{"id":"https://openalex.org/W4386001703","doi":"https://doi.org/10.1007/s40747-023-01213-1","title":"Fundamental properties of fuzzy rough sets based on triangular norms and fuzzy implications: the properties characterized by fuzzy neighborhood and fuzzy topology","display_name":"Fundamental properties of fuzzy rough sets based on triangular norms and fuzzy implications: the properties characterized by fuzzy neighborhood and fuzzy topology","publication_year":2023,"publication_date":"2023-08-19","ids":{"openalex":"https://openalex.org/W4386001703","doi":"https://doi.org/10.1007/s40747-023-01213-1"},"language":"en","primary_location":{"id":"doi:10.1007/s40747-023-01213-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s40747-023-01213-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s40747-023-01213-1.pdf","source":{"id":"https://openalex.org/S3035462843","display_name":"Complex & Intelligent Systems","issn_l":"2198-6053","issn":["2198-6053","2199-4536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complex & Intelligent Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://link.springer.com/content/pdf/10.1007/s40747-023-01213-1.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103064030","display_name":"Zhaohao Wang","orcid":"https://orcid.org/0000-0003-1385-0947"},"institutions":[{"id":"https://openalex.org/I94310126","display_name":"Shanxi Normal University","ror":"https://ror.org/03zd3ta61","country_code":"CN","type":"education","lineage":["https://openalex.org/I94310126"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhaohao Wang","raw_affiliation_strings":["School of Mathematics and Computer Science, Shanxi Normal University, Taiyu Road, Taiyuan, 030000 Shanxi, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computer Science, Shanxi Normal University, Taiyu Road, Taiyuan, 030000 Shanxi, China","institution_ids":["https://openalex.org/I94310126"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5103064030"],"corresponding_institution_ids":["https://openalex.org/I94310126"],"apc_list":{"value":1320,"currency":"GBP","value_usd":1619},"apc_paid":{"value":1320,"currency":"GBP","value_usd":1619},"fwci":0.9831,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.79480287,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"10","issue":"1","first_page":"1103","last_page":"1114"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9998999834060669,"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":0.9176999926567078,"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":0.7216719388961792},{"id":"https://openalex.org/keywords/fuzzy-set-operations","display_name":"Fuzzy set operations","score":0.7038435935974121},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.6747792363166809},{"id":"https://openalex.org/keywords/defuzzification","display_name":"Defuzzification","score":0.6658598780632019},{"id":"https://openalex.org/keywords/fuzzy-classification","display_name":"Fuzzy classification","score":0.6518343687057495},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.6266997456550598},{"id":"https://openalex.org/keywords/fuzzy-mathematics","display_name":"Fuzzy mathematics","score":0.5845298767089844},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.5750541687011719},{"id":"https://openalex.org/keywords/computational-intelligence","display_name":"Computational intelligence","score":0.5372607111930847},{"id":"https://openalex.org/keywords/fuzzy-subalgebra","display_name":"Fuzzy subalgebra","score":0.5188339948654175},{"id":"https://openalex.org/keywords/type-2-fuzzy-sets-and-systems","display_name":"Type-2 fuzzy sets and systems","score":0.5087228417396545},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.471682608127594},{"id":"https://openalex.org/keywords/rough-set","display_name":"Rough set","score":0.46497511863708496},{"id":"https://openalex.org/keywords/fuzzy-measure-theory","display_name":"Fuzzy measure theory","score":0.43239831924438477},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.32843202352523804},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2918100953102112},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2136300504207611},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11960023641586304}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7216719388961792},{"id":"https://openalex.org/C148671577","wikidata":"https://www.wikidata.org/wiki/Q5511133","display_name":"Fuzzy set operations","level":4,"score":0.7038435935974121},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.6747792363166809},{"id":"https://openalex.org/C170260401","wikidata":"https://www.wikidata.org/wiki/Q5251735","display_name":"Defuzzification","level":5,"score":0.6658598780632019},{"id":"https://openalex.org/C127385683","wikidata":"https://www.wikidata.org/wiki/Q1475696","display_name":"Fuzzy classification","level":4,"score":0.6518343687057495},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.6266997456550598},{"id":"https://openalex.org/C166586474","wikidata":"https://www.wikidata.org/wiki/Q5511129","display_name":"Fuzzy mathematics","level":5,"score":0.5845298767089844},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.5750541687011719},{"id":"https://openalex.org/C139502532","wikidata":"https://www.wikidata.org/wiki/Q1122090","display_name":"Computational intelligence","level":2,"score":0.5372607111930847},{"id":"https://openalex.org/C115740575","wikidata":"https://www.wikidata.org/wiki/Q5511136","display_name":"Fuzzy subalgebra","level":5,"score":0.5188339948654175},{"id":"https://openalex.org/C17350324","wikidata":"https://www.wikidata.org/wiki/Q7860605","display_name":"Type-2 fuzzy sets and systems","level":5,"score":0.5087228417396545},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.471682608127594},{"id":"https://openalex.org/C111012933","wikidata":"https://www.wikidata.org/wiki/Q3137210","display_name":"Rough set","level":2,"score":0.46497511863708496},{"id":"https://openalex.org/C100516043","wikidata":"https://www.wikidata.org/wiki/Q4455138","display_name":"Fuzzy measure theory","level":5,"score":0.43239831924438477},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32843202352523804},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2918100953102112},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2136300504207611},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11960023641586304}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s40747-023-01213-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s40747-023-01213-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s40747-023-01213-1.pdf","source":{"id":"https://openalex.org/S3035462843","display_name":"Complex & Intelligent Systems","issn_l":"2198-6053","issn":["2198-6053","2199-4536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complex & Intelligent Systems","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:eac1230fc1374b109f7ec079cafb88ae","is_oa":true,"landing_page_url":"https://doaj.org/article/eac1230fc1374b109f7ec079cafb88ae","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Complex & Intelligent Systems, Vol 10, Iss 1, Pp 1103-1114 (2023)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1007/s40747-023-01213-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s40747-023-01213-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s40747-023-01213-1.pdf","source":{"id":"https://openalex.org/S3035462843","display_name":"Complex & Intelligent Systems","issn_l":"2198-6053","issn":["2198-6053","2199-4536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complex & Intelligent Systems","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2652337534","display_name":null,"funder_award_id":"2021030212","funder_id":"https://openalex.org/F4320322666","funder_display_name":"Natural Science Foundation of Shanxi Province"},{"id":"https://openalex.org/G33727455","display_name":null,"funder_award_id":"202103021224261","funder_id":"https://openalex.org/F4320322666","funder_display_name":"Natural Science Foundation of Shanxi Province"},{"id":"https://openalex.org/G6537479530","display_name":null,"funder_award_id":"20210302122426","funder_id":"https://openalex.org/F4320322666","funder_display_name":"Natural Science Foundation of Shanxi Province"}],"funders":[{"id":"https://openalex.org/F4320322666","display_name":"Natural Science Foundation of Shanxi Province","ror":null}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4386001703.pdf"},"referenced_works_count":41,"referenced_works":["https://openalex.org/W279998616","https://openalex.org/W1453882192","https://openalex.org/W1964432381","https://openalex.org/W1968661412","https://openalex.org/W1978202330","https://openalex.org/W2002680690","https://openalex.org/W2006138243","https://openalex.org/W2006822196","https://openalex.org/W2014827534","https://openalex.org/W2027654459","https://openalex.org/W2036104856","https://openalex.org/W2036135215","https://openalex.org/W2055266411","https://openalex.org/W2073846369","https://openalex.org/W2075496978","https://openalex.org/W2082266564","https://openalex.org/W2084910209","https://openalex.org/W2088499853","https://openalex.org/W2096393821","https://openalex.org/W2097923398","https://openalex.org/W2111011053","https://openalex.org/W2131487297","https://openalex.org/W2137396323","https://openalex.org/W2160307100","https://openalex.org/W2162676707","https://openalex.org/W2168523997","https://openalex.org/W2208338681","https://openalex.org/W2257354639","https://openalex.org/W2441913759","https://openalex.org/W2496924803","https://openalex.org/W2533607442","https://openalex.org/W2559934994","https://openalex.org/W2594455805","https://openalex.org/W2720716879","https://openalex.org/W2732388576","https://openalex.org/W2739263287","https://openalex.org/W2944017292","https://openalex.org/W2954753287","https://openalex.org/W4211007335","https://openalex.org/W4232953319","https://openalex.org/W4234672050"],"related_works":["https://openalex.org/W2037428035","https://openalex.org/W2088978098","https://openalex.org/W2092290989","https://openalex.org/W2048452567","https://openalex.org/W4242545108","https://openalex.org/W2121560876","https://openalex.org/W2116600453","https://openalex.org/W2026829949","https://openalex.org/W1489009679","https://openalex.org/W2586653035"],"abstract_inverted_index":{"Abstract":[0],"Fuzzy":[1],"rough":[2,30,99,113,129],"set":[3,31,130],"models":[4],"are":[5],"useful":[6],"tools":[7],"for":[8,71,127],"dealing":[9],"with":[10,89],"fuzzy":[11,29,38,66,73,77,83,98,102,112,128],"and":[12,37,60,75,101],"real-valued":[13],"data.":[14],"They":[15],"have":[16],"been":[17],"used":[18],"in":[19,45],"many":[20],"real-world":[21],"applications.":[22],"In":[23,104],"this":[24,105],"paper,":[25],"we":[26,41,85,93],"investigate":[27,86],"the":[28,46,51,55,72,76,95,109],"model":[32],"based":[33,81,115],"on":[34,82,108,116],"triangular":[35,58,117],"norms":[36,118],"implications.":[39],"First,":[40],"extend":[42],"some":[43],"results":[44,126],"published":[47],"literature":[48],"by":[49],"removing":[50],"condition":[52],"that":[53],"is":[54],"continuity":[56],"of":[57,111,134],"norms,":[59],"obtain":[61],"more":[62],"general":[63],"conclusion":[64],"about":[65],"upper":[67],"approximation":[68,79],"operators.":[69],"Then,":[70],"neighborhood":[74],"lower":[78],"operator":[80],"implications,":[84],"their":[87],"characterization":[88],"each":[90],"other.":[91],"Finally,":[92],"establish":[94],"relationships":[96],"between":[97],"sets":[100,114],"topology.":[103],"work,":[106],"researches":[107],"properties":[110],"which":[119],"need":[120],"not":[121],"be":[122],"continuous":[123],"provide":[124],"generalization":[125],"theory":[131],"from":[132],"viewpoint":[133],"mathematics.":[135]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}