{"id":"https://openalex.org/W4416928755","doi":"https://doi.org/10.1109/tfuzz.2025.3617293","title":"A Geometric View of Ralescu\u2019s Many-Valued Cardinality","display_name":"A Geometric View of Ralescu\u2019s Many-Valued Cardinality","publication_year":2025,"publication_date":"2025-12-01","ids":{"openalex":"https://openalex.org/W4416928755","doi":"https://doi.org/10.1109/tfuzz.2025.3617293"},"language":null,"primary_location":{"id":"doi:10.1109/tfuzz.2025.3617293","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tfuzz.2025.3617293","pdf_url":null,"source":{"id":"https://openalex.org/S134177497","display_name":"IEEE Transactions on Fuzzy Systems","issn_l":"1063-6706","issn":["1063-6706","1941-0034"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Fuzzy Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5027925658","display_name":"Eduard Bartl","orcid":"https://orcid.org/0000-0002-1273-0268"},"institutions":[{"id":"https://openalex.org/I70703428","display_name":"Palack\u00fd University Olomouc","ror":"https://ror.org/04qxnmv42","country_code":"CZ","type":"education","lineage":["https://openalex.org/I70703428"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Eduard Bartl","raw_affiliation_strings":["Department of Computer Science, Palacký University, Olomouc, Czech Republic"],"raw_orcid":"https://orcid.org/0000-0002-1273-0268","affiliations":[{"raw_affiliation_string":"Department of Computer Science, Palacký University, Olomouc, Czech Republic","institution_ids":["https://openalex.org/I70703428"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004391892","display_name":"Radim B\u011blohl\u00e1vek","orcid":"https://orcid.org/0000-0003-4924-3233"},"institutions":[{"id":"https://openalex.org/I70703428","display_name":"Palack\u00fd University Olomouc","ror":"https://ror.org/04qxnmv42","country_code":"CZ","type":"education","lineage":["https://openalex.org/I70703428"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Radim Belohlavek","raw_affiliation_strings":["Department of Computer Science, Palacký University, Olomouc, Czech Republic"],"raw_orcid":"https://orcid.org/0000-0003-4924-3233","affiliations":[{"raw_affiliation_string":"Department of Computer Science, Palacký University, Olomouc, Czech Republic","institution_ids":["https://openalex.org/I70703428"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I70703428"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.38806607,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"33","issue":"12","first_page":"4443","last_page":"4451"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.45660001039505005,"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":0.45660001039505005,"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/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.3133000135421753,"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":0.13500000536441803,"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/cardinality","display_name":"Cardinality (data modeling)","score":0.8194000124931335},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.6912000179290771},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.44449999928474426},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.42910000681877136},{"id":"https://openalex.org/keywords/geometric-shape","display_name":"Geometric shape","score":0.3458000123500824},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.32839998602867126}],"concepts":[{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.8194000124931335},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6912000179290771},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5924999713897705},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.44449999928474426},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.42910000681877136},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3944000005722046},{"id":"https://openalex.org/C7305733","wikidata":"https://www.wikidata.org/wiki/Q207961","display_name":"Geometric shape","level":2,"score":0.3458000123500824},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3368000090122223},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32839998602867126},{"id":"https://openalex.org/C2778408900","wikidata":"https://www.wikidata.org/wiki/Q1329258","display_name":"Cardinal number (linguistics)","level":2,"score":0.32260000705718994},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3118000030517578},{"id":"https://openalex.org/C49777392","wikidata":"https://www.wikidata.org/wiki/Q5535495","display_name":"Geometric networks","level":3,"score":0.2906999886035919},{"id":"https://openalex.org/C29123130","wikidata":"https://www.wikidata.org/wiki/Q874709","display_name":"Computational geometry","level":2,"score":0.2727000117301941},{"id":"https://openalex.org/C136520226","wikidata":"https://www.wikidata.org/wiki/Q302814","display_name":"Geometric data analysis","level":2,"score":0.2572000026702881},{"id":"https://openalex.org/C104065381","wikidata":"https://www.wikidata.org/wiki/Q1002535","display_name":"Geometric modeling","level":2,"score":0.2549000084400177},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.25440001487731934},{"id":"https://openalex.org/C2776608160","wikidata":"https://www.wikidata.org/wiki/Q4785462","display_name":"Natural (archaeology)","level":2,"score":0.2535000145435333}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tfuzz.2025.3617293","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tfuzz.2025.3617293","pdf_url":null,"source":{"id":"https://openalex.org/S134177497","display_name":"IEEE Transactions on Fuzzy Systems","issn_l":"1063-6706","issn":["1063-6706","1941-0034"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Fuzzy Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W246487436","https://openalex.org/W1998970649","https://openalex.org/W2027018853","https://openalex.org/W2040121225","https://openalex.org/W2083037024","https://openalex.org/W2122211679","https://openalex.org/W2908603685","https://openalex.org/W4393325784","https://openalex.org/W4402129282"],"related_works":[],"abstract_inverted_index":{"We":[0,29,47],"develop":[1],"a":[2,9,43,74,88],"geometric":[3,45,51],"view":[4,16,33,52,71],"of":[5,8,12,21,38,62,77],"Ralescu\u2019s":[6,78],"concept":[7,23,41,79],"many-valued":[10],"cardinality":[11,40,61],"fuzzy":[13,63],"sets.":[14,64],"The":[15],"facilitates":[17],"an":[18],"easy":[19],"understanding":[20],"this":[22],"and":[24],"helps":[25],"elucidate":[26],"its":[27],"nature.":[28],"demonstrate":[30],"that":[31,49,69],"the":[32,39,50,70,82],"enables":[34],"to":[35,56,60,73],"obtain":[36],"properties":[37],"by":[42,87],"straightforward":[44],"reasoning.":[46],"show":[48],"may":[53],"be":[54],"utilized":[55],"analyze":[57],"further":[58],"approaches":[59],"In":[65],"particular,":[66],"we":[67],"observe":[68],"applies":[72],"natural":[75],"generalization":[76],"in":[80],"which":[81],"standard":[83],"minimu":[84],"is":[85],"replaced":[86],"general":[89],"t-norm.":[90]},"counts_by_year":[],"updated_date":"2025-12-03T23:09:05.601824","created_date":"2025-12-02T00:00:00"}