{"id":"https://openalex.org/W4210813888","doi":"https://doi.org/10.3390/sym14020313","title":"Some Fuzzy Riemann\u2013Liouville Fractional Integral Inequalities for Preinvex Fuzzy Interval-Valued Functions","display_name":"Some Fuzzy Riemann\u2013Liouville Fractional Integral Inequalities for Preinvex Fuzzy Interval-Valued Functions","publication_year":2022,"publication_date":"2022-02-03","ids":{"openalex":"https://openalex.org/W4210813888","doi":"https://doi.org/10.3390/sym14020313"},"language":"en","primary_location":{"id":"doi:10.3390/sym14020313","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14020313","pdf_url":"https://www.mdpi.com/2073-8994/14/2/313/pdf?version=1644842233","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/14/2/313/pdf?version=1644842233","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5026342382","display_name":"Muhammad Bilal Khan","orcid":"https://orcid.org/0000-0001-7450-8067"},"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 Bilal Khan","raw_affiliation_strings":["Department of Mathematics, COMSATS University Islamabad, Islamabad 44000, Pakistan"],"raw_orcid":"https://orcid.org/0000-0001-7450-8067","affiliations":[{"raw_affiliation_string":"Department of Mathematics, COMSATS University Islamabad, Islamabad 44000, Pakistan","institution_ids":["https://openalex.org/I16076960"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068435820","display_name":"Hatim Ghazi Zaini\ufeff","orcid":"https://orcid.org/0000-0002-9121-8552"},"institutions":[{"id":"https://openalex.org/I179331831","display_name":"Taif University","ror":"https://ror.org/014g1a453","country_code":"SA","type":"education","lineage":["https://openalex.org/I179331831"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Hatim Ghazi Zaini","raw_affiliation_strings":["Department of Computer Science, College of Computers and Information Technology, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, College of Computers and Information Technology, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia","institution_ids":["https://openalex.org/I179331831"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055620640","display_name":"Jorge E. Mac\u00edas\u2010D\u00edaz","orcid":"https://orcid.org/0000-0002-7580-7533"},"institutions":[{"id":"https://openalex.org/I190103667","display_name":"Autonomous University of Aguascalientes","ror":"https://ror.org/03ec8vy26","country_code":"MX","type":"education","lineage":["https://openalex.org/I190103667"]},{"id":"https://openalex.org/I193629610","display_name":"Tallinn University","ror":"https://ror.org/05mey9k78","country_code":"EE","type":"education","lineage":["https://openalex.org/I193629610"]}],"countries":["EE","MX"],"is_corresponding":true,"raw_author_name":"Jorge E. Mac\u00edas-D\u00edaz","raw_affiliation_strings":["Departamento de Matem\u00e1ticas y F\u00edsica, Universidad Aut\u00f3noma de Aguascalientes, Avenida, Universidad 940, Ciudad Universitaria, Aguascalientes 20131, Mexico","Department of Mathematics, School of Digital Technologies, Tallinn University, Narva Rd. 25, 10120 Tallinn, Estonia"],"raw_orcid":"https://orcid.org/0000-0002-7580-7533","affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1ticas y F\u00edsica, Universidad Aut\u00f3noma de Aguascalientes, Avenida, Universidad 940, Ciudad Universitaria, Aguascalientes 20131, Mexico","institution_ids":["https://openalex.org/I190103667"]},{"raw_affiliation_string":"Department of Mathematics, School of Digital Technologies, Tallinn University, Narva Rd. 25, 10120 Tallinn, Estonia","institution_ids":["https://openalex.org/I193629610"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046581790","display_name":"Savin Trean\u0163\u0103","orcid":"https://orcid.org/0000-0001-8209-3869"},"institutions":[{"id":"https://openalex.org/I61641377","display_name":"Universitatea Na\u021bional\u0103 de \u0218tiin\u021b\u0103 \u0219i Tehnologie Politehnica Bucure\u0219ti","ror":"https://ror.org/0558j5q12","country_code":"RO","type":"education","lineage":["https://openalex.org/I61641377"]}],"countries":["RO"],"is_corresponding":true,"raw_author_name":"Savin Trean\u021b\u01ce","raw_affiliation_strings":["Department of Applied Mathematics, University Politehnica of Bucharest, 060042 Bucharest, Romania"],"raw_orcid":"https://orcid.org/0000-0001-8209-3869","affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University Politehnica of Bucharest, 060042 Bucharest, Romania","institution_ids":["https://openalex.org/I61641377"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000893884","display_name":"Mohamed S. Soliman","orcid":"https://orcid.org/0000-0002-9431-4195"},"institutions":[{"id":"https://openalex.org/I179331831","display_name":"Taif University","ror":"https://ror.org/014g1a453","country_code":"SA","type":"education","lineage":["https://openalex.org/I179331831"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Mohamed S. Soliman","raw_affiliation_strings":["Department of Electrical Engineering, College of Engineering, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0002-9431-4195","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, College of Engineering, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia","institution_ids":["https://openalex.org/I179331831"]}]}],"institutions":[],"countries_distinct_count":5,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5046581790","https://openalex.org/A5055620640"],"corresponding_institution_ids":["https://openalex.org/I190103667","https://openalex.org/I193629610","https://openalex.org/I61641377"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":5.3334,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.96664902,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":98},"biblio":{"volume":"14","issue":"2","first_page":"313","last_page":"313"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9994000196456909,"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":0.9994000196456909,"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9987999796867371,"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":0.996399998664856,"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":0.7500283122062683},{"id":"https://openalex.org/keywords/hermite-polynomials","display_name":"Hermite polynomials","score":0.6261186003684998},{"id":"https://openalex.org/keywords/hadamard-transform","display_name":"Hadamard transform","score":0.6135457158088684},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5984858870506287},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.571736216545105},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.566895604133606},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5425047278404236},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.489460825920105},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.4157906770706177},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3820599615573883},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3384351432323456},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.24621251225471497},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10938575863838196},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1026691198348999},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.059965282678604126}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7500283122062683},{"id":"https://openalex.org/C201362023","wikidata":"https://www.wikidata.org/wiki/Q658574","display_name":"Hermite polynomials","level":2,"score":0.6261186003684998},{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.6135457158088684},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5984858870506287},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.571736216545105},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.566895604133606},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5425047278404236},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.489460825920105},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.4157906770706177},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3820599615573883},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3384351432323456},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.24621251225471497},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10938575863838196},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1026691198348999},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.059965282678604126},{"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":3,"locations":[{"id":"doi:10.3390/sym14020313","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14020313","pdf_url":"https://www.mdpi.com/2073-8994/14/2/313/pdf?version=1644842233","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:288755bb43bf4c4ca7f0fb366f336e69","is_oa":true,"landing_page_url":"https://doaj.org/article/288755bb43bf4c4ca7f0fb366f336e69","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 14, Iss 2, p 313 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/2/313/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14020313","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym14020313","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14020313","pdf_url":"https://www.mdpi.com/2073-8994/14/2/313/pdf?version=1644842233","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.5400000214576721,"id":"https://metadata.un.org/sdg/10"}],"awards":[{"id":"https://openalex.org/G4820099471","display_name":null,"funder_award_id":"A1-S-45928","funder_id":"https://openalex.org/F4320321739","funder_display_name":"Consejo Nacional de Ciencia y Tecnolog\u00eda"}],"funders":[{"id":"https://openalex.org/F4320321739","display_name":"Consejo Nacional de Ciencia y Tecnolog\u00eda","ror":"https://ror.org/059ex5q34"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4210813888.pdf"},"referenced_works_count":52,"referenced_works":["https://openalex.org/W1965955764","https://openalex.org/W1987832787","https://openalex.org/W1988180087","https://openalex.org/W1989479808","https://openalex.org/W1994178762","https://openalex.org/W2000983337","https://openalex.org/W2006458314","https://openalex.org/W2009049317","https://openalex.org/W2012192004","https://openalex.org/W2034038007","https://openalex.org/W2037592439","https://openalex.org/W2070545443","https://openalex.org/W2070669484","https://openalex.org/W2075223383","https://openalex.org/W2089518238","https://openalex.org/W2749947267","https://openalex.org/W2772603973","https://openalex.org/W2806318370","https://openalex.org/W2945222953","https://openalex.org/W2962519699","https://openalex.org/W2963883129","https://openalex.org/W3043212253","https://openalex.org/W3114355421","https://openalex.org/W3125195770","https://openalex.org/W3132844534","https://openalex.org/W3141308023","https://openalex.org/W3155369488","https://openalex.org/W3155664370","https://openalex.org/W3164799850","https://openalex.org/W3167199206","https://openalex.org/W3174693905","https://openalex.org/W3175032701","https://openalex.org/W3186519738","https://openalex.org/W3191144063","https://openalex.org/W3193094758","https://openalex.org/W3196742127","https://openalex.org/W3197580818","https://openalex.org/W3199409609","https://openalex.org/W3200955369","https://openalex.org/W3201806466","https://openalex.org/W3203163997","https://openalex.org/W3207494788","https://openalex.org/W3212456975","https://openalex.org/W4205935434","https://openalex.org/W4205977837","https://openalex.org/W4206128546","https://openalex.org/W4291016807","https://openalex.org/W4292070096","https://openalex.org/W6732573306","https://openalex.org/W6791606018","https://openalex.org/W6792301176","https://openalex.org/W6796298146"],"related_works":["https://openalex.org/W1982241170","https://openalex.org/W2116282083","https://openalex.org/W2386549147","https://openalex.org/W1978051046","https://openalex.org/W2950361249","https://openalex.org/W2111217632","https://openalex.org/W4293557899","https://openalex.org/W4396753818","https://openalex.org/W4294618985","https://openalex.org/W2518252082"],"abstract_inverted_index":{"The":[0,43,134],"main":[1],"objective":[2],"of":[3,11,27,32,41,45,99,111],"this":[4,67,138,161],"study":[5],"is":[6],"to":[7,24,54],"introduce":[8],"new":[9],"versions":[10],"fractional":[12,17,92,101],"integral":[13],"inequalities":[14,79],"in":[15,38,63,137],"fuzzy":[16,90,100],"calculus":[18],"utilizing":[19],"the":[20,25,30,39,55,71,112,122],"introduced":[21,124],"preinvexity.":[22],"Due":[23],"behavior":[26],"its":[28],"definition,":[29],"idea":[31],"preinvexity":[33,46],"plays":[34],"a":[35,50,141],"significant":[36,56,142],"role":[37],"subject":[40],"inequalities.":[42],"concepts":[44],"and":[47,74,89,131,151,156,163],"symmetry":[48],"have":[49,127],"tight":[51],"connection":[52],"thanks":[53],"correlation":[57],"that":[58],"has":[59],"developed":[60],"between":[61],"both":[62],"recent":[64],"years.":[65],"In":[66],"study,":[68],"we":[69,95,126],"attain":[70],"Hermite-Hadamard":[72],"(H\u00b7H)":[73],"Hermite-Hadamard-Fej\u00e9r":[75],"(H\u00b7H":[76],"Fej\u00e9r)":[77],"type":[78,103],"for":[80,115],"preinvex":[81,117],"fuzzy-interval-valued":[82],"functions":[83,118],"(preinvex":[84],"F\u00b7I\u00b7V\u00b7Fs)":[85],"via":[86],"Condition":[87],"C":[88],"Riemann\u2013Liouville":[91],"integrals.":[93],"Furthermore,":[94],"establish":[96],"some":[97,108,129],"refinements":[98],"H\u00b7H":[102],"inequality.":[104],"There":[105],"are":[106,140],"also":[107],"specific":[109],"examples":[110],"reported":[113],"results":[114,135],"various":[116],"deduced.":[119],"To":[120],"support":[121],"newly":[123],"ideal,":[125],"provided":[128],"nontrivial":[130],"logical":[132],"examples.":[133],"presented":[136],"research":[139,159],"improvement":[143],"over":[144],"earlier":[145],"results.":[146],"This":[147],"paper\u2019s":[148],"awe-inspiring":[149],"notions":[150],"formidable":[152],"tools":[153],"may":[154],"energize":[155],"revitalize":[157],"future":[158],"on":[160],"worthwhile":[162],"fascinating":[164],"topic.":[165]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":6}],"updated_date":"2026-05-22T06:13:13.366637","created_date":"2022-02-08T00:00:00"}