{"id":"https://openalex.org/W2184989861","doi":"https://doi.org/10.1142/s0219622016500012","title":"A Hybrid Method for Pythagorean Fuzzy Multiple-Criteria Decision Making","display_name":"A Hybrid Method for Pythagorean Fuzzy Multiple-Criteria Decision Making","publication_year":2015,"publication_date":"2015-12-01","ids":{"openalex":"https://openalex.org/W2184989861","doi":"https://doi.org/10.1142/s0219622016500012","mag":"2184989861"},"language":"en","primary_location":{"id":"doi:10.1142/s0219622016500012","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219622016500012","pdf_url":null,"source":{"id":"https://openalex.org/S207089700","display_name":"International Journal of Information Technology & Decision Making","issn_l":"0219-6220","issn":["0219-6220","1793-6845"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Information Technology &amp; Decision Making","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/A5101978937","display_name":"Shouzhen Zeng","orcid":"https://orcid.org/0000-0002-3604-0843"},"institutions":[{"id":"https://openalex.org/I109935558","display_name":"Ningbo University","ror":"https://ror.org/03et85d35","country_code":"CN","type":"education","lineage":["https://openalex.org/I109935558"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shouzhen Zeng","raw_affiliation_strings":["School of Business, Ningbo University, Ningbo 315211, P.\u00a0R.\u00a0China"],"affiliations":[{"raw_affiliation_string":"School of Business, Ningbo University, Ningbo 315211, P.\u00a0R.\u00a0China","institution_ids":["https://openalex.org/I109935558"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100437533","display_name":"Jianping Chen","orcid":"https://orcid.org/0000-0002-1724-0727"},"institutions":[{"id":"https://openalex.org/I159389169","display_name":"Ningbo University of Technology","ror":"https://ror.org/037dym702","country_code":"CN","type":"education","lineage":["https://openalex.org/I159389169"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jianping Chen","raw_affiliation_strings":["Ningbo Institute of Technology, Zhejiang University Ningbo, 315100, P.\u00a0R.\u00a0China"],"affiliations":[{"raw_affiliation_string":"Ningbo Institute of Technology, Zhejiang University Ningbo, 315100, P.\u00a0R.\u00a0China","institution_ids":["https://openalex.org/I159389169"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031444823","display_name":"Xingsen Li","orcid":"https://orcid.org/0000-0001-6591-7432"},"institutions":[{"id":"https://openalex.org/I159389169","display_name":"Ningbo University of Technology","ror":"https://ror.org/037dym702","country_code":"CN","type":"education","lineage":["https://openalex.org/I159389169"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xingsen Li","raw_affiliation_strings":["Ningbo Institute of Technology, Zhejiang University Ningbo, 315100, P.\u00a0R.\u00a0China"],"affiliations":[{"raw_affiliation_string":"Ningbo Institute of Technology, Zhejiang University Ningbo, 315100, P.\u00a0R.\u00a0China","institution_ids":["https://openalex.org/I159389169"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5031444823"],"corresponding_institution_ids":["https://openalex.org/I159389169"],"apc_list":null,"apc_paid":null,"fwci":37.4964,"has_fulltext":false,"cited_by_count":292,"citation_normalized_percentile":{"value":0.99868262,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"15","issue":"02","first_page":"403","last_page":"422"},"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":0.9952999949455261,"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":0.9733999967575073,"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/pythagorean-theorem","display_name":"Pythagorean theorem","score":0.8292575478553772},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.643428385257721},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.6150842308998108},{"id":"https://openalex.org/keywords/multiple-criteria-decision-analysis","display_name":"Multiple-criteria decision analysis","score":0.6050394773483276},{"id":"https://openalex.org/keywords/topsis","display_name":"TOPSIS","score":0.5826684236526489},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5337007641792297},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5090777277946472},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.475326806306839},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.4591928720474243},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43926292657852173},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4166772663593292},{"id":"https://openalex.org/keywords/group-decision-making","display_name":"Group decision-making","score":0.4100596010684967},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.26612311601638794},{"id":"https://openalex.org/keywords/operations-research","display_name":"Operations research","score":0.16327142715454102}],"concepts":[{"id":"https://openalex.org/C100461760","wikidata":"https://www.wikidata.org/wiki/Q11518","display_name":"Pythagorean theorem","level":2,"score":0.8292575478553772},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.643428385257721},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6150842308998108},{"id":"https://openalex.org/C11105738","wikidata":"https://www.wikidata.org/wiki/Q1895805","display_name":"Multiple-criteria decision analysis","level":2,"score":0.6050394773483276},{"id":"https://openalex.org/C51566761","wikidata":"https://www.wikidata.org/wiki/Q1235853","display_name":"TOPSIS","level":2,"score":0.5826684236526489},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5337007641792297},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5090777277946472},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.475326806306839},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.4591928720474243},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43926292657852173},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4166772663593292},{"id":"https://openalex.org/C20701700","wikidata":"https://www.wikidata.org/wiki/Q388791","display_name":"Group decision-making","level":2,"score":0.4100596010684967},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.26612311601638794},{"id":"https://openalex.org/C42475967","wikidata":"https://www.wikidata.org/wiki/Q194292","display_name":"Operations research","level":1,"score":0.16327142715454102},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0219622016500012","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219622016500012","pdf_url":null,"source":{"id":"https://openalex.org/S207089700","display_name":"International Journal of Information Technology & Decision Making","issn_l":"0219-6220","issn":["0219-6220","1793-6845"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Information Technology &amp; Decision Making","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:wsi:ijitdm:v:15:y:2016:i:02:p:403-422","is_oa":false,"landing_page_url":"http://www.worldscientific.com/doi/abs/10.1142/S0219622016500012","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,"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":"","raw_type":"article"}],"best_oa_location":null,"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":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":57,"referenced_works":["https://openalex.org/W173895910","https://openalex.org/W315551019","https://openalex.org/W1008336339","https://openalex.org/W1410720978","https://openalex.org/W1422679120","https://openalex.org/W1668569279","https://openalex.org/W1746729662","https://openalex.org/W1829951598","https://openalex.org/W1964346230","https://openalex.org/W1967053552","https://openalex.org/W1971875039","https://openalex.org/W1972001268","https://openalex.org/W1975977312","https://openalex.org/W1980564456","https://openalex.org/W1983343002","https://openalex.org/W1989995659","https://openalex.org/W1991446918","https://openalex.org/W1991875445","https://openalex.org/W2011808790","https://openalex.org/W2013932252","https://openalex.org/W2014939815","https://openalex.org/W2021909147","https://openalex.org/W2024428474","https://openalex.org/W2026249172","https://openalex.org/W2029377923","https://openalex.org/W2031299513","https://openalex.org/W2031523830","https://openalex.org/W2032412319","https://openalex.org/W2033249289","https://openalex.org/W2033917481","https://openalex.org/W2035572150","https://openalex.org/W2041949587","https://openalex.org/W2044794538","https://openalex.org/W2045361756","https://openalex.org/W2051440091","https://openalex.org/W2055671933","https://openalex.org/W2060907774","https://openalex.org/W2063149790","https://openalex.org/W2068402605","https://openalex.org/W2072597121","https://openalex.org/W2075809784","https://openalex.org/W2080986991","https://openalex.org/W2091045782","https://openalex.org/W2093815139","https://openalex.org/W2109641321","https://openalex.org/W2120230944","https://openalex.org/W2144954597","https://openalex.org/W2147910644","https://openalex.org/W2151739142","https://openalex.org/W2159068858","https://openalex.org/W2167967165","https://openalex.org/W2193399188","https://openalex.org/W2506768821","https://openalex.org/W2912565176","https://openalex.org/W3140407031","https://openalex.org/W4211007335","https://openalex.org/W4248444468"],"related_works":["https://openalex.org/W2963319272","https://openalex.org/W3154161952","https://openalex.org/W2778781604","https://openalex.org/W3196600246","https://openalex.org/W4235219488","https://openalex.org/W2047025039","https://openalex.org/W2765931357","https://openalex.org/W1928481587","https://openalex.org/W2613305061","https://openalex.org/W2906568202"],"abstract_inverted_index":{"As":[0],"a":[1,29,73,115,129],"generalization":[2],"of":[3,62,91,93,100,140],"intuitionistic":[4],"fuzzy":[5,9,34,50,125],"set,":[6],"the":[7,48,63,77,89,97,112,136,141],"Pythagorean":[8,33,49,124],"set":[10],"is":[11,66,121,132],"interesting":[12],"and":[13,42,83,104,138],"very":[14],"useful":[15],"in":[16,20,72,96],"modeling":[17],"uncertain":[18],"information":[19],"real-world":[21],"decision-making":[22,36],"problems.":[23],"In":[24],"this":[25],"paper,":[26],"we":[27,46],"develop":[28],"new":[30],"method":[31],"for":[32,123],"multiple-criteria":[35],"(MCDM)":[37],"problems":[38],"with":[39],"aggregation":[40],"operators":[41],"distance":[43,56,70],"measures.":[44],"First,":[45],"present":[47],"ordered":[51,78],"weighted":[52,54,79,84],"averaging":[53,80],"average":[55,85],"(PFOWAWAD)":[57],"operator.":[58],"The":[59],"main":[60,102],"advantage":[61],"PFOWAWAD":[64],"operator":[65,82],"that":[67,87],"it":[68],"uses":[69],"measures":[71],"unified":[74],"framework":[75],"between":[76],"(OWA)":[81],"(WA)":[86],"considers":[88],"degree":[90],"importance":[92],"each":[94],"concept":[95],"aggregation.":[98],"Some":[99],"its":[101],"properties":[103],"special":[105],"cases":[106],"are":[107],"studied.":[108],"Then,":[109],"based":[110],"on":[111],"proposed":[113],"operator,":[114],"hybrid":[116],"TOPSIS":[117],"method,":[118],"called":[119],"PFOWAWAD-TOPSIS":[120],"introduced":[122],"MCDM":[126],"problem.":[127],"Finally,":[128],"numerical":[130],"example":[131],"provided":[133],"to":[134],"illustrate":[135],"practicality":[137],"feasibility":[139],"developed":[142],"method.":[143]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":11},{"year":2023,"cited_by_count":20},{"year":2022,"cited_by_count":26},{"year":2021,"cited_by_count":33},{"year":2020,"cited_by_count":42},{"year":2019,"cited_by_count":56},{"year":2018,"cited_by_count":50},{"year":2017,"cited_by_count":32},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":1}],"updated_date":"2026-04-07T14:57:38.498316","created_date":"2025-10-10T00:00:00"}
