{"id":"https://openalex.org/W3105173213","doi":"https://doi.org/10.3233/faia200681","title":"Study on Generalized Directional Differentiability Problems of Fuzzy Mappings","display_name":"Study on Generalized Directional Differentiability Problems of Fuzzy Mappings","publication_year":2020,"publication_date":"2020-11-09","ids":{"openalex":"https://openalex.org/W3105173213","doi":"https://doi.org/10.3233/faia200681","mag":"3105173213"},"language":"en","primary_location":{"id":"doi:10.3233/faia200681","is_oa":true,"landing_page_url":"https://doi.org/10.3233/faia200681","pdf_url":"https://ebooks.iospress.nl/pdf/doi/10.3233/FAIA200681","source":{"id":"https://openalex.org/S4210201731","display_name":"Frontiers in artificial intelligence and applications","issn_l":"0922-6389","issn":["0922-6389","1879-8314"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Artificial Intelligence and Applications","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://ebooks.iospress.nl/pdf/doi/10.3233/FAIA200681","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005369478","display_name":"Yue Bao","orcid":"https://orcid.org/0000-0001-6179-6135"},"institutions":[{"id":"https://openalex.org/I64222039","display_name":"National University of Mongolia","ror":"https://ror.org/04855bv47","country_code":"MN","type":"education","lineage":["https://openalex.org/I64222039"]},{"id":"https://openalex.org/I108743333","display_name":"Inner Mongolia University for Nationalities","ror":"https://ror.org/04cwap208","country_code":"CN","type":"education","lineage":["https://openalex.org/I108743333"]}],"countries":["CN","MN"],"is_corresponding":true,"raw_author_name":"Yu-e Bao","raw_affiliation_strings":["College of Mathematics, Inner Mongolia University for Nationalities, China","College of Mathematics, Inner Mongolia University for Nationalities"],"affiliations":[{"raw_affiliation_string":"College of Mathematics, Inner Mongolia University for Nationalities, China","institution_ids":["https://openalex.org/I108743333"]},{"raw_affiliation_string":"College of Mathematics, Inner Mongolia University for Nationalities","institution_ids":["https://openalex.org/I64222039"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101746257","display_name":"Tingting Li","orcid":"https://orcid.org/0000-0001-6807-9382"},"institutions":[{"id":"https://openalex.org/I108743333","display_name":"Inner Mongolia University for Nationalities","ror":"https://ror.org/04cwap208","country_code":"CN","type":"education","lineage":["https://openalex.org/I108743333"]},{"id":"https://openalex.org/I64222039","display_name":"National University of Mongolia","ror":"https://ror.org/04855bv47","country_code":"MN","type":"education","lineage":["https://openalex.org/I64222039"]}],"countries":["CN","MN"],"is_corresponding":false,"raw_author_name":"Tingting Li","raw_affiliation_strings":["College of Mathematics, Inner Mongolia University for Nationalities, China","College of Mathematics, Inner Mongolia University for Nationalities"],"affiliations":[{"raw_affiliation_string":"College of Mathematics, Inner Mongolia University for Nationalities, China","institution_ids":["https://openalex.org/I108743333"]},{"raw_affiliation_string":"College of Mathematics, Inner Mongolia University for Nationalities","institution_ids":["https://openalex.org/I64222039"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009039976","display_name":"Linfen Zhang","orcid":null},"institutions":[{"id":"https://openalex.org/I64222039","display_name":"National University of Mongolia","ror":"https://ror.org/04855bv47","country_code":"MN","type":"education","lineage":["https://openalex.org/I64222039"]},{"id":"https://openalex.org/I108743333","display_name":"Inner Mongolia University for Nationalities","ror":"https://ror.org/04cwap208","country_code":"CN","type":"education","lineage":["https://openalex.org/I108743333"]}],"countries":["CN","MN"],"is_corresponding":false,"raw_author_name":"Linfen Zhang","raw_affiliation_strings":["College of Mathematics, Inner Mongolia University for Nationalities, China","College of Mathematics, Inner Mongolia University for Nationalities"],"affiliations":[{"raw_affiliation_string":"College of Mathematics, Inner Mongolia University for Nationalities, China","institution_ids":["https://openalex.org/I108743333"]},{"raw_affiliation_string":"College of Mathematics, Inner Mongolia University for Nationalities","institution_ids":["https://openalex.org/I64222039"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5005369478"],"corresponding_institution_ids":["https://openalex.org/I108743333","https://openalex.org/I64222039"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.2476618,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9998999834060669,"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/T10050","display_name":"Multi-Criteria Decision Making","score":0.9904999732971191,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9878000020980835,"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/differentiable-function","display_name":"Differentiable function","score":0.9563401937484741},{"id":"https://openalex.org/keywords/directional-derivative","display_name":"Directional derivative","score":0.8731124401092529},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.7170840501785278},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6679741144180298},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.36743342876434326},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3603786826133728},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.28097325563430786},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.190931499004364},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08116716146469116}],"concepts":[{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.9563401937484741},{"id":"https://openalex.org/C2011187","wikidata":"https://www.wikidata.org/wiki/Q383851","display_name":"Directional derivative","level":2,"score":0.8731124401092529},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.7170840501785278},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6679741144180298},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36743342876434326},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3603786826133728},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28097325563430786},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.190931499004364},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08116716146469116}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3233/faia200681","is_oa":true,"landing_page_url":"https://doi.org/10.3233/faia200681","pdf_url":"https://ebooks.iospress.nl/pdf/doi/10.3233/FAIA200681","source":{"id":"https://openalex.org/S4210201731","display_name":"Frontiers in artificial intelligence and applications","issn_l":"0922-6389","issn":["0922-6389","1879-8314"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Artificial Intelligence and Applications","raw_type":"book-chapter"}],"best_oa_location":{"id":"doi:10.3233/faia200681","is_oa":true,"landing_page_url":"https://doi.org/10.3233/faia200681","pdf_url":"https://ebooks.iospress.nl/pdf/doi/10.3233/FAIA200681","source":{"id":"https://openalex.org/S4210201731","display_name":"Frontiers in artificial intelligence and applications","issn_l":"0922-6389","issn":["0922-6389","1879-8314"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Artificial Intelligence and Applications","raw_type":"book-chapter"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322868","display_name":"Natural Science Foundation of Inner Mongolia","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3105173213.pdf","grobid_xml":"https://content.openalex.org/works/W3105173213.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W218921885","https://openalex.org/W1680454679","https://openalex.org/W1982606567","https://openalex.org/W1995123739","https://openalex.org/W2014034239","https://openalex.org/W2038354216","https://openalex.org/W2056215967","https://openalex.org/W2070545443","https://openalex.org/W2076628063","https://openalex.org/W2336761277","https://openalex.org/W2520462203","https://openalex.org/W2765691494","https://openalex.org/W2792064160","https://openalex.org/W2989901967","https://openalex.org/W6633776228"],"related_works":["https://openalex.org/W3105173213","https://openalex.org/W2226784581","https://openalex.org/W2049339417","https://openalex.org/W942533424","https://openalex.org/W2097846334","https://openalex.org/W4255276256","https://openalex.org/W2531699496","https://openalex.org/W4301135054","https://openalex.org/W1968850685","https://openalex.org/W1506713792"],"abstract_inverted_index":{"This":[0],"paper":[1],"discusses":[2],"the":[3,11,21,43,46,76,79],"gH-directional":[4,14,24,36,51],"differentiability":[5,15,25,37,52],"of":[6,13,16,23,26,35,72,78],"fuzzy":[7,17,38,55,73],"mappings,":[8],"and":[9,29,50,59,66],"proposes":[10],"concept":[12,22],"mappings.":[18],"Based":[19],"on":[20],"interval-valued":[27],"mappings":[28,39,74],"its":[30],"related":[31],"properties,":[32],"two":[33],"properties":[34],"are":[40,69],"proposed.":[41],"At":[42],"same":[44],"time,":[45],"relation":[47],"between":[48],"gH-differentiability":[49],"for":[53],"a":[54],"mapping":[56],"is":[57,61],"discussed,":[58],"it":[60],"proved":[62],"that":[63],"both":[64],"gH-derivative":[65],"gH-partial":[67],"derivative":[68],"directional":[70],"derivatives":[71],"in":[75],"direction":[77],"coordinate":[80],"axis.":[81]},"counts_by_year":[],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}