{"id":"https://openalex.org/W2001779316","doi":"https://doi.org/10.1016/s0165-0114(01)00039-2","title":"A probabilistic definition of a nonconvex fuzzy cardinality","display_name":"A probabilistic definition of a nonconvex fuzzy cardinality","publication_year":2002,"publication_date":"2002-03-01","ids":{"openalex":"https://openalex.org/W2001779316","doi":"https://doi.org/10.1016/s0165-0114(01)00039-2","mag":"2001779316"},"language":"en","primary_location":{"id":"doi:10.1016/s0165-0114(01)00039-2","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0165-0114(01)00039-2","pdf_url":null,"source":{"id":"https://openalex.org/S169411308","display_name":"Fuzzy Sets and Systems","issn_l":"0165-0114","issn":["0165-0114","1872-6801"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fuzzy Sets and 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/A5100771081","display_name":"Miguel Delgado","orcid":"https://orcid.org/0000-0001-5333-5179"},"institutions":[{"id":"https://openalex.org/I173304897","display_name":"Universidad de Granada","ror":"https://ror.org/04njjy449","country_code":"ES","type":"education","lineage":["https://openalex.org/I173304897"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Miguel Delgado","raw_affiliation_strings":["Department of Computer Science and Artificial Intelligence, University of Granada, Avda. Andalucia 38, 18071 Granada, Spain","Department of Computer Science and Artificial Intelligence, University of Granada, Avda. Andalucia 38, Granada, Spain#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Artificial Intelligence, University of Granada, Avda. Andalucia 38, 18071 Granada, Spain","institution_ids":["https://openalex.org/I173304897"]},{"raw_affiliation_string":"Department of Computer Science and Artificial Intelligence, University of Granada, Avda. Andalucia 38, Granada, Spain#TAB#","institution_ids":["https://openalex.org/I173304897"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051586110","display_name":"Daniel S\u00e1nchez","orcid":"https://orcid.org/0000-0002-6048-3994"},"institutions":[{"id":"https://openalex.org/I173304897","display_name":"Universidad de Granada","ror":"https://ror.org/04njjy449","country_code":"ES","type":"education","lineage":["https://openalex.org/I173304897"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Daniel S\u00e1nchez","raw_affiliation_strings":["Department of Computer Science and Artificial Intelligence, University of Granada, Avda. Andalucia 38, 18071 Granada, Spain","Department of Computer Science and Artificial Intelligence, University of Granada, Avda. Andalucia 38, Granada, Spain#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Artificial Intelligence, University of Granada, Avda. Andalucia 38, 18071 Granada, Spain","institution_ids":["https://openalex.org/I173304897"]},{"raw_affiliation_string":"Department of Computer Science and Artificial Intelligence, University of Granada, Avda. Andalucia 38, Granada, Spain#TAB#","institution_ids":["https://openalex.org/I173304897"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000475040","display_name":"Mar\u0131\u0301a J. Mart\u0131\u0301n-Bautista","orcid":"https://orcid.org/0000-0002-6973-477X"},"institutions":[{"id":"https://openalex.org/I173304897","display_name":"Universidad de Granada","ror":"https://ror.org/04njjy449","country_code":"ES","type":"education","lineage":["https://openalex.org/I173304897"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Mar\u0131\u0301a J. Mart\u0131\u0301n-Bautista","raw_affiliation_strings":["Department of Computer Science and Artificial Intelligence, University of Granada, Avda. Andalucia 38, 18071 Granada, Spain","Department of Computer Science and Artificial Intelligence, University of Granada, Avda. Andalucia 38, Granada, Spain#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Artificial Intelligence, University of Granada, Avda. Andalucia 38, 18071 Granada, Spain","institution_ids":["https://openalex.org/I173304897"]},{"raw_affiliation_string":"Department of Computer Science and Artificial Intelligence, University of Granada, Avda. Andalucia 38, Granada, Spain#TAB#","institution_ids":["https://openalex.org/I173304897"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5084143284","display_name":"M.A. Vila","orcid":"https://orcid.org/0000-0002-2773-3306"},"institutions":[{"id":"https://openalex.org/I173304897","display_name":"Universidad de Granada","ror":"https://ror.org/04njjy449","country_code":"ES","type":"education","lineage":["https://openalex.org/I173304897"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Mar\u0131\u0301a Amparo Vila","raw_affiliation_strings":["Department of Computer Science and Artificial Intelligence, University of Granada, Avda. Andalucia 38, 18071 Granada, Spain","Department of Computer Science and Artificial Intelligence, University of Granada, Avda. Andalucia 38, Granada, Spain#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Artificial Intelligence, University of Granada, Avda. Andalucia 38, 18071 Granada, Spain","institution_ids":["https://openalex.org/I173304897"]},{"raw_affiliation_string":"Department of Computer Science and Artificial Intelligence, University of Granada, Avda. Andalucia 38, Granada, Spain#TAB#","institution_ids":["https://openalex.org/I173304897"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5100771081"],"corresponding_institution_ids":["https://openalex.org/I173304897"],"apc_list":{"value":2600,"currency":"USD","value_usd":2600},"apc_paid":null,"fwci":3.701,"has_fulltext":false,"cited_by_count":60,"citation_normalized_percentile":{"value":0.93035497,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"126","issue":"2","first_page":"177","last_page":"190"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9993000030517578,"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":0.9993000030517578,"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":0.9872999787330627,"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/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9818999767303467,"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/mathematics","display_name":"Mathematics","score":0.7463374137878418},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.673340380191803},{"id":"https://openalex.org/keywords/type-2-fuzzy-sets-and-systems","display_name":"Type-2 fuzzy sets and systems","score":0.65594083070755},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.6453683376312256},{"id":"https://openalex.org/keywords/fuzzy-set-operations","display_name":"Fuzzy set operations","score":0.5619579553604126},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.5489339828491211},{"id":"https://openalex.org/keywords/fuzzy-measure-theory","display_name":"Fuzzy measure theory","score":0.5274850726127625},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.5016584396362305},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.49333348870277405},{"id":"https://openalex.org/keywords/fuzzy-classification","display_name":"Fuzzy classification","score":0.4840940237045288},{"id":"https://openalex.org/keywords/defuzzification","display_name":"Defuzzification","score":0.4400845468044281},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.43637505173683167},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.42811036109924316},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3384701609611511},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.33148127794265747},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.2779276967048645},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20872274041175842},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.18272483348846436},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.061891376972198486}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7463374137878418},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.673340380191803},{"id":"https://openalex.org/C17350324","wikidata":"https://www.wikidata.org/wiki/Q7860605","display_name":"Type-2 fuzzy sets and systems","level":5,"score":0.65594083070755},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.6453683376312256},{"id":"https://openalex.org/C148671577","wikidata":"https://www.wikidata.org/wiki/Q5511133","display_name":"Fuzzy set operations","level":4,"score":0.5619579553604126},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.5489339828491211},{"id":"https://openalex.org/C100516043","wikidata":"https://www.wikidata.org/wiki/Q4455138","display_name":"Fuzzy measure theory","level":5,"score":0.5274850726127625},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.5016584396362305},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.49333348870277405},{"id":"https://openalex.org/C127385683","wikidata":"https://www.wikidata.org/wiki/Q1475696","display_name":"Fuzzy classification","level":4,"score":0.4840940237045288},{"id":"https://openalex.org/C170260401","wikidata":"https://www.wikidata.org/wiki/Q5251735","display_name":"Defuzzification","level":5,"score":0.4400845468044281},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.43637505173683167},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.42811036109924316},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3384701609611511},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33148127794265747},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.2779276967048645},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20872274041175842},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.18272483348846436},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.061891376972198486},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/s0165-0114(01)00039-2","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0165-0114(01)00039-2","pdf_url":null,"source":{"id":"https://openalex.org/S169411308","display_name":"Fuzzy Sets and Systems","issn_l":"0165-0114","issn":["0165-0114","1872-6801"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fuzzy Sets and Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.4000000059604645,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W151226564","https://openalex.org/W655976868","https://openalex.org/W1223790611","https://openalex.org/W1566211337","https://openalex.org/W1965239040","https://openalex.org/W1966008295","https://openalex.org/W1980080444","https://openalex.org/W1997793673","https://openalex.org/W1998970649","https://openalex.org/W2000763566","https://openalex.org/W2013868015","https://openalex.org/W2027018853","https://openalex.org/W2040121225","https://openalex.org/W2054714119","https://openalex.org/W2080253716","https://openalex.org/W2083037024","https://openalex.org/W2114748720","https://openalex.org/W2157041604","https://openalex.org/W2170853747","https://openalex.org/W2402970597","https://openalex.org/W2598771954","https://openalex.org/W6606244048","https://openalex.org/W6633996426","https://openalex.org/W6713632296"],"related_works":["https://openalex.org/W2674573885","https://openalex.org/W2960454922","https://openalex.org/W2060486654","https://openalex.org/W1514480137","https://openalex.org/W2152639368","https://openalex.org/W1977153944","https://openalex.org/W2007696012","https://openalex.org/W1998970649","https://openalex.org/W2276421572","https://openalex.org/W2402970597"],"abstract_inverted_index":null,"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
