{"id":"https://openalex.org/W3172074980","doi":"https://doi.org/10.3390/sym13061053","title":"Interval Valued T-Spherical Fuzzy Information Aggregation Based on Dombi t-Norm and Dombi t-Conorm for Multi-Attribute Decision Making Problems","display_name":"Interval Valued T-Spherical Fuzzy Information Aggregation Based on Dombi t-Norm and Dombi t-Conorm for Multi-Attribute Decision Making Problems","publication_year":2021,"publication_date":"2021-06-10","ids":{"openalex":"https://openalex.org/W3172074980","doi":"https://doi.org/10.3390/sym13061053","mag":"3172074980"},"language":"en","primary_location":{"id":"doi:10.3390/sym13061053","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13061053","pdf_url":"https://www.mdpi.com/2073-8994/13/6/1053/pdf?version=1624331863","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/2073-8994/13/6/1053/pdf?version=1624331863","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037136946","display_name":"Kifayat Ullah","orcid":"https://orcid.org/0000-0002-1438-6413"},"institutions":[{"id":"https://openalex.org/I195024194","display_name":"Riphah International University","ror":"https://ror.org/02kdm5630","country_code":"PK","type":"education","lineage":["https://openalex.org/I195024194"]},{"id":"https://openalex.org/I32597200","display_name":"Ghent University","ror":"https://ror.org/00cv9y106","country_code":"BE","type":"education","lineage":["https://openalex.org/I32597200"]}],"countries":["BE","PK"],"is_corresponding":true,"raw_author_name":"Kifayat Ullah","raw_affiliation_strings":["Department of Data Analysis and Mathematical Modelling, Ghent University Belgium, 9000 Ghent, Belgium","Department of Mathematics, Riphah Institute of Computing and Applied Sciences, Riphah International University Lahore, Lahore 54000, Pakistan"],"raw_orcid":"https://orcid.org/0000-0002-1438-6413","affiliations":[{"raw_affiliation_string":"Department of Data Analysis and Mathematical Modelling, Ghent University Belgium, 9000 Ghent, Belgium","institution_ids":["https://openalex.org/I32597200"]},{"raw_affiliation_string":"Department of Mathematics, Riphah Institute of Computing and Applied Sciences, Riphah International University Lahore, Lahore 54000, Pakistan","institution_ids":["https://openalex.org/I195024194"]}]},{"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/I162030827","display_name":"Thapar Institute of Engineering & Technology","ror":"https://ror.org/00wdq3744","country_code":"IN","type":"education","lineage":["https://openalex.org/I162030827"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Harish Garg","raw_affiliation_strings":["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":"School of Mathematics, Thapar Institute of Engineering & Technology, Deemed University, Patiala 147004, Punjab, India","institution_ids":["https://openalex.org/I162030827"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082207896","display_name":"Zunaira Gul","orcid":null},"institutions":[{"id":"https://openalex.org/I195024194","display_name":"Riphah International University","ror":"https://ror.org/02kdm5630","country_code":"PK","type":"education","lineage":["https://openalex.org/I195024194"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Zunaira Gul","raw_affiliation_strings":["Department of Mathematics, Riphah Institute of Computing and Applied Sciences, Riphah International University Lahore, Lahore 54000, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Riphah Institute of Computing and Applied Sciences, Riphah International University Lahore, Lahore 54000, Pakistan","institution_ids":["https://openalex.org/I195024194"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100646948","display_name":"Tahir Mahmood","orcid":"https://orcid.org/0000-0002-3871-3845"},"institutions":[{"id":"https://openalex.org/I121243025","display_name":"International Islamic University, Islamabad","ror":"https://ror.org/047w75g40","country_code":"PK","type":"education","lineage":["https://openalex.org/I121243025"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Tahir Mahmood","raw_affiliation_strings":["Department of Mathematics, International Islamic University Islamabad, Islamabad 44000, Pakistan"],"raw_orcid":"https://orcid.org/0000-0002-3871-3845","affiliations":[{"raw_affiliation_string":"Department of Mathematics, International Islamic University Islamabad, Islamabad 44000, Pakistan","institution_ids":["https://openalex.org/I121243025"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056312459","display_name":"Qaisar Khan","orcid":"https://orcid.org/0000-0001-7859-7730"},"institutions":[{"id":"https://openalex.org/I2801349156","display_name":"University of Haripur","ror":"https://ror.org/05vtb1235","country_code":"PK","type":"education","lineage":["https://openalex.org/I2801349156"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Qaisar Khan","raw_affiliation_strings":["Department of Mathematics, University of Haripur, Haripur 22620, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Haripur, Haripur 22620, Pakistan","institution_ids":["https://openalex.org/I2801349156"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100740852","display_name":"Zeeshan Ali","orcid":"https://orcid.org/0000-0001-5878-714X"},"institutions":[{"id":"https://openalex.org/I121243025","display_name":"International Islamic University, Islamabad","ror":"https://ror.org/047w75g40","country_code":"PK","type":"education","lineage":["https://openalex.org/I121243025"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Zeeshan Ali","raw_affiliation_strings":["Department of Mathematics, International Islamic University Islamabad, Islamabad 44000, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, International Islamic University Islamabad, Islamabad 44000, Pakistan","institution_ids":["https://openalex.org/I121243025"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5037136946"],"corresponding_institution_ids":["https://openalex.org/I195024194","https://openalex.org/I32597200"],"apc_list":{"value":1800,"currency":"CHF","value_usd":1944},"apc_paid":{"value":1800,"currency":"CHF","value_usd":1944},"fwci":6.7327,"has_fulltext":false,"cited_by_count":55,"citation_normalized_percentile":{"value":0.97214119,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":99},"biblio":{"volume":"13","issue":"6","first_page":"1053","last_page":"1053"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9753999710083008,"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9520000219345093,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5685402750968933},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5648524761199951},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5646274089813232},{"id":"https://openalex.org/keywords/ranking","display_name":"Ranking (information retrieval)","score":0.44844090938568115},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.44522446393966675},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.43216192722320557},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.43191269040107727},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.43170350790023804},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.41788381338119507},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.33019524812698364},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.29315581917762756},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.23250561952590942}],"concepts":[{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5685402750968933},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5648524761199951},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5646274089813232},{"id":"https://openalex.org/C189430467","wikidata":"https://www.wikidata.org/wiki/Q7293293","display_name":"Ranking (information retrieval)","level":2,"score":0.44844090938568115},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.44522446393966675},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.43216192722320557},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43191269040107727},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.43170350790023804},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.41788381338119507},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.33019524812698364},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.29315581917762756},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.23250561952590942},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"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":2,"locations":[{"id":"doi:10.3390/sym13061053","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13061053","pdf_url":"https://www.mdpi.com/2073-8994/13/6/1053/pdf?version=1624331863","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:2092c59b8d544e62b3e034988a140e1e","is_oa":true,"landing_page_url":"https://doaj.org/article/2092c59b8d544e62b3e034988a140e1e","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 13, Iss 6, p 1053 (2021)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym13061053","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13061053","pdf_url":"https://www.mdpi.com/2073-8994/13/6/1053/pdf?version=1624331863","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":[{"id":"https://metadata.un.org/sdg/16","score":0.8299999833106995,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3172074980.pdf"},"referenced_works_count":46,"referenced_works":["https://openalex.org/W2211233","https://openalex.org/W1489487994","https://openalex.org/W1560893303","https://openalex.org/W1965777053","https://openalex.org/W1971875039","https://openalex.org/W1980564456","https://openalex.org/W1981107087","https://openalex.org/W1983286635","https://openalex.org/W2003115337","https://openalex.org/W2079457935","https://openalex.org/W2160185911","https://openalex.org/W2269905947","https://openalex.org/W2514754342","https://openalex.org/W2573110008","https://openalex.org/W2591936123","https://openalex.org/W2605666115","https://openalex.org/W2765516692","https://openalex.org/W2794285243","https://openalex.org/W2804105936","https://openalex.org/W2883720524","https://openalex.org/W2895274233","https://openalex.org/W2896010100","https://openalex.org/W2896634720","https://openalex.org/W2899193396","https://openalex.org/W2900419240","https://openalex.org/W2910272534","https://openalex.org/W2911066936","https://openalex.org/W2922175244","https://openalex.org/W2942416053","https://openalex.org/W2953932150","https://openalex.org/W2962826554","https://openalex.org/W2976297801","https://openalex.org/W2992655446","https://openalex.org/W3007573849","https://openalex.org/W3009761115","https://openalex.org/W3037338019","https://openalex.org/W3046108428","https://openalex.org/W3047313007","https://openalex.org/W3127188235","https://openalex.org/W3136511698","https://openalex.org/W3160245528","https://openalex.org/W4285719527","https://openalex.org/W6600092282","https://openalex.org/W6683950865","https://openalex.org/W6789928911","https://openalex.org/W7038340056"],"related_works":["https://openalex.org/W2188500270","https://openalex.org/W2303858293","https://openalex.org/W2915512527","https://openalex.org/W51364034","https://openalex.org/W2793336762","https://openalex.org/W2091548507","https://openalex.org/W2368816706","https://openalex.org/W3159414774","https://openalex.org/W4385728102","https://openalex.org/W2381957916"],"abstract_inverted_index":{"Multi-attribute":[0],"decision-making":[1],"(MADM)":[2],"is":[3,17,32,46,63,90,124,132,160,183,193],"commonly":[4],"used":[5],"to":[6,64,134],"investigate":[7],"fuzzy":[8,81],"information":[9,16,31,37,89,130,195],"effectively.":[10],"However,":[11],"selecting":[12],"the":[13,22,36,66,75,78,85,93,117,121,127,157,163,166,172],"best":[14],"alternative":[15],"not":[18,25],"always":[19],"symmetric":[20],"because":[21],"alternatives":[23],"do":[24],"have":[26],"complete":[27],"information,":[28],"so":[29],"asymmetric":[30,194],"often":[33],"involved.":[34],"Expressing":[35],"under":[38],"uncertainty":[39],"using":[40,52,109],"closed":[41,110],"subintervals":[42],"of":[43,51,60,68,95,112,116,120,129,141,156,165],"[0,":[44,56,113],"1]":[45],"beneficial":[47],"and":[48,87,105,147,162],"effective":[49],"instead":[50],"crisp":[53],"numbers":[54],"from":[55],"1].":[57,114],"The":[58,154],"goal":[59],"this":[61],"paper":[62],"enhance":[65],"notion":[67],"Dombi":[69,143,149],"aggregation":[70],"operators":[71],"(DAOs)":[72],"by":[73],"introducing":[74],"DAOs":[76,159],"in":[77,126,177],"interval-valued":[79],"T-spherical":[80],"(IVTSF)":[82],"environment":[83,128],"where":[84,181],"uncertain":[86],"ambiguous":[88],"described":[91],"with":[92,169],"help":[94],"membership":[96],"grade":[97,100,103,107],"(MG),":[98],"abstinence":[99],"(AG),":[101],"non-membership":[102],"(NMG),":[104],"refusal":[106],"(RG)":[108],"sub-intervals":[111],"One":[115],"key":[118],"benefits":[119],"proposed":[122,139],"work":[123],"that":[125],"loss":[131],"reduced":[133],"a":[135,178,186],"negligible":[136],"limit.":[137],"We":[138],"concepts":[140],"IVTSF":[142,148,158],"weighted":[144,150],"averaging":[145],"(IVTSFDWA)":[146],"geometric":[151],"(IVTSFDWG)":[152],"operators.":[153],"diversity":[155],"proved":[161],"influences":[164],"parameters,":[167],"associated":[168],"DAOs,":[170],"on":[171],"ranking":[173],"results":[174],"are":[175],"observed":[176],"MADM":[179],"problem":[180],"it":[182],"discussed":[184],"how":[185],"decision":[187],"can":[188],"be":[189],"made":[190],"when":[191],"there":[192],"about":[196],"alternatives.":[197]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":12},{"year":2024,"cited_by_count":14},{"year":2023,"cited_by_count":13},{"year":2022,"cited_by_count":11},{"year":2021,"cited_by_count":4}],"updated_date":"2026-08-28T12:50:07.497085","created_date":"2025-10-10T00:00:00"}
