{"id":"https://openalex.org/W2897273681","doi":"https://doi.org/10.3390/math6100201","title":"Approaches to Multiple Attribute Decision Making with Interval-Valued 2-Tuple Linguistic Pythagorean Fuzzy Information","display_name":"Approaches to Multiple Attribute Decision Making with Interval-Valued 2-Tuple Linguistic Pythagorean Fuzzy Information","publication_year":2018,"publication_date":"2018-10-13","ids":{"openalex":"https://openalex.org/W2897273681","doi":"https://doi.org/10.3390/math6100201","mag":"2897273681"},"language":"en","primary_location":{"id":"doi:10.3390/math6100201","doi":"https://doi.org/10.3390/math6100201","is_oa":true,"landing_page_url":"https://doi.org/10.3390/math6100201","pdf_url":"https://www.mdpi.com/2227-7390/6/10/201/pdf?version=1539594899","source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","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":"Mathematics","raw_type":"journal-article"},"parent_works":[],"lineage":["https://openalex.org/W2897273681"],"child_works_count":0,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2227-7390/6/10/201/pdf?version=1539594899","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100772690","display_name":"Jie Wang","orcid":"https://orcid.org/0000-0001-5681-7755","observed_orcids":["https://orcid.org/0000-0001-5681-7755"]},"institutions":[{"id":"https://openalex.org/I63354593","display_name":"Sichuan Normal University","ror":"https://ror.org/043dxc061","country_code":"CN","type":"education","lineage":["https://openalex.org/I63354593"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jie Wang","raw_affiliation_strings":["School of Business, Sichuan Normal University, Chengdu 610101, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Business, Sichuan Normal University, Chengdu 610101, China","institution_ids":["https://openalex.org/I63354593"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029662492","display_name":"Guiwu Wei","orcid":"https://orcid.org/0000-0001-9074-2005","observed_orcids":["https://orcid.org/0000-0001-9074-2005"]},"institutions":[{"id":"https://openalex.org/I63354593","display_name":"Sichuan Normal University","ror":"https://ror.org/043dxc061","country_code":"CN","type":"education","lineage":["https://openalex.org/I63354593"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Guiwu Wei","raw_affiliation_strings":["School of Business, Sichuan Normal University, Chengdu 610101, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Business, Sichuan Normal University, Chengdu 610101, China","institution_ids":["https://openalex.org/I63354593"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007814097","display_name":"Hui Gao","orcid":"https://orcid.org/0000-0001-6394-0217","observed_orcids":["https://orcid.org/0000-0001-6394-0217"]},"institutions":[{"id":"https://openalex.org/I63354593","display_name":"Sichuan Normal University","ror":"https://ror.org/043dxc061","country_code":"CN","type":"education","lineage":["https://openalex.org/I63354593"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Hui Gao","raw_affiliation_strings":["School of Business, Sichuan Normal University, Chengdu 610101, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Business, Sichuan Normal University, Chengdu 610101, China","institution_ids":["https://openalex.org/I63354593"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5007814097","https://openalex.org/A5029662492"],"corresponding_institution_ids":["https://openalex.org/I63354593"],"apc_list":{"value":2600,"currency":"CHF","value_usd":3137},"apc_paid":{"value":2600,"currency":"CHF","value_usd":3137},"fwci":13.1454,"has_fulltext":true,"cited_by_count":78,"citation_normalized_percentile":{"value":0.99038412,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":100},"biblio":{"volume":"6","issue":"10","first_page":"201","last_page":"201"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9976000189781189,"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":0.9976000189781189,"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":0.0005000000237487257,"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":9.999999747378752e-05,"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/multiple-attribute-decision-making","display_name":"multiple attribute decision making","score":0.9300000071525574},{"id":"https://openalex.org/keywords/pythagorean-fuzzy-numbers","display_name":"Pythagorean fuzzy numbers","score":0.8370000123977661},{"id":"https://openalex.org/keywords/maclaurin-symmetric-mean-operator","display_name":"Maclaurin symmetric mean operator","score":0.9850000143051147},{"id":"https://openalex.org/keywords/aggregation-operators","display_name":"aggregation operators","score":0.9290000200271606},{"id":"https://openalex.org/keywords/green-supplier-selection","display_name":"green supplier selection","score":0.656000018119812}],"concepts":[{"id":"https://openalex.org/C100461760","wikidata":"https://www.wikidata.org/wiki/Q11518","display_name":"Pythagorean theorem","level":2,"score":0.851202130317688},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.7264602780342102},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6785941123962402},{"id":"https://openalex.org/C118930307","wikidata":"https://www.wikidata.org/wiki/Q600590","display_name":"Tuple","level":2,"score":0.5838731527328491},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.44224950671195984},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.42395496368408203},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.41797754168510437},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.36958080530166626},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3617445230484009},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34190475940704346},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2878471910953522},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23352843523025513},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.18429908156394958},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1405453085899353},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/math6100201","doi":"https://doi.org/10.3390/math6100201","is_oa":true,"landing_page_url":"https://doi.org/10.3390/math6100201","pdf_url":"https://www.mdpi.com/2227-7390/6/10/201/pdf?version=1539594899","source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","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":"Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:gam:jmathe:v:6:y:2018:i:10:p:201-:d:175407","doi":null,"is_oa":false,"landing_page_url":"https://www.mdpi.com/2227-7390/6/10/201/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:f91e1aa5f4324bc88ad39a0117d13f71","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/f91e1aa5f4324bc88ad39a0117d13f71","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":"Mathematics, Vol 6, Iss 10, p 201 (2018)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/math6100201","doi":"https://doi.org/10.3390/math6100201","is_oa":true,"landing_page_url":"https://doi.org/10.3390/math6100201","pdf_url":"https://www.mdpi.com/2227-7390/6/10/201/pdf?version=1539594899","source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","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":"Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G6141332717","display_name":null,"funder_award_id":"71571128","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7369548983","display_name":null,"funder_award_id":"17XJA630003","funder_id":"https://openalex.org/F4320321106","funder_display_name":"Ministry of Education of the People's Republic of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321106","display_name":"Ministry of Education of the People's Republic of China","ror":"https://ror.org/01mv9t934"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2897273681.pdf","grobid_xml":"https://content.openalex.org/works/W2897273681.grobid-xml"},"referenced_works_count":81,"referenced_works":["https://openalex.org/W1137073519","https://openalex.org/W1829951598","https://openalex.org/W1963511358","https://openalex.org/W1967218248","https://openalex.org/W1976073056","https://openalex.org/W1977184551","https://openalex.org/W1980564456","https://openalex.org/W2003194756","https://openalex.org/W2013932252","https://openalex.org/W2039650820","https://openalex.org/W2062791290","https://openalex.org/W2064505134","https://openalex.org/W2074605814","https://openalex.org/W2079457935","https://openalex.org/W2104077967","https://openalex.org/W2117827905","https://openalex.org/W2134933192","https://openalex.org/W2144232912","https://openalex.org/W2157687268","https://openalex.org/W2184989861","https://openalex.org/W2218209912","https://openalex.org/W2289047752","https://openalex.org/W2292359941","https://openalex.org/W2345848912","https://openalex.org/W2391648306","https://openalex.org/W2412590235","https://openalex.org/W2437782838","https://openalex.org/W2512740879","https://openalex.org/W2515391243","https://openalex.org/W2526675547","https://openalex.org/W2533445771","https://openalex.org/W2545220476","https://openalex.org/W2548735830","https://openalex.org/W2549733045","https://openalex.org/W2587083986","https://openalex.org/W2590846539","https://openalex.org/W2591008318","https://openalex.org/W2593530789","https://openalex.org/W2595406791","https://openalex.org/W2624112931","https://openalex.org/W2664295321","https://openalex.org/W2669156789","https://openalex.org/W2732135403","https://openalex.org/W2734452893","https://openalex.org/W2734467534","https://openalex.org/W2734543528","https://openalex.org/W2736639157","https://openalex.org/W2743408393","https://openalex.org/W2744824089","https://openalex.org/W2753862205","https://openalex.org/W2759777718","https://openalex.org/W2765829946","https://openalex.org/W2767160721","https://openalex.org/W2768661755","https://openalex.org/W2769072697","https://openalex.org/W2769278513","https://openalex.org/W2778309520","https://openalex.org/W2782087892","https://openalex.org/W2784775847","https://openalex.org/W2787434823","https://openalex.org/W2789682920","https://openalex.org/W2790677216","https://openalex.org/W2790795792","https://openalex.org/W2791638390","https://openalex.org/W2792103616","https://openalex.org/W2792671092","https://openalex.org/W2792780258","https://openalex.org/W2794272320","https://openalex.org/W2800188091","https://openalex.org/W2800390840","https://openalex.org/W2802084959","https://openalex.org/W2804122402","https://openalex.org/W2883333523","https://openalex.org/W2885459375","https://openalex.org/W2886589302","https://openalex.org/W2889230580","https://openalex.org/W2891138446","https://openalex.org/W2895874096","https://openalex.org/W2900619190","https://openalex.org/W4211007335","https://openalex.org/W4239855057"],"related_works":["https://openalex.org/W3005662247","https://openalex.org/W3028192223","https://openalex.org/W2992501239","https://openalex.org/W2899072869","https://openalex.org/W2798722133","https://openalex.org/W3088143162","https://openalex.org/W3111003120","https://openalex.org/W2898190680","https://openalex.org/W2782959219","https://openalex.org/W2732135403"],"abstract_inverted_index":{"The":[0,26],"Maclaurin":[1],"symmetric":[2],"mean":[3,9],"(MSM)":[4],"operator":[5,12,32,67],"is":[6,20,33,151],"a":[7],"classical":[8],"type":[10],"aggregation":[11],"used":[13,152],"in":[14,52],"modern":[15],"information":[16],"fusion":[17],"theory,":[18],"which":[19],"suitable":[21],"to":[22,76,153],"aggregate":[23],"numerical":[24],"values.":[25],"prominent":[27],"characteristic":[28,47],"of":[29,48,147],"the":[30,38,45,49,57,78,131,155],"MSM":[31,50,58,61,65,84,93],"that":[34],"it":[35],"can":[36],"capture":[37],"interrelationship":[39],"among":[40],"multi-input":[41],"arguments.":[42],"Motivated":[43],"by":[44],"ideal":[46],"operator,":[51,59,86,95,103,112,120],"this":[53],"paper,":[54],"we":[55],"expand":[56],"generalized":[60],"(GMSM),":[62],"and":[63],"dual":[64],"(DMSM)":[66],"with":[68,140],"interval-valued":[69,79,87,96,104,113],"2-tuple":[70,80,88,97,105,114,122],"linguistic":[71,81,89,98,106,115,123],"Pythagorean":[72,82,90,99,107,116,124],"fuzzy":[73,83,91,100,108,117,125],"numbers":[74],"(IV2TLPFNs)":[75],"propose":[77],"(IV2TLPFMSM)":[85],"weighted":[92,109,126],"(IV2TLPFWMSM)":[94],"GMSM":[101,110],"(IN2TLPFGMSM)":[102],"(IV2TLPFWGMSM)":[111],"DMSM":[118,127],"(IN2TLPFDMSM)":[119],"Interval-valued":[121],"(IV2TLPFWDMSM)":[128],"operator.":[129],"Then":[130],"multiple":[132],"attribute":[133],"decision":[134],"making":[135],"(MADM)":[136],"methods":[137],"are":[138],"developed":[139],"these":[141],"three":[142],"operators.":[143],"Finally,":[144],"an":[145],"example":[146],"green":[148],"supplier":[149],"selection":[150],"show":[154],"proposed":[156],"methods.":[157]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":11},{"year":2019,"cited_by_count":42},{"year":2018,"cited_by_count":10}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2018-10-26T00:00:00"}
