{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:52:07Z","timestamp":1760151127830,"version":"build-2065373602"},"reference-count":56,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,2,3]],"date-time":"2022-02-03T00:00:00Z","timestamp":1643846400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003141","name":"Consejo Nacional de Ciencia y Tecnolog\u00eda","doi-asserted-by":"publisher","award":["A1-S-45928"],"award-info":[{"award-number":["A1-S-45928"]}],"id":[{"id":"10.13039\/501100003141","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The main objective of this study is to introduce new versions of fractional integral inequalities in fuzzy fractional calculus utilizing the introduced preinvexity. Due to the behavior of its definition, the idea of preinvexity plays a significant role in the subject of inequalities. The concepts of preinvexity and symmetry have a tight connection thanks to the significant correlation that has developed between both in recent years. In this study, we attain the Hermite-Hadamard (H\u00b7H) and Hermite-Hadamard-Fej\u00e9r (H\u00b7H Fej\u00e9r) type inequalities for preinvex fuzzy-interval-valued functions (preinvex F\u00b7I\u00b7V\u00b7Fs) via Condition C and fuzzy Riemann\u2013Liouville fractional integrals. Furthermore, we establish some refinements of fuzzy fractional H\u00b7H type inequality. There are also some specific examples of the reported results for various preinvex functions deduced. To support the newly introduced ideal, we have provided some nontrivial and logical examples. The results presented in this research are a significant improvement over earlier results. This paper\u2019s awe-inspiring notions and formidable tools may energize and revitalize future research on this worthwhile and fascinating topic.<\/jats:p>","DOI":"10.3390\/sym14020313","type":"journal-article","created":{"date-parts":[[2022,2,6]],"date-time":"2022-02-06T20:40:18Z","timestamp":1644180018000},"page":"313","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Some Fuzzy Riemann\u2013Liouville Fractional Integral Inequalities for Preinvex Fuzzy Interval-Valued Functions"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7450-8067","authenticated-orcid":false,"given":"Muhammad Bilal","family":"Khan","sequence":"first","affiliation":[{"name":"Department of Mathematics, COMSATS University Islamabad, Islamabad 44000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hatim Ghazi","family":"Zaini","sequence":"additional","affiliation":[{"name":"Department of Computer Science, College of Computers and Information Technology, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7580-7533","authenticated-orcid":false,"given":"Jorge E.","family":"Mac\u00edas-D\u00edaz","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas y F\u00edsica, Universidad Aut\u00f3noma de Aguascalientes, Avenida, Universidad 940, Ciudad Universitaria, Aguascalientes 20131, Mexico"},{"name":"Department of Mathematics, School of Digital Technologies, Tallinn University, Narva Rd. 25, 10120 Tallinn, Estonia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8209-3869","authenticated-orcid":false,"given":"Savin","family":"Trean\u021b\u01ce","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, University Politehnica of Bucharest, 060042 Bucharest, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9431-4195","authenticated-orcid":false,"given":"Mohamed S.","family":"Soliman","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, College of Engineering, Taif University, P.O. 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