{"id":"https://openalex.org/W3095365262","doi":"https://doi.org/10.1007/s00500-021-06251-w","title":"Generalized Hukuhara-Clarke Derivative of Interval-valued Functions and its Properties","display_name":"Generalized Hukuhara-Clarke Derivative of Interval-valued Functions and its Properties","publication_year":2021,"publication_date":"2021-10-04","ids":{"openalex":"https://openalex.org/W3095365262","doi":"https://doi.org/10.1007/s00500-021-06251-w","mag":"3095365262"},"language":"en","primary_location":{"id":"doi:10.1007/s00500-021-06251-w","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00500-021-06251-w","pdf_url":null,"source":{"id":"https://openalex.org/S65753830","display_name":"Soft Computing","issn_l":"1432-7643","issn":["1432-7643","1433-7479"],"is_oa":false,"is_in_doaj":false,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Soft Computing","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/A5080013844","display_name":"Ram Surat Chauhan","orcid":null},"institutions":[{"id":"https://openalex.org/I56404289","display_name":"Indian Institute of Technology BHU","ror":"https://ror.org/01kh5gc44","country_code":"IN","type":"education","lineage":["https://openalex.org/I56404289","https://openalex.org/I91357014"]},{"id":"https://openalex.org/I91357014","display_name":"Banaras Hindu University","ror":"https://ror.org/04cdn2797","country_code":"IN","type":"education","lineage":["https://openalex.org/I91357014"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Ram Surat Chauhan","raw_affiliation_strings":["Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi, 221005, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi, 221005, India","institution_ids":["https://openalex.org/I56404289","https://openalex.org/I91357014"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087372767","display_name":"Debdas Ghosh","orcid":"https://orcid.org/0000-0003-2419-7082"},"institutions":[{"id":"https://openalex.org/I56404289","display_name":"Indian Institute of Technology BHU","ror":"https://ror.org/01kh5gc44","country_code":"IN","type":"education","lineage":["https://openalex.org/I56404289","https://openalex.org/I91357014"]},{"id":"https://openalex.org/I91357014","display_name":"Banaras Hindu University","ror":"https://ror.org/04cdn2797","country_code":"IN","type":"education","lineage":["https://openalex.org/I91357014"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Debdas Ghosh","raw_affiliation_strings":["Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi, 221005, India"],"raw_orcid":"https://orcid.org/0000-0003-2419-7082","affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi, 221005, India","institution_ids":["https://openalex.org/I56404289","https://openalex.org/I91357014"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002141572","display_name":"Jaroslav Ram\u0131\u0301k","orcid":"https://orcid.org/0000-0002-5211-9535"},"institutions":[{"id":"https://openalex.org/I32366509","display_name":"Silesian University in Opava","ror":"https://ror.org/02w4f2z17","country_code":"CZ","type":"education","lineage":["https://openalex.org/I32366509"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Jaroslav Ram\u00edk","raw_affiliation_strings":["School of Business Administration in Karvina, Silesian University Opava, Opava, Czechia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Business Administration in Karvina, Silesian University Opava, Opava, Czechia","institution_ids":["https://openalex.org/I32366509"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005729985","display_name":"Amit Kumar Debnath","orcid":"https://orcid.org/0000-0003-3752-9939"},"institutions":[{"id":"https://openalex.org/I56404289","display_name":"Indian Institute of Technology BHU","ror":"https://ror.org/01kh5gc44","country_code":"IN","type":"education","lineage":["https://openalex.org/I56404289","https://openalex.org/I91357014"]},{"id":"https://openalex.org/I91357014","display_name":"Banaras Hindu University","ror":"https://ror.org/04cdn2797","country_code":"IN","type":"education","lineage":["https://openalex.org/I91357014"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Amit Kumar Debnath","raw_affiliation_strings":["Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi, 221005, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi, 221005, India","institution_ids":["https://openalex.org/I56404289","https://openalex.org/I91357014"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5087372767"],"corresponding_institution_ids":["https://openalex.org/I56404289","https://openalex.org/I91357014"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":2.2464,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.8892636,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"25","issue":"23","first_page":"14629","last_page":"14643"},"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9975000023841858,"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/T12709","display_name":"Optimization and Mathematical Programming","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/sublinear-function","display_name":"Sublinear function","score":0.8078182935714722},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.7964967489242554},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.767911434173584},{"id":"https://openalex.org/keywords/derivative","display_name":"Derivative (finance)","score":0.705122172832489},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.6759137511253357},{"id":"https://openalex.org/keywords/directional-derivative","display_name":"Directional derivative","score":0.6472486257553101},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.6102164387702942},{"id":"https://openalex.org/keywords/generalizations-of-the-derivative","display_name":"Generalizations of the derivative","score":0.46266651153564453},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.429463267326355},{"id":"https://openalex.org/keywords/fr\u00e9chet-derivative","display_name":"Fr\u00e9chet derivative","score":0.4215327501296997},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.42024803161621094},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4182271957397461},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.38030755519866943},{"id":"https://openalex.org/keywords/second-derivative","display_name":"Second derivative","score":0.37496769428253174},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3456290066242218},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3398629426956177},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.32325929403305054},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06691431999206543}],"concepts":[{"id":"https://openalex.org/C117160843","wikidata":"https://www.wikidata.org/wiki/Q338652","display_name":"Sublinear function","level":2,"score":0.8078182935714722},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.7964967489242554},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.767911434173584},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.705122172832489},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.6759137511253357},{"id":"https://openalex.org/C2011187","wikidata":"https://www.wikidata.org/wiki/Q383851","display_name":"Directional derivative","level":2,"score":0.6472486257553101},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.6102164387702942},{"id":"https://openalex.org/C184537036","wikidata":"https://www.wikidata.org/wiki/Q14163503","display_name":"Generalizations of the derivative","level":3,"score":0.46266651153564453},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.429463267326355},{"id":"https://openalex.org/C118335899","wikidata":"https://www.wikidata.org/wiki/Q1305350","display_name":"Fr\u00e9chet derivative","level":3,"score":0.4215327501296997},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.42024803161621094},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4182271957397461},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.38030755519866943},{"id":"https://openalex.org/C33257320","wikidata":"https://www.wikidata.org/wiki/Q1932744","display_name":"Second derivative","level":2,"score":0.37496769428253174},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3456290066242218},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3398629426956177},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.32325929403305054},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06691431999206543},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00500-021-06251-w","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00500-021-06251-w","pdf_url":null,"source":{"id":"https://openalex.org/S65753830","display_name":"Soft Computing","issn_l":"1432-7643","issn":["1432-7643","1433-7479"],"is_oa":false,"is_in_doaj":false,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Soft Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W259920056","https://openalex.org/W561707741","https://openalex.org/W580431932","https://openalex.org/W596728863","https://openalex.org/W1045104688","https://openalex.org/W1542253753","https://openalex.org/W1551251595","https://openalex.org/W1551360398","https://openalex.org/W1603419833","https://openalex.org/W1967779834","https://openalex.org/W1972280390","https://openalex.org/W1975578510","https://openalex.org/W1986928005","https://openalex.org/W2001359285","https://openalex.org/W2006748591","https://openalex.org/W2009054772","https://openalex.org/W2013367574","https://openalex.org/W2034038007","https://openalex.org/W2039795101","https://openalex.org/W2041782481","https://openalex.org/W2066191367","https://openalex.org/W2070545443","https://openalex.org/W2080680537","https://openalex.org/W2081026153","https://openalex.org/W2088735768","https://openalex.org/W2089191214","https://openalex.org/W2092122905","https://openalex.org/W2110942140","https://openalex.org/W2123898522","https://openalex.org/W2146795783","https://openalex.org/W2253109038","https://openalex.org/W2259353398","https://openalex.org/W2306603513","https://openalex.org/W2743875864","https://openalex.org/W2766367445","https://openalex.org/W2801266866","https://openalex.org/W2958182118","https://openalex.org/W2973604913","https://openalex.org/W2975304533","https://openalex.org/W2985551577","https://openalex.org/W3011285224","https://openalex.org/W3210374693","https://openalex.org/W4254238256","https://openalex.org/W6604466195"],"related_works":["https://openalex.org/W2364861597","https://openalex.org/W2064205779","https://openalex.org/W2097846334","https://openalex.org/W2196251960","https://openalex.org/W2351274863","https://openalex.org/W2345868000","https://openalex.org/W2066286387","https://openalex.org/W2363328912","https://openalex.org/W1978625593","https://openalex.org/W2372512380"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":2}],"updated_date":"2026-07-07T14:30:12.667765","created_date":"2025-10-10T00:00:00"}
