{"id":"https://openalex.org/W3155061880","doi":"https://doi.org/10.3233/jifs-202643","title":"The arity of convex spaces","display_name":"The arity of convex spaces","publication_year":2021,"publication_date":"2021-04-20","ids":{"openalex":"https://openalex.org/W3155061880","doi":"https://doi.org/10.3233/jifs-202643","mag":"3155061880"},"language":"en","primary_location":{"id":"doi:10.3233/jifs-202643","is_oa":false,"landing_page_url":"https://doi.org/10.3233/jifs-202643","pdf_url":null,"source":{"id":"https://openalex.org/S179157397","display_name":"Journal of Intelligent & Fuzzy Systems","issn_l":"1064-1246","issn":["1064-1246","1875-8967"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Intelligent & 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/A5083158084","display_name":"Wei Yao","orcid":"https://orcid.org/0000-0003-3320-7609"},"institutions":[{"id":"https://openalex.org/I200845125","display_name":"Nanjing University of Information Science and Technology","ror":"https://ror.org/02y0rxk19","country_code":"CN","type":"education","lineage":["https://openalex.org/I200845125"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Wei Yao","raw_affiliation_strings":["School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, China","institution_ids":["https://openalex.org/I200845125"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100359095","display_name":"Ye Chen","orcid":"https://orcid.org/0000-0002-1080-7671"},"institutions":[{"id":"https://openalex.org/I200845125","display_name":"Nanjing University of Information Science and Technology","ror":"https://ror.org/02y0rxk19","country_code":"CN","type":"education","lineage":["https://openalex.org/I200845125"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ye Chen","raw_affiliation_strings":["School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, China","institution_ids":["https://openalex.org/I200845125"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5083158084"],"corresponding_institution_ids":["https://openalex.org/I200845125"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.05420274,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"40","issue":"6","first_page":"11455","last_page":"11462"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9995999932289124,"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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9947999715805054,"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/arity","display_name":"Arity","score":0.9850998520851135},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7743455171585083},{"id":"https://openalex.org/keywords/convex-hull","display_name":"Convex hull","score":0.7168341875076294},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.501413106918335},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.3836275637149811},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3711346387863159},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.33512067794799805},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.30393755435943604},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09472012519836426}],"concepts":[{"id":"https://openalex.org/C110546421","wikidata":"https://www.wikidata.org/wiki/Q1315869","display_name":"Arity","level":2,"score":0.9850998520851135},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7743455171585083},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.7168341875076294},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.501413106918335},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3836275637149811},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3711346387863159},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33512067794799805},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.30393755435943604},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09472012519836426}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3233/jifs-202643","is_oa":false,"landing_page_url":"https://doi.org/10.3233/jifs-202643","pdf_url":null,"source":{"id":"https://openalex.org/S179157397","display_name":"Journal of Intelligent & Fuzzy Systems","issn_l":"1064-1246","issn":["1064-1246","1875-8967"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Intelligent & Fuzzy Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","score":0.5099999904632568,"display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W121843079","https://openalex.org/W785177669","https://openalex.org/W877498012","https://openalex.org/W884310359","https://openalex.org/W1525647423","https://openalex.org/W1583458608","https://openalex.org/W1978423623","https://openalex.org/W1996471450","https://openalex.org/W1997937473","https://openalex.org/W2007388400","https://openalex.org/W2022137179","https://openalex.org/W2049241857","https://openalex.org/W2070182878","https://openalex.org/W2072578205","https://openalex.org/W2081462933","https://openalex.org/W2093397547","https://openalex.org/W2095179081","https://openalex.org/W2150862113","https://openalex.org/W2158662559","https://openalex.org/W2314015870","https://openalex.org/W2319893799","https://openalex.org/W2509332367","https://openalex.org/W2617047420","https://openalex.org/W2737051083","https://openalex.org/W2803787463","https://openalex.org/W2885745695","https://openalex.org/W2916823488","https://openalex.org/W2942593644","https://openalex.org/W2954704472","https://openalex.org/W2964676272","https://openalex.org/W3005092492","https://openalex.org/W3011540822","https://openalex.org/W3043216256","https://openalex.org/W4248108185","https://openalex.org/W6656138306","https://openalex.org/W6725454132","https://openalex.org/W6774912231"],"related_works":["https://openalex.org/W46644190","https://openalex.org/W1550666490","https://openalex.org/W1479691804","https://openalex.org/W3157925596","https://openalex.org/W1949891039","https://openalex.org/W3097996696","https://openalex.org/W2047460659","https://openalex.org/W4283319830","https://openalex.org/W3000194050","https://openalex.org/W1482218199"],"abstract_inverted_index":{"The":[0,41,119],"arity":[1,46,57,65,76,116,123],"of":[2,13,38,47,58,66,77,88,97],"convex":[3,39,110,120],"spaces":[4,49,68],"is":[5,103,106,112,117],"a":[6,29,89,109],"numerical":[7],"feature":[8],"which":[9],"shows":[10],"the":[11,18,22,36,45,51,56,64,75],"ability":[12],"finite":[14],"subsets":[15],"spanning":[16],"to":[17,127],"whole":[19],"space":[20,111],"via":[21],"hull":[23,132],"operators.":[24,133],"This":[25],"paper":[26],"gives":[27],"it":[28],"formal":[30],"and":[31,50,60,69,72,80],"strict":[32],"definition":[33],"by":[34],"introducing":[35],"truncation":[37],"spaces.":[40],"relations":[42],"that":[43,54,62,73,108],"between":[44,55,63,74],"quotient":[48],"original":[52],"spaces,":[53,71,82],"subspaces":[59],"superspaces,":[61],"product":[67],"factors":[70],"disjoint":[78],"sums":[79],"term":[81],"are":[83,125],"systematically":[84],"studied.":[85],"A":[86],"mistake":[87],"formula":[90],"in":[91],"[M.":[92],"Van":[93],"De":[94],"Vel,":[95],"Theory":[96],"Convex":[98],"Structures,":[99],"North-Holland,":[100],"Amsterdam,":[101],"1993]":[102],"corrected.":[104],"It":[105],"shown":[107],"Alexandrov":[113],"iff":[114],"its":[115],"1.":[118],"structures":[121],"with":[122,130],"\u2264n":[124],"equivalent":[126],"structured":[128],"sets":[129],"n-restricted":[131]},"counts_by_year":[],"updated_date":"2026-02-03T23:48:18.283914","created_date":"2025-10-10T00:00:00"}