{"id":"https://openalex.org/W2970641691","doi":"https://doi.org/10.1515/jisys-2017-0231","title":"Pythagorean Hesitant Fuzzy Information Aggregation and Their Application to Multi-Attribute Group Decision-Making Problems","display_name":"Pythagorean Hesitant Fuzzy Information Aggregation and Their Application to Multi-Attribute Group Decision-Making Problems","publication_year":2018,"publication_date":"2018-01-05","ids":{"openalex":"https://openalex.org/W2970641691","doi":"https://doi.org/10.1515/jisys-2017-0231","mag":"2970641691"},"language":"en","primary_location":{"id":"doi:10.1515/jisys-2017-0231","is_oa":true,"landing_page_url":"https://doi.org/10.1515/jisys-2017-0231","pdf_url":"http://www.degruyter.com/downloadpdf/j/jisys.2020.29.issue-1/jisys-2017-0231/jisys-2017-0231.xml","source":{"id":"https://openalex.org/S2764846071","display_name":"Journal of Intelligent Systems","issn_l":"0334-1860","issn":["0334-1860","2191-026X"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315148","host_organization_name":"IlmuKomputer.Com","host_organization_lineage":["https://openalex.org/P4310315148"],"host_organization_lineage_names":["IlmuKomputer.Com"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Intelligent Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"http://www.degruyter.com/downloadpdf/j/jisys.2020.29.issue-1/jisys-2017-0231/jisys-2017-0231.xml","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5026770895","display_name":"Madad Khan","orcid":"https://orcid.org/0000-0003-0044-961X"},"institutions":[{"id":"https://openalex.org/I263208278","display_name":"Hazara University","ror":"https://ror.org/018y22094","country_code":"PK","type":"education","lineage":["https://openalex.org/I263208278"]}],"countries":["PK"],"is_corresponding":true,"raw_author_name":"Muhammad Sajjad Ali Khan","raw_affiliation_strings":["Department of Mathematics , Hazara University , Mansehra , Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Hazara University , Mansehra , Pakistan","institution_ids":["https://openalex.org/I263208278"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077817609","display_name":"Saleem Abdullah","orcid":"https://orcid.org/0000-0002-7474-5115"},"institutions":[{"id":"https://openalex.org/I181063083","display_name":"Abdul Wali Khan University Mardan","ror":"https://ror.org/03b9y4e65","country_code":"PK","type":"education","lineage":["https://openalex.org/I181063083"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Saleem Abdullah","raw_affiliation_strings":["Department of Mathematics , Abdul Wali Khan University , Mardan , Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Abdul Wali Khan University , Mardan , Pakistan","institution_ids":["https://openalex.org/I181063083"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101991417","display_name":"Asad Ali","orcid":"https://orcid.org/0000-0001-9784-3378"},"institutions":[{"id":"https://openalex.org/I263208278","display_name":"Hazara University","ror":"https://ror.org/018y22094","country_code":"PK","type":"education","lineage":["https://openalex.org/I263208278"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Asad Ali","raw_affiliation_strings":["Department of Mathematics , Hazara University , Mansehra , Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Hazara University , Mansehra , Pakistan","institution_ids":["https://openalex.org/I263208278"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102402405","display_name":"Khaista Rahman","orcid":null},"institutions":[{"id":"https://openalex.org/I263208278","display_name":"Hazara University","ror":"https://ror.org/018y22094","country_code":"PK","type":"education","lineage":["https://openalex.org/I263208278"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Khaista Rahman","raw_affiliation_strings":["Department of Mathematics , Hazara University , Mansehra , Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Hazara University , Mansehra , Pakistan","institution_ids":["https://openalex.org/I263208278"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5026770895"],"corresponding_institution_ids":["https://openalex.org/I263208278"],"apc_list":{"value":1000,"currency":"EUR","value_usd":1078},"apc_paid":{"value":1000,"currency":"EUR","value_usd":1078},"fwci":2.3292,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.8954355,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"29","issue":"1","first_page":"154","last_page":"171"},"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":0.9718000292778015,"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":0.9569000005722046,"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":0.9582885503768921},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.6812591552734375},{"id":"https://openalex.org/keywords/aggregate","display_name":"Aggregate (composite)","score":0.5600056648254395},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5470957159996033},{"id":"https://openalex.org/keywords/group-decision-making","display_name":"Group decision-making","score":0.5359609127044678},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5189199447631836},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.47122204303741455},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.45782384276390076},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4308462142944336},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3839794099330902}],"concepts":[{"id":"https://openalex.org/C100461760","wikidata":"https://www.wikidata.org/wiki/Q11518","display_name":"Pythagorean theorem","level":2,"score":0.9582885503768921},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6812591552734375},{"id":"https://openalex.org/C4679612","wikidata":"https://www.wikidata.org/wiki/Q866298","display_name":"Aggregate (composite)","level":2,"score":0.5600056648254395},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5470957159996033},{"id":"https://openalex.org/C20701700","wikidata":"https://www.wikidata.org/wiki/Q388791","display_name":"Group decision-making","level":2,"score":0.5359609127044678},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5189199447631836},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.47122204303741455},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.45782384276390076},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4308462142944336},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3839794099330902},{"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},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1515/jisys-2017-0231","is_oa":true,"landing_page_url":"https://doi.org/10.1515/jisys-2017-0231","pdf_url":"http://www.degruyter.com/downloadpdf/j/jisys.2020.29.issue-1/jisys-2017-0231/jisys-2017-0231.xml","source":{"id":"https://openalex.org/S2764846071","display_name":"Journal of Intelligent Systems","issn_l":"0334-1860","issn":["0334-1860","2191-026X"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315148","host_organization_name":"IlmuKomputer.Com","host_organization_lineage":["https://openalex.org/P4310315148"],"host_organization_lineage_names":["IlmuKomputer.Com"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Intelligent Systems","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:a4f530abde9d49a1872771b7435ccf7e","is_oa":true,"landing_page_url":"https://doaj.org/article/a4f530abde9d49a1872771b7435ccf7e","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Intelligent Systems, Vol 29, Iss 1, Pp 154-171 (2018)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1515/jisys-2017-0231","is_oa":true,"landing_page_url":"https://doi.org/10.1515/jisys-2017-0231","pdf_url":"http://www.degruyter.com/downloadpdf/j/jisys.2020.29.issue-1/jisys-2017-0231/jisys-2017-0231.xml","source":{"id":"https://openalex.org/S2764846071","display_name":"Journal of Intelligent Systems","issn_l":"0334-1860","issn":["0334-1860","2191-026X"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315148","host_organization_name":"IlmuKomputer.Com","host_organization_lineage":["https://openalex.org/P4310315148"],"host_organization_lineage_names":["IlmuKomputer.Com"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Intelligent Systems","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.8199999928474426,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2970641691.pdf","grobid_xml":"https://content.openalex.org/works/W2970641691.grobid-xml"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W1668569279","https://openalex.org/W1771499885","https://openalex.org/W1829951598","https://openalex.org/W1961335799","https://openalex.org/W1966808269","https://openalex.org/W1980564456","https://openalex.org/W1987177581","https://openalex.org/W2013932252","https://openalex.org/W2013951629","https://openalex.org/W2024919729","https://openalex.org/W2038897934","https://openalex.org/W2050090718","https://openalex.org/W2050262998","https://openalex.org/W2052102691","https://openalex.org/W2056235818","https://openalex.org/W2063170755","https://openalex.org/W2066706286","https://openalex.org/W2068843436","https://openalex.org/W2079457935","https://openalex.org/W2104077967","https://openalex.org/W2111358144","https://openalex.org/W2122379761","https://openalex.org/W2131390763","https://openalex.org/W2139487545","https://openalex.org/W2171715801","https://openalex.org/W2339111061","https://openalex.org/W2391648306","https://openalex.org/W2544090818","https://openalex.org/W2604920622","https://openalex.org/W2773588687","https://openalex.org/W2912565176","https://openalex.org/W2993706351","https://openalex.org/W4211007335","https://openalex.org/W4239165868","https://openalex.org/W4285719527","https://openalex.org/W4292158025","https://openalex.org/W4292295629"],"related_works":["https://openalex.org/W3088234006","https://openalex.org/W200176093","https://openalex.org/W1590933210","https://openalex.org/W1967842420","https://openalex.org/W3208337444","https://openalex.org/W2964184955","https://openalex.org/W4283529156","https://openalex.org/W2775524850","https://openalex.org/W4293192015","https://openalex.org/W2087721013"],"abstract_inverted_index":{"Abstract":[0],"In":[1,38],"this":[2],"paper,":[3],"we":[4,140],"introduce":[5],"the":[6,9,17,20,26,29,88,123,130,136,142,146],"concept":[7],"of":[8,19,32,96,135],"Pythagorean":[10,61,71,78,89,124],"hesitant":[11,22,62,72,90,125],"fuzzy":[12,23,63,73,79,91,126],"set":[13,24],"(PHFS),":[14],"which":[15,117],"is":[16,36,99],"generalization":[18],"intuitionistic":[21],"under":[25],"restriction":[27],"that":[28,100],"square":[30],"sum":[31],"its":[33],"membership":[34],"degrees":[35],"\u22641.":[37],"decision":[39],"making":[40],"with":[41],"PHFSs,":[42],"aggregation":[43],"operators":[44,83,98,110],"play":[45],"a":[46],"key":[47],"role":[48],"because":[49],"they":[50,101],"can":[51],"be":[52],"used":[53,85],"to":[54,86,113,128,145],"synthesize":[55],"multidimensional":[56],"evaluation":[57],"values":[58,64],"represented":[59],"as":[60],"into":[65],"collective":[66],"values.":[67,92],"Under":[68],"PHFS":[69],"environments,":[70],"ordered":[74,80],"weighted":[75,81],"averaging":[76],"and":[77,105,133],"geometric":[82],"are":[84,111],"aggregate":[87],"The":[93],"main":[94],"advantage":[95],"these":[97,109],"provide":[102,119],"more":[103],"accurate":[104],"valuable":[106],"results.":[107],"Furthermore,":[108],"applied":[112],"decision-making":[114],"problems":[115],"in":[116,122],"experts":[118],"their":[120],"preferences":[121],"environment":[127],"show":[129],"validity,":[131],"practicality,":[132],"effectiveness":[134],"new":[137],"approach.":[138],"Finally,":[139],"compare":[141],"proposed":[143],"approach":[144],"existing":[147],"methods.":[148]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":5},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":4}],"updated_date":"2025-12-06T23:10:59.065948","created_date":"2025-10-10T00:00:00"}
