{"id":"https://openalex.org/W7119528512","doi":"https://doi.org/10.3390/sym18010119","title":"Double-Framed Bipolar Fuzzy Soft Sets and Algorithmic Approaches with Symmetry for Multi-Criteria Decision-Making Under Uncertainty","display_name":"Double-Framed Bipolar Fuzzy Soft Sets and Algorithmic Approaches with Symmetry for Multi-Criteria Decision-Making Under Uncertainty","publication_year":2026,"publication_date":"2026-01-08","ids":{"openalex":"https://openalex.org/W7119528512","doi":"https://doi.org/10.3390/sym18010119"},"language":"en","primary_location":{"id":"doi:10.3390/sym18010119","doi":"https://doi.org/10.3390/sym18010119","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym18010119","pdf_url":"https://www.mdpi.com/2073-8994/18/1/119/pdf","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,"listed_in":["cwts-core","norway-1"],"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"},"volume":null,"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/18/1/119/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5039062301","display_name":"Shadya Merkhan Mershkhan","orcid":"https://orcid.org/0009-0008-1667-8664","observed_orcids":["https://orcid.org/0009-0008-1667-8664"]},"institutions":[{"id":"https://openalex.org/I36162470","display_name":"University of Zakho","ror":"https://ror.org/05sd1pz50","country_code":"IQ","type":"education","lineage":["https://openalex.org/I36162470"]}],"countries":["IQ"],"is_corresponding":false,"raw_author_name":"Shadya M. Mershkhan","raw_affiliation_strings":["Department of Mathematics, College of Science, University of Zakho, Zakho 42002, Iraq"],"raw_orcid":"https://orcid.org/0009-0008-1667-8664","affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, University of Zakho, Zakho 42002, Iraq","institution_ids":["https://openalex.org/I36162470"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005561093","display_name":"Baravan A. Asaad","orcid":"https://orcid.org/0000-0002-2049-2044","observed_orcids":["https://orcid.org/0000-0002-2049-2044"]},"institutions":[{"id":"https://openalex.org/I36162470","display_name":"University of Zakho","ror":"https://ror.org/05sd1pz50","country_code":"IQ","type":"education","lineage":["https://openalex.org/I36162470"]},{"id":"https://openalex.org/I4391767809","display_name":"Cihan University - Duhok","ror":"https://ror.org/024j6hc19","country_code":"IQ","type":"education","lineage":["https://openalex.org/I4391767809"]}],"countries":["IQ"],"is_corresponding":true,"raw_author_name":"Baravan A. Asaad","raw_affiliation_strings":["Department of Computer Science, College of Science, Cihan University-Duhok, Duhok 42001, Iraq","Department of Mathematics, College of Science, University of Zakho, Zakho 42002, Iraq"],"raw_orcid":"https://orcid.org/0000-0002-2049-2044","affiliations":[{"raw_affiliation_string":"Department of Computer Science, College of Science, Cihan University-Duhok, Duhok 42001, Iraq","institution_ids":["https://openalex.org/I4391767809"]},{"raw_affiliation_string":"Department of Mathematics, College of Science, University of Zakho, Zakho 42002, Iraq","institution_ids":["https://openalex.org/I36162470"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5005561093"],"corresponding_institution_ids":["https://openalex.org/I36162470","https://openalex.org/I4391767809"],"apc_list":{"value":2400,"currency":"CHF","value_usd":2896},"apc_paid":{"value":2400,"currency":"CHF","value_usd":2896},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.02150338,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"18","issue":"1","first_page":"119","last_page":"119"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11671","display_name":"Fuzzy and Soft Set Theory","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/T11671","display_name":"Fuzzy and Soft Set Theory","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/T10050","display_name":"Multi-Criteria Decision Making","score":0.0,"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":0.0,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/bipolar-fuzzy-sets","display_name":"bipolar fuzzy sets","score":0.8619999885559082},{"id":"https://openalex.org/keywords/bipolar-soft-sets","display_name":"bipolar soft sets","score":0.9909999966621399},{"id":"https://openalex.org/keywords/multi-criteria-decision-making","display_name":"multi-criteria decision making","score":0.878000020980835},{"id":"https://openalex.org/keywords/decision-making-under-uncertainty","display_name":"decision making under uncertainty","score":0.875},{"id":"https://openalex.org/keywords/decision-making-algorithm","display_name":"decision-making algorithm","score":0.5429999828338623}],"concepts":[{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5849000215530396},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.5843999981880188},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.5824999809265137},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5185999870300293},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5060999989509583},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.4553000032901764},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42080000042915344},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.41659998893737793},{"id":"https://openalex.org/C2777037408","wikidata":"https://www.wikidata.org/wiki/Q4310193","display_name":"Soft set","level":3,"score":0.3774000108242035},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.35019999742507935},{"id":"https://openalex.org/C148671577","wikidata":"https://www.wikidata.org/wiki/Q5511133","display_name":"Fuzzy set operations","level":4,"score":0.3440000116825104},{"id":"https://openalex.org/C195975749","wikidata":"https://www.wikidata.org/wiki/Q1475705","display_name":"Fuzzy control system","level":3,"score":0.3375999927520752},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.31839999556541443},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3181000053882599},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2870999872684479},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.2851000130176544},{"id":"https://openalex.org/C140073362","wikidata":"https://www.wikidata.org/wiki/Q738759","display_name":"Soft computing","level":3,"score":0.26170000433921814},{"id":"https://openalex.org/C127385683","wikidata":"https://www.wikidata.org/wiki/Q1475696","display_name":"Fuzzy classification","level":4,"score":0.25929999351501465},{"id":"https://openalex.org/C17350324","wikidata":"https://www.wikidata.org/wiki/Q7860605","display_name":"Type-2 fuzzy sets and systems","level":5,"score":0.2529999911785126},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.25049999356269836}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3390/sym18010119","doi":"https://doi.org/10.3390/sym18010119","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym18010119","pdf_url":"https://www.mdpi.com/2073-8994/18/1/119/pdf","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,"listed_in":["cwts-core","norway-1"],"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"}],"best_oa_location":{"id":"doi:10.3390/sym18010119","doi":"https://doi.org/10.3390/sym18010119","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym18010119","pdf_url":"https://www.mdpi.com/2073-8994/18/1/119/pdf","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,"listed_in":["cwts-core","norway-1"],"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":[],"sustainable_development_goals_aurora":[{"display_name":"Peace, justice, and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.8183683753013611}],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7119528512.pdf","grobid_xml":"https://content.openalex.org/works/W7119528512.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0,48,60,83],"bipolar":[1,5,18],"fuzzy":[2,19,97],"set":[3,7,89,100],"and":[4,27,41,51,58,98,112,129],"soft":[6,20,99],"have":[8],"inspired":[9],"the":[10,66,69,87,120,126],"development":[11],"of":[12,38,53,71,78,86,93],"a":[13,35,104,115],"new":[14],"framework":[15],"called":[16],"double-framed":[17,61],"sets":[21],"(DFBFSSs).":[22],"This":[23,73],"structure":[24,70],"represents":[25],"positive":[26],"negative":[28],"membership":[29],"information":[30,43],"through":[31],"ordered":[32],"pairs,":[33],"enabling":[34],"balanced":[36,76],"treatment":[37],"uncertainty,":[39],"imprecision,":[40],"bi-directional":[42],"in":[44,131],"complex":[45],"decision-making":[46,105],"scenarios.":[47],"fundamental":[49],"concepts":[50],"operations":[52],"DFBFSSs":[54,109],"are":[55],"rigorously":[56],"defined":[57],"analyzed.":[59],"formulation":[62],"is":[63,110],"symmetric:":[64],"exchanging":[65],"frames":[67],"preserves":[68],"DFBFSSs.":[72],"symmetry":[74],"enables":[75],"handling":[77,92],"opposing":[79],"or":[80],"complementary":[81],"information.":[82],"key":[84],"properties":[85],"proposed":[88],"show":[90],"improved":[91],"uncertainty":[94],"over":[95],"existing":[96],"models.":[101],"In":[102],"addition,":[103],"algorithm":[106],"based":[107],"on":[108],"developed":[111],"applied":[113],"to":[114,118],"real-world":[116],"problem":[117],"validate":[119],"framework\u2019s":[121],"feasibility.":[122],"Comparative":[123],"analysis":[124],"confirms":[125],"method\u2019s":[127],"robustness":[128],"advantages":[130],"uncertain,":[132],"dual-information":[133],"settings.":[134]},"counts_by_year":[],"updated_date":"2026-09-27T08:07:27.782135","created_date":"2026-01-09T00:00:00"}
