{"id":"https://openalex.org/W2906701795","doi":"https://doi.org/10.3390/sym11010039","title":"Probabilistic Linguistic Aggregation Operators Based on Einstein t-Norm and t-Conorm and Their Application in Multi-Criteria Group Decision Making","display_name":"Probabilistic Linguistic Aggregation Operators Based on Einstein t-Norm and t-Conorm and Their Application in Multi-Criteria Group Decision Making","publication_year":2019,"publication_date":"2019-01-02","ids":{"openalex":"https://openalex.org/W2906701795","doi":"https://doi.org/10.3390/sym11010039","mag":"2906701795"},"language":"en","primary_location":{"id":"doi:10.3390/sym11010039","doi":"https://doi.org/10.3390/sym11010039","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/sym11010039","pdf_url":null,"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,"listed_in":["anvur-scientific","cwts-core","norway-1","poland-70","russia-white-list-1","vabb-shw"],"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"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"http://dx.doi.org/10.3390/sym11010039","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5032655922","display_name":"Kobina Agbodah","orcid":"https://orcid.org/0000-0002-7357-7340","observed_orcids":["https://orcid.org/0000-0002-7357-7340"]},"institutions":[{"id":"https://openalex.org/I150229711","display_name":"University of Electronic Science and Technology of China","ror":"https://ror.org/04qr3zq92","country_code":"CN","type":"education","lineage":["https://openalex.org/I150229711"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Kobina Agbodah","raw_affiliation_strings":["Center for West African Studies, University of Electronic Science and Technology of China, Chengdu 610054, China","School of Management and Economics, University of Electronic Science and Technology of China, Chengdu 610054, China"],"raw_orcid":"https://orcid.org/0000-0002-7357-7340","affiliations":[{"raw_affiliation_string":"Center for West African Studies, University of Electronic Science and Technology of China, Chengdu 610054, China","institution_ids":["https://openalex.org/I150229711"]},{"raw_affiliation_string":"School of Management and Economics, University of Electronic Science and Technology of China, Chengdu 610054, China","institution_ids":["https://openalex.org/I150229711"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047319327","display_name":"Adjei Peter Darko","orcid":"https://orcid.org/0000-0003-1621-4209","observed_orcids":["https://orcid.org/0000-0003-1621-4209"]},"institutions":[{"id":"https://openalex.org/I150229711","display_name":"University of Electronic Science and Technology of China","ror":"https://ror.org/04qr3zq92","country_code":"CN","type":"education","lineage":["https://openalex.org/I150229711"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Adjei Peter Darko","raw_affiliation_strings":["Center for West African Studies, University of Electronic Science and Technology of China, Chengdu 610054, China","School of Management and Economics, University of Electronic Science and Technology of China, Chengdu 610054, China"],"raw_orcid":"https://orcid.org/0000-0003-1621-4209","affiliations":[{"raw_affiliation_string":"Center for West African Studies, University of Electronic Science and Technology of China, Chengdu 610054, China","institution_ids":["https://openalex.org/I150229711"]},{"raw_affiliation_string":"School of Management and Economics, University of Electronic Science and Technology of China, Chengdu 610054, China","institution_ids":["https://openalex.org/I150229711"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5032655922"],"corresponding_institution_ids":["https://openalex.org/I150229711"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1418},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1418},"fwci":1.8732,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.85206354,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":97},"biblio":{"volume":"11","issue":"1","first_page":"39","last_page":"39"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9940999746322632,"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":0.9940999746322632,"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":0.0010000000474974513,"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/T13955","display_name":"Evaluation Methods in Various Fields","score":0.00019999999494757503,"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/probabilistic-linguistic-term-sets","display_name":"probabilistic linguistic term sets","score":0.9710000157356262},{"id":"https://openalex.org/keywords/multi-criteria-group-decision-making","display_name":"multi-criteria group decision-making","score":0.9100000262260437},{"id":"https://openalex.org/keywords/information-aggregation","display_name":"information aggregation","score":0.6179999709129333},{"id":"https://openalex.org/keywords/fuzzy-information-fusion","display_name":"fuzzy information fusion","score":0.5590000152587891}],"concepts":[{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.8554568886756897},{"id":"https://openalex.org/C146846114","wikidata":"https://www.wikidata.org/wiki/Q901448","display_name":"Einstein","level":2,"score":0.8379051685333252},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5787895321846008},{"id":"https://openalex.org/C2721081","wikidata":"https://www.wikidata.org/wiki/Q2383161","display_name":"T-norm","level":5,"score":0.4993305206298828},{"id":"https://openalex.org/C20701700","wikidata":"https://www.wikidata.org/wiki/Q388791","display_name":"Group decision-making","level":2,"score":0.4952181875705719},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.49399739503860474},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4774389863014221},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4688962996006012},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.4189274311065674},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4051276445388794},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2349768877029419},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.23199599981307983},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.14745119214057922},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12020307779312134},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.09414979815483093},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.09212341904640198},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.0910559892654419},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","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},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/sym11010039","doi":"https://doi.org/10.3390/sym11010039","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/sym11010039","pdf_url":null,"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,"listed_in":["anvur-scientific","cwts-core","norway-1","poland-70","russia-white-list-1","vabb-shw"],"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:3a3d9f26c8484d89a065e8c180259e0b","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/3a3d9f26c8484d89a065e8c180259e0b","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,"listed_in":[],"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 11, Iss 1, p 39 (2019)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym11010039","doi":"https://doi.org/10.3390/sym11010039","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/sym11010039","pdf_url":null,"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,"listed_in":["anvur-scientific","cwts-core","norway-1","poland-70","russia-white-list-1","vabb-shw"],"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":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W1488217585","https://openalex.org/W1530367293","https://openalex.org/W1550703529","https://openalex.org/W1585083398","https://openalex.org/W1978062397","https://openalex.org/W1995875735","https://openalex.org/W2002144979","https://openalex.org/W2008103229","https://openalex.org/W2030677354","https://openalex.org/W2054984345","https://openalex.org/W2062665604","https://openalex.org/W2077868349","https://openalex.org/W2079522214","https://openalex.org/W2084926750","https://openalex.org/W2091864293","https://openalex.org/W2125044913","https://openalex.org/W2131202053","https://openalex.org/W2131390763","https://openalex.org/W2139283723","https://openalex.org/W2141847884","https://openalex.org/W2296990582","https://openalex.org/W2474884296","https://openalex.org/W2507975617","https://openalex.org/W2563726421","https://openalex.org/W2604409575","https://openalex.org/W2737908918","https://openalex.org/W2780442278","https://openalex.org/W2782809306","https://openalex.org/W2789809558","https://openalex.org/W2792719031","https://openalex.org/W2807664507","https://openalex.org/W2912565176","https://openalex.org/W2948049976","https://openalex.org/W4211007335","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2980126332","https://openalex.org/W4407913426","https://openalex.org/W2780442278","https://openalex.org/W3000405524","https://openalex.org/W1576735256","https://openalex.org/W2474884296","https://openalex.org/W2997493847","https://openalex.org/W3036548215","https://openalex.org/W2927009511","https://openalex.org/W2997325129"],"abstract_inverted_index":{"One":[0],"of":[1,5,23,37,45,126,160,166,178],"the":[2,49,84,114,119,124,164,167,173,176,186],"major":[3],"problems":[4],"varied":[6],"knowledge-based":[7],"systems":[8],"has":[9,28],"to":[10,41,147,198],"do":[11],"with":[12,185],"aggregation":[13,22,47,81,140],"and":[14,26,72,118,135,142,152,169,203],"fusion.":[15],"Pang\u2019s":[16],"probabilistic":[17,50,63,79,85,91,98,105,128,187],"linguistic":[18,51,64,80,86,92,99,106,129,188],"term":[19,65,189],"sets":[20,190],"denotes":[21],"fuzzy":[24],"information":[25,46],"it":[27],"attracted":[29],"tremendous":[30],"interest":[31],"from":[32],"researchers":[33],"recently.":[34],"The":[35],"purpose":[36,125],"this":[38,54],"article":[39],"is":[40],"deal":[42],"investigating":[43],"methods":[44,202],"under":[48],"environment.":[52],"In":[53],"situation":[55],"we":[56,76,171,193],"defined":[57],"certain":[58],"Einstein":[59,70,73,87,93,100,107,133,136],"operational":[60],"laws":[61],"on":[62,69],"elements":[66],"(PLTESs)":[67],"based":[68],"product":[71],"sum.":[74],"Consequently,":[75],"develop":[77],"some":[78],"operators,":[82,90,96,103],"notably":[83],"average":[88,101],"(PLEA)":[89],"geometric":[94,108,121],"(PLEG)":[95],"weighted":[97,104,115,120],"(WPLEA)":[102],"(WPLEG)":[109],"operators.":[110,162],"These":[111],"operators":[112],"extend":[113],"averaging":[116],"operator":[117,122],"for":[123,175],"aggregating":[127],"terms":[130],"values":[131],"respectively.":[132,154],"t-norm":[134],"t-conorm":[137],"constitute":[138],"effective":[139],"tools":[141],"they":[143],"allow":[144],"input":[145],"arguments":[146],"reinforce":[148],"each":[149],"other":[150],"downwardly":[151],"upwardly":[153],"We":[155],"then":[156],"generate":[157],"various":[158],"properties":[159],"these":[161],"With":[163],"aid":[165],"WPLEA":[168],"WPLEG,":[170],"originate":[172],"approaches":[174],"application":[177],"multiple":[179],"attribute":[180],"group":[181],"decision":[182],"making":[183],"(MAGDM)":[184],"(PLTSs).":[191],"Lastly,":[192],"apply":[194],"an":[195],"illustrative":[196],"example":[197],"elucidate":[199],"our":[200],"proposed":[201],"also":[204],"validate":[205],"their":[206],"potentials.":[207]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1}],"updated_date":"2026-10-27T15:51:10.671819","created_date":"2019-01-11T00:00:00"}