{"id":"https://openalex.org/W3201806466","doi":"https://doi.org/10.1007/s44196-021-00009-w","title":"Some Integral Inequalities for Generalized Convex Fuzzy-Interval-Valued Functions via Fuzzy Riemann Integrals","display_name":"Some Integral Inequalities for Generalized Convex Fuzzy-Interval-Valued Functions via Fuzzy Riemann Integrals","publication_year":2021,"publication_date":"2021-09-17","ids":{"openalex":"https://openalex.org/W3201806466","doi":"https://doi.org/10.1007/s44196-021-00009-w","mag":"3201806466"},"language":"en","primary_location":{"id":"doi:10.1007/s44196-021-00009-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s44196-021-00009-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s44196-021-00009-w.pdf","source":{"id":"https://openalex.org/S190680769","display_name":"International Journal of Computational Intelligence Systems","issn_l":"1875-6883","issn":["1875-6883","1875-6891"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["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":"International Journal of Computational Intelligence 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/s44196-021-00009-w.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023084872","display_name":"Muhammad Bilal Khan","orcid":"https://orcid.org/0009-0001-5074-9672"},"institutions":[{"id":"https://openalex.org/I16076960","display_name":"COMSATS University Islamabad","ror":"https://ror.org/00nqqvk19","country_code":"PK","type":"education","lineage":["https://openalex.org/I16076960"]}],"countries":["PK"],"is_corresponding":true,"raw_author_name":"Muhammad Bilal Khan","raw_affiliation_strings":["Department of Mathematics, COMSATS University Islamabad, Islamabad, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, COMSATS University Islamabad, Islamabad, Pakistan","institution_ids":["https://openalex.org/I16076960"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087578803","display_name":"Muhammad Aslam Noor","orcid":"https://orcid.org/0000-0001-6105-2435"},"institutions":[{"id":"https://openalex.org/I16076960","display_name":"COMSATS University Islamabad","ror":"https://ror.org/00nqqvk19","country_code":"PK","type":"education","lineage":["https://openalex.org/I16076960"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Muhammad Aslam Noor","raw_affiliation_strings":["Department of Mathematics, COMSATS University Islamabad, Islamabad, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, COMSATS University Islamabad, Islamabad, Pakistan","institution_ids":["https://openalex.org/I16076960"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059025015","display_name":"Pshtiwan Othman Mohammed","orcid":"https://orcid.org/0000-0001-6837-8075"},"institutions":[{"id":"https://openalex.org/I64952554","display_name":"University of Sulaimani","ror":"https://ror.org/00saanr69","country_code":"IQ","type":"education","lineage":["https://openalex.org/I64952554"]}],"countries":["IQ"],"is_corresponding":false,"raw_author_name":"Pshtiwan Othman Mohammed","raw_affiliation_strings":["Department of Mathematics, College of Education, University of Sulaimani, Sulaimani, Kurdistan Region, Iraq"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Education, University of Sulaimani, Sulaimani, Kurdistan Region, Iraq","institution_ids":["https://openalex.org/I64952554"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049648837","display_name":"Juan L. G. Guirao","orcid":"https://orcid.org/0000-0003-2788-809X"},"institutions":[{"id":"https://openalex.org/I1341604212","display_name":"Northwest African American Museum","ror":"https://ror.org/01c3enh80","country_code":"US","type":"archive","lineage":["https://openalex.org/I1341604212"]},{"id":"https://openalex.org/I3123212020","display_name":"Universidad Polit\u00e9cnica de Cartagena","ror":"https://ror.org/02k5kx966","country_code":"ES","type":"education","lineage":["https://openalex.org/I3123212020"]}],"countries":["ES","US"],"is_corresponding":false,"raw_author_name":"Juan L. G. Guirao","raw_affiliation_strings":["Department of Applied Mathematics and Statistics, Technical University of Cartagena, Hospital de Marina, 30203, Cartagena, Spain","Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jidda, 21589, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Statistics, Technical University of Cartagena, Hospital de Marina, 30203, Cartagena, Spain","institution_ids":["https://openalex.org/I3123212020"]},{"raw_affiliation_string":"Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jidda, 21589, Saudi Arabia","institution_ids":["https://openalex.org/I1341604212"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060630057","display_name":"Khalida Inayat Noor","orcid":"https://orcid.org/0000-0002-5000-3870"},"institutions":[{"id":"https://openalex.org/I16076960","display_name":"COMSATS University Islamabad","ror":"https://ror.org/00nqqvk19","country_code":"PK","type":"education","lineage":["https://openalex.org/I16076960"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Khalida Inayat Noor","raw_affiliation_strings":["Department of Mathematics, COMSATS University Islamabad, Islamabad, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, COMSATS University Islamabad, Islamabad, Pakistan","institution_ids":["https://openalex.org/I16076960"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5023084872"],"corresponding_institution_ids":["https://openalex.org/I16076960"],"apc_list":{"value":1390,"currency":"GBP","value_usd":1704},"apc_paid":{"value":1390,"currency":"GBP","value_usd":1704},"fwci":6.6035,"has_fulltext":true,"cited_by_count":25,"citation_normalized_percentile":{"value":0.97945717,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"14","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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":0.9968000054359436,"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9919999837875366,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5677643418312073},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5659353733062744},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.48741963505744934},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.45924192667007446},{"id":"https://openalex.org/keywords/relation","display_name":"Relation (database)","score":0.42390722036361694},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.42080390453338623},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.3985317051410675},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2590130865573883},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.21433386206626892},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09551414847373962},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.08701714873313904}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5677643418312073},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5659353733062744},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.48741963505744934},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.45924192667007446},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.42390722036361694},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.42080390453338623},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3985317051410675},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2590130865573883},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.21433386206626892},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09551414847373962},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.08701714873313904},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s44196-021-00009-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s44196-021-00009-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s44196-021-00009-w.pdf","source":{"id":"https://openalex.org/S190680769","display_name":"International Journal of Computational Intelligence Systems","issn_l":"1875-6883","issn":["1875-6883","1875-6891"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["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":"International Journal of Computational Intelligence Systems","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s44196-021-00009-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s44196-021-00009-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s44196-021-00009-w.pdf","source":{"id":"https://openalex.org/S190680769","display_name":"International Journal of Computational Intelligence Systems","issn_l":"1875-6883","issn":["1875-6883","1875-6891"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["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":"International Journal of Computational Intelligence Systems","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.7200000286102295}],"awards":[{"id":"https://openalex.org/G2657747242","display_name":null,"funder_award_id":"PGC2018-0971-B-100","funder_id":"https://openalex.org/F4320310087","funder_display_name":"Fundaci\u00f3n S\u00e9neca"},{"id":"https://openalex.org/G92039846","display_name":null,"funder_award_id":"20783/PI/18","funder_id":"https://openalex.org/F4320310087","funder_display_name":"Fundaci\u00f3n S\u00e9neca"}],"funders":[{"id":"https://openalex.org/F4320310087","display_name":"Fundaci\u00f3n S\u00e9neca","ror":"https://ror.org/03q68pf65"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3201806466.pdf","grobid_xml":"https://content.openalex.org/works/W3201806466.grobid-xml"},"referenced_works_count":49,"referenced_works":["https://openalex.org/W565587792","https://openalex.org/W1588000771","https://openalex.org/W1908629854","https://openalex.org/W1965955764","https://openalex.org/W1976977542","https://openalex.org/W1977914365","https://openalex.org/W1987832787","https://openalex.org/W1994178762","https://openalex.org/W1997679081","https://openalex.org/W2007120062","https://openalex.org/W2028419520","https://openalex.org/W2049888876","https://openalex.org/W2053149227","https://openalex.org/W2072882480","https://openalex.org/W2079760134","https://openalex.org/W2093827652","https://openalex.org/W2184889396","https://openalex.org/W2218043766","https://openalex.org/W2322767775","https://openalex.org/W2420464821","https://openalex.org/W2461102131","https://openalex.org/W2556396095","https://openalex.org/W2581129351","https://openalex.org/W2587428017","https://openalex.org/W2749947267","https://openalex.org/W2782050230","https://openalex.org/W2787696370","https://openalex.org/W2788828518","https://openalex.org/W2789458122","https://openalex.org/W2800481507","https://openalex.org/W2900139894","https://openalex.org/W2900786704","https://openalex.org/W3001553400","https://openalex.org/W3017944170","https://openalex.org/W3020127197","https://openalex.org/W3021074187","https://openalex.org/W3043531732","https://openalex.org/W3117213761","https://openalex.org/W3125195770","https://openalex.org/W3141308023","https://openalex.org/W3155369488","https://openalex.org/W3155664370","https://openalex.org/W3160011385","https://openalex.org/W3164799850","https://openalex.org/W3165481893","https://openalex.org/W3167199206","https://openalex.org/W3187280372","https://openalex.org/W3189745929","https://openalex.org/W3191144063"],"related_works":["https://openalex.org/W4234874385","https://openalex.org/W2323648130","https://openalex.org/W2157140558","https://openalex.org/W2378782423","https://openalex.org/W4233308809","https://openalex.org/W2388988621","https://openalex.org/W2357797405","https://openalex.org/W2366623913","https://openalex.org/W2374905595","https://openalex.org/W4387635768"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2,157,173],"study,":[3],"we":[4,22,93,112],"introduce":[5],"the":[6,19,87,101,150,153],"new":[7,20,24],"concept":[8],"of":[9,26,56,89,103,152],"$$h$$":[10,38,47,104,124],"<mml:math":[11,39,48,105,125],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[12,40,49,106,126],"<mml:mi>h</mml:mi>":[13,41,50,107,127],"</mml:math>":[14,42,51,108,128],"-convex":[15,43,52,109,129],"fuzzy-interval-valued":[16,44],"functions.":[17],"Under":[18],"concept,":[21],"present":[23,95],"versions":[25],"Hermite\u2013Hadamard":[27,34],"inequalities":[28,36,99],"(H\u2013H":[29],"inequalities)":[30],"are":[31,82,132,144],"called":[32],"fuzzy-interval":[33,74],"type":[35,98,121],"for":[37,100,169],"functions":[45],"(":[46],"FIVF)":[53],"by":[54],"means":[55],"fuzzy":[57,61,90],"order":[58,62,70,77,91],"relation.":[59],"This":[60,159],"relation":[63,71,78,81],"is":[64],"defined":[65,72],"level":[66],"wise":[67],"through":[68],"Kulisch\u2013Miranker":[69],"on":[73],"space.":[75],"Fuzzy":[76],"and":[79,123,162],"inclusion":[80],"two":[83],"different":[84],"concepts.":[85],"With":[86],"help":[88],"relation,":[92],"also":[94,114,133],"some":[96,134],"H\u2013H":[97],"product":[102],"FIVFs.":[110],"Moreover,":[111],"have":[113],"established":[115],"strong":[116],"relationship":[117],"between":[118],"Hermite\u2013Hadamard\u2013Fej\u00b4er":[119],"(H\u2013H\u2013Fej\u00b4er)":[120],"inequality":[122],"FIVF.":[130],"There":[131,143],"special":[135],"cases":[136],"presented":[137],"that":[138],"can":[139],"be":[140],"considered":[141],"applications.":[142],"useful":[145],"examples":[146],"provided":[147],"to":[148],"demonstrate":[149],"applicability":[151],"concepts":[154],"proposed":[155],"in":[156,172],"study.":[158],"paper's":[160],"thoughts":[161],"methodologies":[163],"could":[164],"serve":[165],"as":[166],"a":[167],"springboard":[168],"more":[170],"research":[171],"field.":[174]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":4}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}