{"id":"https://openalex.org/W2900419240","doi":"https://doi.org/10.3390/sym10110593","title":"Some Picture Fuzzy Dombi Heronian Mean Operators with Their Application to Multi-Attribute Decision-Making","display_name":"Some Picture Fuzzy Dombi Heronian Mean Operators with Their Application to Multi-Attribute Decision-Making","publication_year":2018,"publication_date":"2018-11-04","ids":{"openalex":"https://openalex.org/W2900419240","doi":"https://doi.org/10.3390/sym10110593","mag":"2900419240"},"language":"en","primary_location":{"id":"doi:10.3390/sym10110593","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym10110593","pdf_url":"https://www.mdpi.com/2073-8994/10/11/593/pdf?version=1542424484","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/2073-8994/10/11/593/pdf?version=1542424484","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040994388","display_name":"Hongran Zhang","orcid":"https://orcid.org/0000-0002-6228-5668"},"institutions":[{"id":"https://openalex.org/I21193070","display_name":"Beijing Jiaotong University","ror":"https://ror.org/01yj56c84","country_code":"CN","type":"education","lineage":["https://openalex.org/I21193070"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hongran Zhang","raw_affiliation_strings":["School of Economics and Management, Beijing Jiaotong University, Beijing 100044, China"],"raw_orcid":"https://orcid.org/0000-0002-6228-5668","affiliations":[{"raw_affiliation_string":"School of Economics and Management, Beijing Jiaotong University, Beijing 100044, China","institution_ids":["https://openalex.org/I21193070"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008891083","display_name":"Runtong Zhang","orcid":"https://orcid.org/0000-0003-0246-5058"},"institutions":[{"id":"https://openalex.org/I21193070","display_name":"Beijing Jiaotong University","ror":"https://ror.org/01yj56c84","country_code":"CN","type":"education","lineage":["https://openalex.org/I21193070"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Runtong Zhang","raw_affiliation_strings":["School of Economics and Management, Beijing Jiaotong University, Beijing 100044, China"],"raw_orcid":"https://orcid.org/0000-0003-0246-5058","affiliations":[{"raw_affiliation_string":"School of Economics and Management, Beijing Jiaotong University, Beijing 100044, China","institution_ids":["https://openalex.org/I21193070"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089956362","display_name":"Huiqun Huang","orcid":"https://orcid.org/0009-0007-5262-472X"},"institutions":[{"id":"https://openalex.org/I21193070","display_name":"Beijing Jiaotong University","ror":"https://ror.org/01yj56c84","country_code":"CN","type":"education","lineage":["https://openalex.org/I21193070"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Huiqun Huang","raw_affiliation_strings":["School of Software Engineering, Beijing Jiaotong University, Beijing 100044, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Software Engineering, Beijing Jiaotong University, Beijing 100044, China","institution_ids":["https://openalex.org/I21193070"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100384616","display_name":"Jun Wang","orcid":"https://orcid.org/0000-0001-7522-8593"},"institutions":[{"id":"https://openalex.org/I21193070","display_name":"Beijing Jiaotong University","ror":"https://ror.org/01yj56c84","country_code":"CN","type":"education","lineage":["https://openalex.org/I21193070"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jun Wang","raw_affiliation_strings":["School of Economics and Management, Beijing Jiaotong University, Beijing 100044, China"],"raw_orcid":"https://orcid.org/0000-0001-7522-8593","affiliations":[{"raw_affiliation_string":"School of Economics and Management, Beijing Jiaotong University, Beijing 100044, China","institution_ids":["https://openalex.org/I21193070"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5008891083"],"corresponding_institution_ids":["https://openalex.org/I21193070"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":7.0365,"has_fulltext":false,"cited_by_count":76,"citation_normalized_percentile":{"value":0.9719301,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"10","issue":"11","first_page":"593","last_page":"593"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9376000165939331,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/fuse","display_name":"Fuse (electrical)","score":0.7294040322303772},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.6227826476097107},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5509490370750427},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.4729565978050232},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.45720773935317993},{"id":"https://openalex.org/keywords/fuzzy-set-operations","display_name":"Fuzzy set operations","score":0.45148828625679016},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4486079216003418},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.40786027908325195},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.39127397537231445},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.37868478894233704},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.37462738156318665},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.34201353788375854}],"concepts":[{"id":"https://openalex.org/C141353440","wikidata":"https://www.wikidata.org/wiki/Q182221","display_name":"Fuse (electrical)","level":2,"score":0.7294040322303772},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.6227826476097107},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5509490370750427},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.4729565978050232},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.45720773935317993},{"id":"https://openalex.org/C148671577","wikidata":"https://www.wikidata.org/wiki/Q5511133","display_name":"Fuzzy set operations","level":4,"score":0.45148828625679016},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4486079216003418},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.40786027908325195},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.39127397537231445},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37868478894233704},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.37462738156318665},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.34201353788375854},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym10110593","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym10110593","pdf_url":"https://www.mdpi.com/2073-8994/10/11/593/pdf?version=1542424484","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:2309e3d7e3ae402587ae75adfc641fd5","is_oa":true,"landing_page_url":"https://doaj.org/article/2309e3d7e3ae402587ae75adfc641fd5","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 10, Iss 11, p 593 (2018)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/10/11/593/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym10110593","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/sym10110593","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym10110593","pdf_url":"https://www.mdpi.com/2073-8994/10/11/593/pdf?version=1542424484","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":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.8299999833106995}],"awards":[{"id":"https://openalex.org/G3376678438","display_name":null,"funder_award_id":"71532002","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":61,"referenced_works":["https://openalex.org/W1174510090","https://openalex.org/W1580581679","https://openalex.org/W1967753042","https://openalex.org/W1971875039","https://openalex.org/W1980564456","https://openalex.org/W1981107087","https://openalex.org/W1983286635","https://openalex.org/W2003115337","https://openalex.org/W2008103229","https://openalex.org/W2013908206","https://openalex.org/W2016698635","https://openalex.org/W2032284775","https://openalex.org/W2036575376","https://openalex.org/W2143050169","https://openalex.org/W2236517793","https://openalex.org/W2287374056","https://openalex.org/W2295963161","https://openalex.org/W2305863142","https://openalex.org/W2326707701","https://openalex.org/W2329317779","https://openalex.org/W2336936753","https://openalex.org/W2385257316","https://openalex.org/W2395060331","https://openalex.org/W2463044584","https://openalex.org/W2479843152","https://openalex.org/W2508556687","https://openalex.org/W2530680027","https://openalex.org/W2533445771","https://openalex.org/W2540140736","https://openalex.org/W2548735830","https://openalex.org/W2579304191","https://openalex.org/W2591483750","https://openalex.org/W2591936123","https://openalex.org/W2592542840","https://openalex.org/W2611011107","https://openalex.org/W2620840857","https://openalex.org/W2624112931","https://openalex.org/W2734543528","https://openalex.org/W2739534728","https://openalex.org/W2765516692","https://openalex.org/W2767160721","https://openalex.org/W2767344862","https://openalex.org/W2769125990","https://openalex.org/W2772336371","https://openalex.org/W2774209583","https://openalex.org/W2784775847","https://openalex.org/W2803479614","https://openalex.org/W2806055845","https://openalex.org/W2807807069","https://openalex.org/W2810614033","https://openalex.org/W2831026053","https://openalex.org/W2872158697","https://openalex.org/W2876035269","https://openalex.org/W2897422271","https://openalex.org/W4211007335","https://openalex.org/W6728217526","https://openalex.org/W6737311338","https://openalex.org/W6746205570","https://openalex.org/W6748582889","https://openalex.org/W6752877161","https://openalex.org/W6753128344"],"related_works":["https://openalex.org/W2121560876","https://openalex.org/W2253053392","https://openalex.org/W2184441312","https://openalex.org/W4206081075","https://openalex.org/W2331106272","https://openalex.org/W2366385051","https://openalex.org/W1470403688","https://openalex.org/W1486684451","https://openalex.org/W4361984403","https://openalex.org/W4361273540"],"abstract_inverted_index":{"As":[0],"an":[1],"extension":[2],"of":[3,32,79,172],"the":[4,9,77,125,152,158],"intuitionistic":[5],"fuzzy":[6,13,28,42,57,65,98,105,188,199],"set":[7,14],"(IFS),":[8],"recently":[10],"proposed":[11,109,153],"picture":[12,41,56,64,97,104,187,198],"(PFS)":[15],"is":[16,52,201],"more":[17,132],"suitable":[18,133],"to":[19,53,95,123,147],"describe":[20],"decision-makers\u2019":[21],"evaluation":[22],"information":[23,92],"in":[24,35,46,164],"decision-making":[25,37,43],"problems.":[26,140],"Picture":[27],"aggregation":[29,58,93,106,189],"operators":[30,110,190],"are":[31,175,183,191],"high":[33],"importance":[34],"multi-attribute":[36],"(MADM)":[38],"within":[39],"a":[40,80,120,144,165,194],"environment.":[44],"Hence,":[45,141],"this":[47,173],"paper":[48],"our":[49],"main":[50,170],"work":[51,174],"introduce":[54,143],"novel":[55,186],"operators.":[59,107,154],"Firstly,":[60,177],"we":[61,87,142,156],"propose":[62,102],"new":[63,103,145,178,195],"operational":[66,179],"rules":[67],"based":[68,150],"on":[69,151],"Dombi":[70],"t-conorm":[71],"and":[72,82,101,162],"t-norm":[73],"(DTT).":[74],"Secondly,":[75,185],"considering":[76],"existence":[78],"broad":[81],"widespread":[83,126],"correlation":[84,127],"between":[85],"attributes,":[86,129],"use":[88],"Heronian":[89],"mean":[90],"(HM)":[91],"technology":[94],"fuse":[96,113],"numbers":[99],"(PFNs)":[100],"The":[108,169],"not":[111],"only":[112],"individual":[114],"attribute":[115],"values,":[116],"but":[117],"also":[118],"have":[119],"good":[121],"ability":[122],"model":[124],"among":[128],"making":[130],"them":[131],"for":[134,181,197],"effectively":[135],"solving":[136],"increasingly":[137],"complicated":[138],"MADM":[139,149,200],"algorithm":[146,163],"handle":[148],"Finally,":[155],"apply":[157],"newly":[159],"developed":[160],"method":[161],"supplier":[166],"selection":[167],"issue.":[168],"novelties":[171],"three-fold.":[176],"laws":[180],"PFSs":[182],"proposed.":[184,202],"developed.":[192],"Thirdly,":[193],"approach":[196]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":11},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":12},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":15},{"year":2020,"cited_by_count":10},{"year":2019,"cited_by_count":12}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
