{"id":"https://openalex.org/W2062431081","doi":"https://doi.org/10.1142/s0218488503002351","title":"SCALAR CARDINALITIES OF FINITE FUZZY SETS FOR t-NORMS AND t-CONORMS","display_name":"SCALAR CARDINALITIES OF FINITE FUZZY SETS FOR t-NORMS AND t-CONORMS","publication_year":2003,"publication_date":"2003-10-01","ids":{"openalex":"https://openalex.org/W2062431081","doi":"https://doi.org/10.1142/s0218488503002351","mag":"2062431081"},"language":"en","primary_location":{"id":"doi:10.1142/s0218488503002351","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218488503002351","pdf_url":null,"source":{"id":"https://openalex.org/S69518169","display_name":"International Journal of Uncertainty Fuzziness and Knowledge-Based Systems","issn_l":"0218-4885","issn":["0218-4885","1793-6411"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Uncertainty, Fuzziness and Knowledge-Based 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/A5079493248","display_name":"Jaume Casasnovas","orcid":null},"institutions":[{"id":"https://openalex.org/I50441567","display_name":"Universitat de les Illes Balears","ror":"https://ror.org/03e10x626","country_code":"ES","type":"education","lineage":["https://openalex.org/I50441567"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"J. CASASNOVAS","raw_affiliation_strings":["Department of Mathematics and Computer Science, University of Balearic Islands, Crta. de Valldemossa, Km. 7.5, 07071 Palma de Mallorca, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, University of Balearic Islands, Crta. de Valldemossa, Km. 7.5, 07071 Palma de Mallorca, Spain","institution_ids":["https://openalex.org/I50441567"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010033209","display_name":"Joan Torrens","orcid":"https://orcid.org/0000-0002-5066-2913"},"institutions":[{"id":"https://openalex.org/I50441567","display_name":"Universitat de les Illes Balears","ror":"https://ror.org/03e10x626","country_code":"ES","type":"education","lineage":["https://openalex.org/I50441567"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"J. TORRENS","raw_affiliation_strings":["Department of Mathematics and Computer Science, University of Balearic Islands, Crta. de Valldemossa, Km. 7.5, 07071 Palma de Mallorca, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, University of Balearic Islands, Crta. de Valldemossa, Km. 7.5, 07071 Palma de Mallorca, Spain","institution_ids":["https://openalex.org/I50441567"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.648,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.89681661,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"11","issue":"05","first_page":"599","last_page":"614"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9995999932289124,"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":0.9995999932289124,"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9923999905586243,"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"}},{"id":"https://openalex.org/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9908000230789185,"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/subadditivity","display_name":"Subadditivity","score":0.8680529594421387},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8022612929344177},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.5366020202636719},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.48715445399284363},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.47072067856788635},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.44773760437965393},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.4360577166080475},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.39348334074020386},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09308135509490967},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.046136051416397095}],"concepts":[{"id":"https://openalex.org/C19220575","wikidata":"https://www.wikidata.org/wiki/Q1934099","display_name":"Subadditivity","level":2,"score":0.8680529594421387},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8022612929344177},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.5366020202636719},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.48715445399284363},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.47072067856788635},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.44773760437965393},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.4360577166080475},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.39348334074020386},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09308135509490967},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.046136051416397095},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218488503002351","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218488503002351","pdf_url":null,"source":{"id":"https://openalex.org/S69518169","display_name":"International Journal of Uncertainty Fuzziness and Knowledge-Based Systems","issn_l":"0218-4885","issn":["0218-4885","1793-6411"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1555744295","https://openalex.org/W2027018853","https://openalex.org/W2071200009","https://openalex.org/W2164429865","https://openalex.org/W2478003959","https://openalex.org/W2496338429","https://openalex.org/W3158113069","https://openalex.org/W4234672050"],"related_works":["https://openalex.org/W3009872175","https://openalex.org/W2522774808","https://openalex.org/W2328182802","https://openalex.org/W2078280270","https://openalex.org/W4249580765","https://openalex.org/W2096753949","https://openalex.org/W3124740411","https://openalex.org/W2990473846","https://openalex.org/W1966791450","https://openalex.org/W1985218657"],"abstract_inverted_index":{"An":[0],"axiomatic":[1],"approach":[2],"to":[3],"scalar":[4],"cardinalities":[5,21],"of":[6],"finite":[7,41,46],"fuzzy":[8],"sets":[9],"involving":[10],"t-norms":[11],"and":[12,24,52],"t-conorms":[13],"is":[14,22,26],"presented.":[15],"A":[16],"characterization":[17],"theorem":[18],"for":[19],"these":[20],"proved":[23,28],"it":[25],"also":[27],"that":[29],"some":[30],"standard":[31],"properties":[32,39],"remain":[33],"true.":[34],"On":[35],"the":[36,50,53],"other":[37],"hand,":[38],"like":[40],"additivity,":[42],"valuation":[43],"property":[44],"or":[45],"subadditivity":[47],"depend":[48],"on":[49],"t-norm":[51],"t-conorm.":[54]},"counts_by_year":[{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}