{"id":"https://openalex.org/W4405847778","doi":"https://doi.org/10.3390/sym17010034","title":"Spontaneous Symmetry Breaking in Group Decision-Making with Complex Polytopic Fuzzy System","display_name":"Spontaneous Symmetry Breaking in Group Decision-Making with Complex Polytopic Fuzzy System","publication_year":2024,"publication_date":"2024-12-27","ids":{"openalex":"https://openalex.org/W4405847778","doi":"https://doi.org/10.3390/sym17010034"},"language":"en","primary_location":{"id":"doi:10.3390/sym17010034","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17010034","pdf_url":"https://www.mdpi.com/2073-8994/17/1/34/pdf?version=1735304545","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/2073-8994/17/1/34/pdf?version=1735304545","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5069417193","display_name":"Muhammad Bilal","orcid":"https://orcid.org/0000-0002-5518-6370"},"institutions":[{"id":"https://openalex.org/I189210763","display_name":"Yunnan University","ror":"https://ror.org/0040axw97","country_code":"CN","type":"education","lineage":["https://openalex.org/I189210763"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Muhammad Bilal","raw_affiliation_strings":["School of Mathematics and Statistics, Yunnan University, Kunming 650106, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Yunnan University, Kunming 650106, China","institution_ids":["https://openalex.org/I189210763"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5069417193"],"corresponding_institution_ids":["https://openalex.org/I189210763"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.0217,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.81227235,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":96},"biblio":{"volume":"17","issue":"1","first_page":"34","last_page":"34"},"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/T12709","display_name":"Optimization and Mathematical Programming","score":0.9908000230789185,"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":0.9890999794006348,"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/fuzzy-logic","display_name":"Fuzzy logic","score":0.6762955188751221},{"id":"https://openalex.org/keywords/group-decision-making","display_name":"Group decision-making","score":0.5078347325325012},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.4959934651851654},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4831813871860504},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.43982747197151184},{"id":"https://openalex.org/keywords/fuzzy-set-operations","display_name":"Fuzzy set operations","score":0.4376779794692993},{"id":"https://openalex.org/keywords/type-2-fuzzy-sets-and-systems","display_name":"Type-2 fuzzy sets and systems","score":0.430563747882843},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42100659012794495},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.40457797050476074},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.38313496112823486},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.26225560903549194}],"concepts":[{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.6762955188751221},{"id":"https://openalex.org/C20701700","wikidata":"https://www.wikidata.org/wiki/Q388791","display_name":"Group decision-making","level":2,"score":0.5078347325325012},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.4959934651851654},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4831813871860504},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.43982747197151184},{"id":"https://openalex.org/C148671577","wikidata":"https://www.wikidata.org/wiki/Q5511133","display_name":"Fuzzy set operations","level":4,"score":0.4376779794692993},{"id":"https://openalex.org/C17350324","wikidata":"https://www.wikidata.org/wiki/Q7860605","display_name":"Type-2 fuzzy sets and systems","level":5,"score":0.430563747882843},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42100659012794495},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.40457797050476074},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.38313496112823486},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.26225560903549194},{"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/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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/sym17010034","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17010034","pdf_url":"https://www.mdpi.com/2073-8994/17/1/34/pdf?version=1735304545","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:e89c5a655c3c42fabd5efec120761439","is_oa":true,"landing_page_url":"https://doaj.org/article/e89c5a655c3c42fabd5efec120761439","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","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 17, Iss 1, p 34 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym17010034","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17010034","pdf_url":"https://www.mdpi.com/2073-8994/17/1/34/pdf?version=1735304545","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","id":"https://metadata.un.org/sdg/16","score":0.800000011920929}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4405847778.pdf","grobid_xml":"https://content.openalex.org/works/W4405847778.grobid-xml"},"referenced_works_count":55,"referenced_works":["https://openalex.org/W1965777053","https://openalex.org/W1980564456","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/W2514754342","https://openalex.org/W2549733045","https://openalex.org/W2746747652","https://openalex.org/W2790860809","https://openalex.org/W2810449588","https://openalex.org/W2816396220","https://openalex.org/W2871390967","https://openalex.org/W2883333523","https://openalex.org/W2901104715","https://openalex.org/W2940516091","https://openalex.org/W2945404912","https://openalex.org/W2953160093","https://openalex.org/W2953509089","https://openalex.org/W2981772589","https://openalex.org/W2995299237","https://openalex.org/W3043586643","https://openalex.org/W3121700030","https://openalex.org/W4205769419","https://openalex.org/W4211007335","https://openalex.org/W4220786204","https://openalex.org/W4226280148","https://openalex.org/W4229078348","https://openalex.org/W4229370309","https://openalex.org/W4280642307","https://openalex.org/W4306249322","https://openalex.org/W4310478664","https://openalex.org/W4312205568","https://openalex.org/W4361268590","https://openalex.org/W4365128455","https://openalex.org/W4382070193","https://openalex.org/W4387978821","https://openalex.org/W4388576727","https://openalex.org/W4388877651","https://openalex.org/W4389203636","https://openalex.org/W4389250123","https://openalex.org/W4390918398","https://openalex.org/W4399904323","https://openalex.org/W4401398134","https://openalex.org/W4402619483","https://openalex.org/W4404195667","https://openalex.org/W6645914205","https://openalex.org/W6663558164","https://openalex.org/W6809642882","https://openalex.org/W6852109968","https://openalex.org/W6853951174"],"related_works":["https://openalex.org/W2674573885","https://openalex.org/W2253053392","https://openalex.org/W2614887008","https://openalex.org/W4206081075","https://openalex.org/W2121560876","https://openalex.org/W2211233","https://openalex.org/W2331106272","https://openalex.org/W1486684451","https://openalex.org/W4361984403","https://openalex.org/W4361273540"],"abstract_inverted_index":{"Beginning":[0],"with":[1,215],"a":[2,11,37,143,158,170,257,266],"symmetrical":[3],"multiple-choice":[4],"individual":[5],"as":[6],"the":[7,18,22,25,67,78,107,131,162,167,179,199,221,252,273,278],"foundation,":[8],"I":[9],"develop":[10],"sociophysics":[12],"model":[13,29,110],"of":[14,20,40,147,169,203,251,277],"decision-making.":[15],"By":[16],"simplifying":[17],"range":[19],"choices,":[21],"framework":[23,168],"incorporates":[24],"complex":[26,125,137,150,171,186,211,222,230,239],"Polytopic":[27,126,132,172,187,212,223,231,240],"fuzzy":[28,94,127,133,138,173,188,213,224,232,241],"to":[30,61,109,119,156,271],"capture":[31],"nuanced":[32,100],"dynamics.":[33],"This":[34,85,153,196],"approach":[35],"enables":[36],"deeper":[38],"analysis":[39],"decision-making":[41,96],"processes":[42,205],"within":[43,166],"social":[44],"systems.":[45],"Decision-making":[46],"problems":[47],"commonly":[48,89],"involve":[49],"uncertainty":[50],"and":[51,58,64,71,82,91,111,114,136,164,182,191,201,265,275],"complexity,":[52],"posing":[53],"considerable":[54],"challenges":[55],"for":[56,142,185],"organizations":[57],"individuals.":[59],"Due":[60],"their":[62,193],"structure":[63],"variable":[65],"parameters,":[66],"Einstein":[68,180,225,233,242],"t-norm":[69,80],"(ETN)":[70],"t-conorm":[72,83],"(ETCN)":[73],"offer":[74],"more":[75,120,144],"elasticity":[76],"than":[77],"algebraic":[79],"(ATN)":[81],"(ATCN).":[84],"flexibility":[86],"makes":[87],"them":[88],"effective":[90],"valuable":[92],"in":[93,149,206],"multi-attribute":[95],"(MADM)":[97,151],"problems,":[98],"where":[99],"valuations":[101],"are":[102,219,254],"critical.":[103],"Their":[104],"application":[105],"enhances":[106,198],"ability":[108],"analyze":[112],"vagueness":[113],"uncertain":[115],"information,":[116],"eventually":[117],"leading":[118],"informed":[121],"decision":[122],"outcomes.":[123],"The":[124],"set":[128,134,139],"(CPFS)":[129],"improves":[130],"(PFS)":[135],"(CPFS),":[140],"allowing":[141],"precise":[145],"valuation":[146],"attributes":[148],"problems.":[152],"study":[154],"aims":[155],"propose":[157],"MADM":[159],"scheme":[160],"using":[161],"ETN":[163],"ETCN":[165],"environment.":[174],"It":[175],"begins":[176],"by":[177],"presenting":[178],"product":[181],"sum":[183],"operations":[184],"numbers":[189],"(CPFNs)":[190],"explores":[192],"necessary":[194],"properties.":[195],"method":[197,258],"accuracy":[200],"applicability":[202],"DM":[204],"ambiguous":[207],"environments.":[208],"Subsequently,":[209],"three":[210],"operators":[214,253,262],"known":[216],"weighted":[217,226,235],"vectors":[218],"developed:":[220],"averaging":[227,236,244],"(CPFEWA)":[228],"operator,":[229,238],"ordered":[234],"(CPFEOWA)":[237],"hybrid":[243],"(CPFEHA)":[245],"operator.":[246],"Moreover,":[247],"some":[248],"substantial":[249],"properties":[250],"studied.":[255],"Finally,":[256],"based":[259],"on":[260],"novel":[261],"is":[263,269],"planned,":[264],"numerical":[267],"example":[268],"provided":[270],"prove":[272],"practicality":[274],"effectiveness":[276],"new":[279],"proposed":[280],"methods.":[281]},"counts_by_year":[{"year":2025,"cited_by_count":2}],"updated_date":"2026-03-10T14:07:55.174380","created_date":"2025-10-10T00:00:00"}
