{"id":"https://openalex.org/W4361268590","doi":"https://doi.org/10.3390/sym15040826","title":"Geometric Aggregation Operators for Solving Multicriteria Group Decision-Making Problems Based on Complex Pythagorean Fuzzy Sets","display_name":"Geometric Aggregation Operators for Solving Multicriteria Group Decision-Making Problems Based on Complex Pythagorean Fuzzy Sets","publication_year":2023,"publication_date":"2023-03-29","ids":{"openalex":"https://openalex.org/W4361268590","doi":"https://doi.org/10.3390/sym15040826"},"language":"en","primary_location":{"id":"doi:10.3390/sym15040826","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15040826","pdf_url":"https://www.mdpi.com/2073-8994/15/4/826/pdf?version=1680601961","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/2073-8994/15/4/826/pdf?version=1680601961","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5069353336","display_name":"Ibrahim M. Hezam","orcid":"https://orcid.org/0000-0003-2747-6722"},"institutions":[{"id":"https://openalex.org/I28022161","display_name":"King Saud University","ror":"https://ror.org/02f81g417","country_code":"SA","type":"education","lineage":["https://openalex.org/I28022161"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"Ibrahim M. Hezam","raw_affiliation_strings":["Statistics & Operations Research Department, College of Sciences, King Saud University, Riyadh 11451, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0003-2747-6722","affiliations":[{"raw_affiliation_string":"Statistics & Operations Research Department, College of Sciences, King Saud University, Riyadh 11451, Saudi Arabia","institution_ids":["https://openalex.org/I28022161"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102402405","display_name":"Khaista Rahman","orcid":null},"institutions":[{"id":"https://openalex.org/I1308893265","display_name":"Shaheed Benazir Bhutto University","ror":"https://ror.org/02zwhz281","country_code":"PK","type":"education","lineage":["https://openalex.org/I1308893265"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Khaista Rahman","raw_affiliation_strings":["Department of Mathematics, Shaheed Benazir Bhutto University, Sheringal 18000, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shaheed Benazir Bhutto University, Sheringal 18000, Pakistan","institution_ids":["https://openalex.org/I1308893265"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018298333","display_name":"Ahmad M. Alshamrani","orcid":"https://orcid.org/0000-0001-7103-8872"},"institutions":[{"id":"https://openalex.org/I28022161","display_name":"King Saud University","ror":"https://ror.org/02f81g417","country_code":"SA","type":"education","lineage":["https://openalex.org/I28022161"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Ahmad Alshamrani","raw_affiliation_strings":["Statistics & Operations Research Department, College of Sciences, King Saud University, Riyadh 11451, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0001-7103-8872","affiliations":[{"raw_affiliation_string":"Statistics & Operations Research Department, College of Sciences, King Saud University, Riyadh 11451, Saudi Arabia","institution_ids":["https://openalex.org/I28022161"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078330420","display_name":"Darko Bo\u017eani\u0107","orcid":"https://orcid.org/0000-0002-9657-0889"},"institutions":[{"id":"https://openalex.org/I4210153194","display_name":"University of Defence","ror":"https://ror.org/04mmq3h75","country_code":"RS","type":"education","lineage":["https://openalex.org/I4210153194"]}],"countries":["RS"],"is_corresponding":false,"raw_author_name":"Darko Bo\u017eani\u0107","raw_affiliation_strings":["Military Academy, University of Defence in Belgarde, 11000 Belgrade, Serbia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Military Academy, University of Defence in Belgarde, 11000 Belgrade, Serbia","institution_ids":["https://openalex.org/I4210153194"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5069353336"],"corresponding_institution_ids":["https://openalex.org/I28022161"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":4.1489,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.94043683,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"15","issue":"4","first_page":"826","last_page":"826"},"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":0.9835000038146973,"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/T13058","display_name":"Soil and Land Suitability Analysis","score":0.9726999998092651,"subfield":{"id":"https://openalex.org/subfields/2308","display_name":"Management, Monitoring, Policy and Law"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/pythagorean-theorem","display_name":"Pythagorean theorem","score":0.9004553556442261},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.628955066204071},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5523487329483032},{"id":"https://openalex.org/keywords/algebraic-structure","display_name":"Algebraic structure","score":0.4829508662223816},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.4229907989501953},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.4144333600997925},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.40723785758018494},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.37268713116645813},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3675500154495239},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.30809593200683594},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.12370389699935913}],"concepts":[{"id":"https://openalex.org/C100461760","wikidata":"https://www.wikidata.org/wiki/Q11518","display_name":"Pythagorean theorem","level":2,"score":0.9004553556442261},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.628955066204071},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5523487329483032},{"id":"https://openalex.org/C182419690","wikidata":"https://www.wikidata.org/wiki/Q205464","display_name":"Algebraic structure","level":2,"score":0.4829508662223816},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.4229907989501953},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.4144333600997925},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.40723785758018494},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37268713116645813},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3675500154495239},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.30809593200683594},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.12370389699935913},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym15040826","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15040826","pdf_url":"https://www.mdpi.com/2073-8994/15/4/826/pdf?version=1680601961","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:9852fc7f6f1447d09ac7df3fb9d96221","is_oa":false,"landing_page_url":"https://doaj.org/article/9852fc7f6f1447d09ac7df3fb9d96221","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 15, Iss 4, p 826 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/15/4/826/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym15040826","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/sym15040826","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15040826","pdf_url":"https://www.mdpi.com/2073-8994/15/4/826/pdf?version=1680601961","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":[{"score":0.8199999928474426,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4361268590.pdf","grobid_xml":"https://content.openalex.org/works/W4361268590.grobid-xml"},"referenced_works_count":43,"referenced_works":["https://openalex.org/W1965777053","https://openalex.org/W1971875039","https://openalex.org/W1980564456","https://openalex.org/W1981107087","https://openalex.org/W2008103229","https://openalex.org/W2012575173","https://openalex.org/W2013932252","https://openalex.org/W2053405721","https://openalex.org/W2097403045","https://openalex.org/W2153478942","https://openalex.org/W2343846868","https://openalex.org/W2345848912","https://openalex.org/W2407616923","https://openalex.org/W2549733045","https://openalex.org/W2612056196","https://openalex.org/W2618345998","https://openalex.org/W2756768858","https://openalex.org/W2790860809","https://openalex.org/W2810971783","https://openalex.org/W2816396220","https://openalex.org/W2871390967","https://openalex.org/W2883333523","https://openalex.org/W2889768290","https://openalex.org/W2945404912","https://openalex.org/W2953509089","https://openalex.org/W2962753525","https://openalex.org/W2995299237","https://openalex.org/W3111618493","https://openalex.org/W3171535324","https://openalex.org/W3215047300","https://openalex.org/W4211007335","https://openalex.org/W4213045795","https://openalex.org/W4220671272","https://openalex.org/W4226075680","https://openalex.org/W4280642307","https://openalex.org/W4297323780","https://openalex.org/W4311049995","https://openalex.org/W4316673350","https://openalex.org/W6663558164","https://openalex.org/W6737708842","https://openalex.org/W6744609909","https://openalex.org/W6803865269","https://openalex.org/W6808492934"],"related_works":["https://openalex.org/W2995447873","https://openalex.org/W2541537839","https://openalex.org/W1486684451","https://openalex.org/W2116249946","https://openalex.org/W2801459815","https://openalex.org/W2099285375","https://openalex.org/W4361273540","https://openalex.org/W4361984403","https://openalex.org/W4317826560","https://openalex.org/W2006136802"],"abstract_inverted_index":{"The":[0],"Complex":[1],"Pythagorean":[2,60,68,74,81,88,97],"fuzzy":[3,21,61,69,75,82,89,98,126,131],"set":[4,127],"(CPyFS)":[5],"is":[6,27],"an":[7,135,141],"efficient":[8],"tool":[9],"to":[10,148],"handle":[11],"two-dimensional":[12],"periodic":[13],"uncertain":[14,53],"information,":[15],"which":[16],"has":[17],"various":[18],"applications":[19],"in":[20,46,146],"modeling":[22],"and":[23,42,94,102,110,128,153],"decision":[24,47],"making.":[25],"It":[26],"known":[28],"that":[29,50],"the":[30,40,116,138,150,156],"aggregation":[31,37,63,158],"operators":[32,38,45],"influence":[33],"decision-making":[34],"processes.":[35],"Algebraic":[36],"are":[39],"important":[41],"widely":[43],"used":[44],"making":[48],"techniques":[49],"deal":[51],"with":[52,119],"problems.":[54],"This":[55],"paper":[56],"investigates":[57],"some":[58],"complex":[59,67,73,80,87,96,125,129],"geometric":[62,71,78,84,92,100],"operators,":[64],"such":[65,106,123],"as":[66,107,124],"weighted":[70,77,91],"(CPyFWG),":[72],"ordered":[76,90],"(CPyFOWG),":[79],"hybrid":[83,99],"(CPyFHG),":[85],"induced":[86,95],"(I-CPyFOWG),":[93],"(I-CPyFHG),":[101],"their":[103,120],"structure":[104],"properties,":[105],"idempotency,":[108],"boundedness,":[109],"monotonicity.":[111],"In":[112],"addition,":[113],"we":[114],"compare":[115],"proposed":[117],"model":[118],"existing":[121],"models,":[122],"intuitionistic":[130],"set.":[132],"We":[133],"analyze":[134],"example":[136],"involving":[137],"selection":[139],"of":[140,155],"acceptable":[142],"location":[143],"for":[144],"hospitals":[145],"order":[147],"demonstrate":[149],"effectiveness,":[151],"appropriateness,":[152],"efficiency":[154],"novel":[157],"operators.":[159]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":3}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}