1/85/pdf?version=1672965350","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055782027","display_name":"Jawad Ali","orcid":"https://orcid.org/0000-0002-3372-0034"},"institutions":[{"id":"https://openalex.org/I178777954","display_name":"Kohat University of Science and Technology","ror":"https://ror.org/057d2v504","country_code":"PK","type":"education","lineage":["https://openalex.org/I178777954"]}],"countries":["PK"],"is_corresponding":true,"raw_author_name":"Jawad Ali","raw_affiliation_strings":["Institute of Numerical Sciences, Kohat University of Science and Technology, Kohat 26000, KPK, Pakistan"],"raw_orcid":"https://orcid.org/0000-0002-3372-0034","affiliations":[{"raw_affiliation_string":"Institute of Numerical Sciences, Kohat University of Science and Technology, Kohat 26000, KPK, Pakistan","institution_ids":["https://openalex.org/I178777954"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034707465","display_name":"Muhammad Naeem","orcid":"https://orcid.org/0000-0003-4755-9381"},"institutions":[{"id":"https://openalex.org/I199693650","display_name":"Umm al-Qura University","ror":"https://ror.org/01xjqrm90","country_code":"SA","type":"education","lineage":["https://openalex.org/I199693650"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"Muhammad Naeem","raw_affiliation_strings":["Department of Mathematics, Deanship of Applied Sciences, Umm Al-Qura University, Makkah 24231, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Deanship of Applied Sciences, Umm Al-Qura University, Makkah 24231, Saudi Arabia","institution_ids":["https://openalex.org/I199693650"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5034707465","https://openalex.org/A5055782027"],"corresponding_institution_ids":["https://openalex.org/I178777954","https://openalex.org/I199693650"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":2.8707,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.91352564,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":99},"biblio":{"volume":"15","issue":"1","first_page":"85","last_page":"85"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9998000264167786,"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":0.9998000264167786,"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/T12709","display_name":"Optimization and Mathematical Programming","score":0.9853000044822693,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13058","display_name":"Soil and Land Suitability Analysis","score":0.9847000241279602,"subfield":{"id":"https://openalex.org/subfields/2308","display_name":"Management, Monitoring, Policy and Law"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental 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":0.6032148599624634},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5385985970497131},{"id":"https://openalex.org/keywords/scalar-multiplication","display_name":"Scalar multiplication","score":0.49841880798339844},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.44982028007507324},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.4263969361782074},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42266520857810974},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.4161027669906616},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4093296229839325},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.39136800169944763},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.380353182554245},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.22038325667381287},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08996361494064331}],"concepts":[{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.6032148599624634},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5385985970497131},{"id":"https://openalex.org/C171182647","wikidata":"https://www.wikidata.org/wiki/Q126736","display_name":"Scalar multiplication","level":3,"score":0.49841880798339844},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.44982028007507324},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.4263969361782074},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42266520857810974},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.4161027669906616},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4093296229839325},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.39136800169944763},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.380353182554245},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.22038325667381287},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08996361494064331},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym15010085","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15010085","pdf_url":"https://www.mdpi.com/2073-8994/15/1/85/pdf?version=1672965350","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:b03bcb561664403382f90edd0ad71f7a","is_oa":false,"landing_page_url":"https://doaj.org/article/b03bcb561664403382f90edd0ad71f7a","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 1, p 85 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/15/1/85/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym15010085","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","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym15010085","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15010085","pdf_url":"https://www.mdpi.com/2073-8994/15/1/85/pdf?version=1672965350","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":[{"score":0.8100000023841858,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4313472543.pdf"},"referenced_works_count":65,"referenced_works":["https://openalex.org/W1969882757","https://openalex.org/W1980564456","https://openalex.org/W2012575173","https://openalex.org/W2038050603","https://openalex.org/W2079457935","https://openalex.org/W2092580384","https://openalex.org/W2097403045","https://openalex.org/W2514754342","https://openalex.org/W2578456536","https://openalex.org/W2754849094","https://openalex.org/W2789682920","https://openalex.org/W2804105936","https://openalex.org/W2871390967","https://openalex.org/W2883333523","https://openalex.org/W2892128625","https://openalex.org/W2903466805","https://openalex.org/W2912231494","https://openalex.org/W2940364126","https://openalex.org/W2945404912","https://openalex.org/W2953949208","https://openalex.org/W2963817324","https://openalex.org/W2974202854","https://openalex.org/W2995542036","https://openalex.org/W3006111734","https://openalex.org/W3047313007","https://openalex.org/W3085706381","https://openalex.org/W3087450306","https://openalex.org/W3092086320","https://openalex.org/W3092966490","https://openalex.org/W3097352379","https://openalex.org/W3097841884","https://openalex.org/W3106666892","https://openalex.org/W3118818955","https://openalex.org/W3121700030","https://openalex.org/W3139437306","https://openalex.org/W3152967177","https://openalex.org/W3155690611","https://openalex.org/W3172074980","https://openalex.org/W3174694819","https://openalex.org/W3182424782","https://openalex.org/W3197745065","https://openalex.org/W3201566509","https://openalex.org/W3204698454","https://openalex.org/W3206013364","https://openalex.org/W3214620214","https://openalex.org/W3217106012","https://openalex.org/W3217511497","https://openalex.org/W4200146675","https://openalex.org/W4206318007","https://openalex.org/W4206537762","https://openalex.org/W4211007335","https://openalex.org/W4213029788","https://openalex.org/W4214579779","https://openalex.org/W4214837472","https://openalex.org/W4220703325","https://openalex.org/W4224285720","https://openalex.org/W4226075824","https://openalex.org/W4281615235","https://openalex.org/W4283029080","https://openalex.org/W4290712395","https://openalex.org/W4299417699","https://openalex.org/W4309474360","https://openalex.org/W6645914205","https://openalex.org/W6806227516","https://openalex.org/W6810463066"],"related_works":["https://openalex.org/W2034604290","https://openalex.org/W2867317277","https://openalex.org/W1576294153","https://openalex.org/W2078886092","https://openalex.org/W2362283711","https://openalex.org/W2002792918","https://openalex.org/W2360049128","https://openalex.org/W1485234189","https://openalex.org/W4386773944","https://openalex.org/W2495172928"],"abstract_inverted_index":{"The":[0,37],"complex":[1,82,93,132],"t-spherical":[2,83,94,133],"fuzzy":[3,19,23,84,95,134],"set":[4],"(Ct-SFS)":[5],"is":[6],"a":[7,27,79,127,145,160],"potent":[8],"tool":[9],"for":[10,129],"representing":[11],"fuzziness":[12],"and":[13,21,72,86,111,121,163],"uncertainty":[14],"compared":[15],"to":[16,90,125,152],"the":[17,41,47,64,101,154],"picture":[18],"sets":[20],"spherical":[22],"sets.":[24],"It":[25],"plays":[26],"key":[28],"role":[29],"in":[30],"modeling":[31],"problems":[32,136],"that":[33],"require":[34],"two-dimensional":[35],"data.":[36,96,141],"present":[38],"study":[39,147],"purposes":[40],"aggregation":[42,88],"technique":[43],"of":[44,49,60,81,104],"Ct-SFSs":[45],"with":[46,131,137],"aid":[48],"Aczel\u2013-Alsina":[50],"(AA)":[51],"operations.":[52],"We":[53],"first":[54],"introduce":[55],"certain":[56,108],"novel":[57],"AA":[58,65,67,69,73],"operations":[59],"Ct-SFSs,":[61],"such":[62],"as":[63],"sum,":[66],"product,":[68],"scalar":[70,74],"multiplication,":[71],"power.":[75],"Subsequently,":[76],"we":[77,99,117,143],"propound":[78],"series":[80],"averaging":[85],"geometric":[87],"operators":[89,120],"efficiently":[91],"aggregate":[92],"In":[97],"addition,":[98],"explore":[100],"different":[102],"characteristics":[103],"these":[105,119],"operators,":[106],"discuss":[107],"peculiar":[109],"cases,":[110],"prove":[112],"their":[113],"fundamental":[114],"results.":[115],"Thereafter,":[116],"utilize":[118],"propose":[122],"entropy":[123],"measures":[124],"frame":[126],"methodology":[128],"dealing":[130],"decision-making":[135],"unknown":[138],"criteria":[139],"weight":[140],"Finally,":[142],"provide":[144],"case":[146],"about":[148],"vehicle":[149],"model":[150],"selection":[151],"illustrate":[153],"presented":[155],"method\u2019s":[156],"applicability":[157],"followed":[158],"by":[159],"parameter":[161],"analysis":[162],"comparative":[164],"study.":[165]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":5}],"updated_date":"2026-05-22T06:13:13.366637","created_date":"2023-01-06T00:00:00"}