{"id":"https://openalex.org/W2952721730","doi":"https://doi.org/10.3390/sym11060795","title":"Multi-Criteria Group Decision-Making Using an m-Polar Hesitant Fuzzy TOPSIS Approach","display_name":"Multi-Criteria Group Decision-Making Using an m-Polar Hesitant Fuzzy TOPSIS Approach","publication_year":2019,"publication_date":"2019-06-14","ids":{"openalex":"https://openalex.org/W2952721730","doi":"https://doi.org/10.3390/sym11060795","mag":"2952721730"},"language":"en","primary_location":{"id":"doi:10.3390/sym11060795","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11060795","pdf_url":"https://www.mdpi.com/2073-8994/11/6/795/pdf?version=1561083299","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/2073-8994/11/6/795/pdf?version=1561083299","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001270995","display_name":"Muhammad Akram","orcid":"https://orcid.org/0000-0001-7217-7962"},"institutions":[{"id":"https://openalex.org/I172780181","display_name":"University of the Punjab","ror":"https://ror.org/011maz450","country_code":"PK","type":"education","lineage":["https://openalex.org/I172780181"]}],"countries":["PK"],"is_corresponding":true,"raw_author_name":"Muhammad Akram","raw_affiliation_strings":["Department of Mathematics, University of the Punjab, New Campus, Lahore 54590, Pakistan"],"raw_orcid":"https://orcid.org/0000-0001-7217-7962","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of the Punjab, New Campus, Lahore 54590, Pakistan","institution_ids":["https://openalex.org/I172780181"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045942889","display_name":"Arooj Adeel","orcid":null},"institutions":[{"id":"https://openalex.org/I172780181","display_name":"University of the Punjab","ror":"https://ror.org/011maz450","country_code":"PK","type":"education","lineage":["https://openalex.org/I172780181"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Arooj Adeel","raw_affiliation_strings":["Department of Mathematics, University of the Punjab, New Campus, Lahore 54590, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of the Punjab, New Campus, Lahore 54590, Pakistan","institution_ids":["https://openalex.org/I172780181"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024802129","display_name":"Jos\u00e9 Carlos R. Alcantud","orcid":"https://orcid.org/0000-0002-4533-9281"},"institutions":[{"id":"https://openalex.org/I184999862","display_name":"Universidad de Salamanca","ror":"https://ror.org/02f40zc51","country_code":"ES","type":"education","lineage":["https://openalex.org/I184999862"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Jos\u00e9 Carlos R. Alcantud","raw_affiliation_strings":["BORDA Research Unit and IME, Universidad de Salamanca, Salamanca 37008, Spain"],"raw_orcid":"https://orcid.org/0000-0002-4533-9281","affiliations":[{"raw_affiliation_string":"BORDA Research Unit and IME, Universidad de Salamanca, Salamanca 37008, Spain","institution_ids":["https://openalex.org/I184999862"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5001270995"],"corresponding_institution_ids":["https://openalex.org/I172780181"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":3.5649,"has_fulltext":true,"cited_by_count":37,"citation_normalized_percentile":{"value":0.92846191,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":99},"biblio":{"volume":"11","issue":"6","first_page":"795","last_page":"795"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":1.0,"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":1.0,"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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9610999822616577,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.9449999928474426,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/topsis","display_name":"TOPSIS","score":0.7224708199501038},{"id":"https://openalex.org/keywords/group-decision-making","display_name":"Group decision-making","score":0.6557585000991821},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5792621374130249},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.5102396011352539},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5034098029136658},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.46668750047683716},{"id":"https://openalex.org/keywords/polar","display_name":"Polar","score":0.45375585556030273},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.4143259823322296},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.41050124168395996},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3672175407409668},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.326621413230896},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3234262466430664},{"id":"https://openalex.org/keywords/operations-research","display_name":"Operations research","score":0.31034380197525024},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2790434956550598}],"concepts":[{"id":"https://openalex.org/C51566761","wikidata":"https://www.wikidata.org/wiki/Q1235853","display_name":"TOPSIS","level":2,"score":0.7224708199501038},{"id":"https://openalex.org/C20701700","wikidata":"https://www.wikidata.org/wiki/Q388791","display_name":"Group decision-making","level":2,"score":0.6557585000991821},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5792621374130249},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.5102396011352539},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5034098029136658},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.46668750047683716},{"id":"https://openalex.org/C29705727","wikidata":"https://www.wikidata.org/wiki/Q294562","display_name":"Polar","level":2,"score":0.45375585556030273},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.4143259823322296},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.41050124168395996},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3672175407409668},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.326621413230896},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3234262466430664},{"id":"https://openalex.org/C42475967","wikidata":"https://www.wikidata.org/wiki/Q194292","display_name":"Operations research","level":1,"score":0.31034380197525024},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2790434956550598},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","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},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym11060795","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11060795","pdf_url":"https://www.mdpi.com/2073-8994/11/6/795/pdf?version=1561083299","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:1d31e36d3ce84ab1825367ca1a17be49","is_oa":true,"landing_page_url":"https://doaj.org/article/1d31e36d3ce84ab1825367ca1a17be49","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 11, Iss 6, p 795 (2019)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/11/6/795/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/sym11060795","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym11060795","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11060795","pdf_url":"https://www.mdpi.com/2073-8994/11/6/795/pdf?version=1561083299","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":[{"display_name":"Peace, Justice and strong institutions","score":0.6399999856948853,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2952721730.pdf","grobid_xml":"https://content.openalex.org/works/W2952721730.grobid-xml"},"referenced_works_count":48,"referenced_works":["https://openalex.org/W792530008","https://openalex.org/W1967510083","https://openalex.org/W1969386683","https://openalex.org/W1990148280","https://openalex.org/W1991162355","https://openalex.org/W2002210528","https://openalex.org/W2009788305","https://openalex.org/W2015439528","https://openalex.org/W2042102899","https://openalex.org/W2047025039","https://openalex.org/W2050090718","https://openalex.org/W2050262998","https://openalex.org/W2062352770","https://openalex.org/W2063202994","https://openalex.org/W2063472729","https://openalex.org/W2065043952","https://openalex.org/W2068069653","https://openalex.org/W2069071173","https://openalex.org/W2070527116","https://openalex.org/W2126460072","https://openalex.org/W2131390763","https://openalex.org/W2198113157","https://openalex.org/W2477591619","https://openalex.org/W2506768821","https://openalex.org/W2537964419","https://openalex.org/W2584571300","https://openalex.org/W2745622724","https://openalex.org/W2760428913","https://openalex.org/W2767547464","https://openalex.org/W2769758921","https://openalex.org/W2803719421","https://openalex.org/W2804939729","https://openalex.org/W2885385239","https://openalex.org/W2886810670","https://openalex.org/W2888992950","https://openalex.org/W2901036476","https://openalex.org/W2905428494","https://openalex.org/W2912565176","https://openalex.org/W2914560372","https://openalex.org/W2932003108","https://openalex.org/W2941657186","https://openalex.org/W2942795911","https://openalex.org/W2947861994","https://openalex.org/W4211007335","https://openalex.org/W4249164233","https://openalex.org/W6622692305","https://openalex.org/W6679780668","https://openalex.org/W6721188728"],"related_works":["https://openalex.org/W2041949587","https://openalex.org/W2958553423","https://openalex.org/W2358217305","https://openalex.org/W2359186709","https://openalex.org/W4282827651","https://openalex.org/W3015638941","https://openalex.org/W2047025039","https://openalex.org/W1928481587","https://openalex.org/W2613305061","https://openalex.org/W4237248107"],"abstract_inverted_index":{"The":[0,19],"m-polar":[1,54,86,114],"fuzzy":[2,56,87,116],"sets":[3,23,57],"(mF":[4],"sets)":[5],"have":[6],"a":[7,32,59,127,164],"representative":[8],"and":[9,17,63,99,106],"fundamental":[10],"role":[11],"in":[12,142],"several":[13,25],"fields":[14],"of":[15,21,28,39,61,81,95,104,130,140,150,175],"science":[16],"decision-making.":[18,144],"fusion":[20],"mF":[22,64],"with":[24,73],"other":[26],"theories":[27],"mathematics":[29],"has":[30],"become":[31],"favorable":[33],"practice":[34],"for":[35,90,120,173],"depicting":[36],"numerous":[37],"types":[38],"uncertainties":[40],"under":[41],"multi-polar":[42,71],"information.":[43,96],"In":[44],"this":[45,135],"article,":[46],"we":[47,111,146,162],"introduce":[48],"an":[49,113],"innovative":[50],"hybrid":[51],"model,":[52],"called":[53],"hesitant":[55,115],"(mHF-sets),":[58],"hybridization":[60],"hesitancy":[62],"sets,":[65],"which":[66,125],"enables":[67],"us":[68],"to":[69,134,157],"tackle":[70],"information":[72],"hesitancy.":[74],"Hesitancy":[75],"incorporates":[76],"symmetry":[77],"into":[78],"the":[79,82,85,131,148,158],"treatment":[80],"data,":[83],"whereas":[84],"format":[88],"allows":[89],"differentiated":[91],"or":[92],"asymmetric":[93],"sources":[94],"We":[97,137],"highlight":[98],"explore":[100],"basic":[101],"key":[102],"properties":[103],"mHF-sets":[105,141],"formulate":[107],"intrinsic":[108],"operations.":[109],"Moreover,":[110],"develop":[112],"TOPSIS":[117,132],"(mHF-TOPSIS)":[118],"approach":[119,153],"multi-criteria":[121],"group":[122,143],"decision-making":[123,171],"(MCGDM),":[124],"is":[126],"natural":[128],"extension":[129],"method":[133],"framework.":[136],"describe":[138],"applications":[139],"Further,":[145],"show":[147],"efficiency":[149],"our":[151,170],"proposed":[152],"by":[154],"applying":[155],"it":[156],"industrial":[159],"field.":[160],"Finally,":[161],"generate":[163],"computer":[165],"programming":[166],"code":[167],"that":[168],"implements":[169],"procedure":[172],"ease":[174],"lengthy":[176],"calculations.":[177]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":9},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":6}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}