{"id":"https://openalex.org/W7225463531","doi":"https://doi.org/10.7546/nifs.2026.32.3.296-308","title":"Algebraic structures of circular intuitionistic fuzzy triples: Monoids, multi-unitary groups, and lattice properties","display_name":"Algebraic structures of circular intuitionistic fuzzy triples: Monoids, multi-unitary groups, and lattice properties","publication_year":2026,"publication_date":"2026-11-06","ids":{"openalex":"https://openalex.org/W7225463531","doi":"https://doi.org/10.7546/nifs.2026.32.3.296-308"},"language":"en","primary_location":{"id":"doi:10.7546/nifs.2026.32.3.296-308","doi":"https://doi.org/10.7546/nifs.2026.32.3.296-308","is_oa":true,"landing_page_url":"https://doi.org/10.7546/nifs.2026.32.3.296-308","pdf_url":"https://ifigenia.org/images/7/7f/NIFS-32-3-296-308.pdf","source":{"id":"https://openalex.org/S4210236489","display_name":"Notes on Intuitionistic Fuzzy Sets","issn_l":"1310-4926","issn":["1310-4926","2367-8283"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["doaj"],"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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notes on Intuitionistic Fuzzy Sets","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://ifigenia.org/images/7/7f/NIFS-32-3-296-308.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018332517","display_name":"Velichka Traneva","orcid":"https://orcid.org/0000-0002-8929-4126","observed_orcids":["https://orcid.org/0000-0002-8929-4126"]},"institutions":[{"id":"https://openalex.org/I4210108077","display_name":"Prof. Assen Zlatarov University","ror":"https://ror.org/020ak9w19","country_code":"BG","type":"education","lineage":["https://openalex.org/I4210108077"]}],"countries":["BG"],"is_corresponding":false,"raw_author_name":"Velichka Traneva","raw_affiliation_strings":["Burgas State University \"Prof. Dr. Assen Zlatarov\""],"raw_orcid":"https://orcid.org/0000-0002-8929-4126","affiliations":[{"raw_affiliation_string":"Burgas State University \"Prof. Dr. Assen Zlatarov\"","institution_ids":["https://openalex.org/I4210108077"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019841551","display_name":"Stoyan Tranev","orcid":"https://orcid.org/0000-0002-5807-4139","observed_orcids":["https://orcid.org/0000-0002-5807-4139"]},"institutions":[{"id":"https://openalex.org/I4210108077","display_name":"Prof. Assen Zlatarov University","ror":"https://ror.org/020ak9w19","country_code":"BG","type":"education","lineage":["https://openalex.org/I4210108077"]}],"countries":["BG"],"is_corresponding":false,"raw_author_name":"Stoyan Tranev","raw_affiliation_strings":["Burgas State University \"Prof. Dr. Assen Zlatarov\""],"raw_orcid":"https://orcid.org/0000-0002-5807-4139","affiliations":[{"raw_affiliation_string":"Burgas State University \"Prof. Dr. Assen Zlatarov\"","institution_ids":["https://openalex.org/I4210108077"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038199341","display_name":"Krassimir Todorov Atanassov","orcid":"https://orcid.org/0000-0001-5625-071X","observed_orcids":["https://orcid.org/0000-0001-5625-071X"]},"institutions":[{"id":"https://openalex.org/I24768866","display_name":"Bulgarian Academy of Sciences","ror":"https://ror.org/01x8hew03","country_code":"BG","type":"government","lineage":["https://openalex.org/I24768866"]},{"id":"https://openalex.org/I4210103918","display_name":"Institute of Biophysics and Biomedical Engineering","ror":"https://ror.org/01dxqkr82","country_code":"BG","type":"facility","lineage":["https://openalex.org/I24768866","https://openalex.org/I4210103918"]}],"countries":["BG"],"is_corresponding":false,"raw_author_name":"Krassimir Atanassov","raw_affiliation_strings":["Department of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences"],"raw_orcid":"https://orcid.org/0000-0001-5625-071X","affiliations":[{"raw_affiliation_string":"Department of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences","institution_ids":["https://openalex.org/I24768866","https://openalex.org/I4210103918"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"32","issue":"3","first_page":"296","last_page":"308"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9136000275611877,"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":0.9136000275611877,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.062300000339746475,"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/T10050","display_name":"Multi-Criteria Decision Making","score":0.011699999682605267,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/algebraic-structures","display_name":"algebraic structures","score":0.8679999709129333},{"id":"https://openalex.org/keywords/commutative-monoids","display_name":"commutative monoids","score":0.9850000143051147},{"id":"https://openalex.org/keywords/inverse-elements","display_name":"inverse elements","score":0.5849999785423279},{"id":"https://openalex.org/keywords/distributive-lattices","display_name":"distributive lattices","score":0.8090000152587891},{"id":"https://openalex.org/keywords/negation","display_name":"negation","score":0.628000020980835},{"id":"https://openalex.org/keywords/aggregation-operations","display_name":"aggregation operations","score":0.609000027179718}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8374999761581421},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.6626999974250793},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5425999760627747},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.4767000079154968},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4747999906539917},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.4652000069618225},{"id":"https://openalex.org/C182419690","wikidata":"https://www.wikidata.org/wiki/Q205464","display_name":"Algebraic structure","level":2,"score":0.4609000086784363},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4129999876022339},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.39430001378059387},{"id":"https://openalex.org/C2989065042","wikidata":"https://www.wikidata.org/wiki/Q7378971","display_name":"Algebraic properties","level":2,"score":0.39399999380111694},{"id":"https://openalex.org/C185529760","wikidata":"https://www.wikidata.org/wiki/Q164307","display_name":"Binary operation","level":2,"score":0.384799987077713},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3515999913215637},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.3264999985694885},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3237999975681305},{"id":"https://openalex.org/C136003732","wikidata":"https://www.wikidata.org/wiki/Q3854337","display_name":"Algebraic operation","level":3,"score":0.31529998779296875},{"id":"https://openalex.org/C2731732","wikidata":"https://www.wikidata.org/wiki/Q7301119","display_name":"Real algebraic geometry","level":3,"score":0.314300000667572},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.3131999969482422},{"id":"https://openalex.org/C89290136","wikidata":"https://www.wikidata.org/wiki/Q550791","display_name":"Algebraic extension","level":5,"score":0.30720001459121704},{"id":"https://openalex.org/C204707403","wikidata":"https://www.wikidata.org/wiki/Q1152398","display_name":"Canonical form","level":2,"score":0.3010999858379364},{"id":"https://openalex.org/C78313660","wikidata":"https://www.wikidata.org/wiki/Q727659","display_name":"Commutative algebra","level":2,"score":0.29280000925064087},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2822999954223633},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.28130000829696655},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.2630999982357025},{"id":"https://openalex.org/C69653121","wikidata":"https://www.wikidata.org/wiki/Q1434805","display_name":"Algebraic surface","level":3,"score":0.260699987411499},{"id":"https://openalex.org/C161491579","wikidata":"https://www.wikidata.org/wiki/Q858656","display_name":"Commutative ring","level":3,"score":0.25839999318122864}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.7546/nifs.2026.32.3.296-308","doi":"https://doi.org/10.7546/nifs.2026.32.3.296-308","is_oa":true,"landing_page_url":"https://doi.org/10.7546/nifs.2026.32.3.296-308","pdf_url":"https://ifigenia.org/images/7/7f/NIFS-32-3-296-308.pdf","source":{"id":"https://openalex.org/S4210236489","display_name":"Notes on Intuitionistic Fuzzy Sets","issn_l":"1310-4926","issn":["1310-4926","2367-8283"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["doaj"],"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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notes on Intuitionistic Fuzzy Sets","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.7546/nifs.2026.32.3.296-308","doi":"https://doi.org/10.7546/nifs.2026.32.3.296-308","is_oa":true,"landing_page_url":"https://doi.org/10.7546/nifs.2026.32.3.296-308","pdf_url":"https://ifigenia.org/images/7/7f/NIFS-32-3-296-308.pdf","source":{"id":"https://openalex.org/S4210236489","display_name":"Notes on Intuitionistic Fuzzy Sets","issn_l":"1310-4926","issn":["1310-4926","2367-8283"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["doaj"],"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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notes on Intuitionistic Fuzzy Sets","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7225463531.pdf","grobid_xml":"https://content.openalex.org/works/W7225463531.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3101238794","https://openalex.org/W4393299379","https://openalex.org/W7097786769","https://openalex.org/W6967931361","https://openalex.org/W2626176893","https://openalex.org/W3046536008","https://openalex.org/W4390619749","https://openalex.org/W7208778472","https://openalex.org/W4323355786","https://openalex.org/W2366097574"],"abstract_inverted_index":{"This":[0],"paper":[1],"investigates":[2],"the":[3,22,25,31,49,56,76,90,100,121,126,134,138,141,145,150,156,160],"algebraic":[4,35,38,58,157],"structures":[5,59],"induced":[6],"by":[7,137],"binary":[8],"operations":[9,122,163],"on":[10,21,75],"Circular":[11],"Intuitionistic":[12],"Fuzzy":[13],"Triples":[14],"(C-IFTs).":[15],"For":[16],"a":[17,114,166],"fixed":[18],"upper":[19],"bound":[20],"circular":[23,175],"radius,":[24],"neutral":[26],"and":[27,37,45,63,89,107,164,174],"absorbing":[28],"elements":[29,85],"of":[30,48,79,83,147,159,171],"standard":[32,101,127],"union,":[33],"intersection,":[34],"addition,":[36],"multiplication":[39],"are":[40,60,86,93,123],"determined,":[41],"considering":[42],"both":[43],"minimum":[44,110],"maximum":[46,104],"aggregation":[47,106,112,172],"radius":[50,105,111,142],"components.":[51],"It":[52,130],"is":[53,97,131],"proved":[54],"that":[55,99,133],"corresponding":[57],"commutative":[61,64],"monoids":[62],"multi-unitary":[65],"groups":[66,74],"(\u03bc-groups),":[67],"although":[68],"they":[69],"do":[70],"not":[71],"form":[72,113],"ordinary":[73],"entire":[77],"domain":[78],"C-IFTs.":[80],"The":[81,118,153],"sets":[82],"\u03bc-inverse":[84],"described":[87],"explicitly,":[88],"dual":[91],"\u03bc-groups":[92,148],"determined.":[94],"Furthermore,":[95],"it":[96],"established":[98],"union":[102],"with":[103,109],"intersection":[108],"bounded":[115],"distributive":[116],"lattice.":[117],"relationships":[119],"between":[120],"examined":[124],"under":[125],"radius-preserving":[128],"negation.":[129],"shown":[132],"duality":[135,146],"generated":[136],"negation":[139],"preserves":[140],"operation,":[143],"whereas":[144],"requires":[149],"opposite":[151],"one.":[152],"results":[154],"characterize":[155],"properties":[158],"selected":[161],"C-IFT":[162],"provide":[165],"basis":[167],"for":[168],"further":[169],"study":[170],"procedures":[173],"intuitionistic":[176],"fuzzy":[177],"index-matrix":[178],"constructions.":[179]},"counts_by_year":[],"updated_date":"2026-11-09T13:22:03.289127","created_date":"2026-11-08T00:00:00"}