{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T14:06:19Z","timestamp":1778681179484,"version":"3.51.4"},"reference-count":50,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2021,4,13]],"date-time":"2021-04-13T00:00:00Z","timestamp":1618272000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>It is a familiar fact that inequalities have become a very popular method using fractional integrals, and that this method has been the driving force behind many studies in recent years. Many forms of inequality have been studied, resulting in the introduction of new trend in inequality theory. The aim of this paper is to use a fuzzy order relation to introduce various types of inequalities. On the fuzzy interval space, this fuzzy order relation is defined level by level. With the help of this relation, firstly, we derive some discrete Jensen and Schur inequalities for convex fuzzy interval-valued functions (convex fuzzy-IVF), and then, we present Hermite\u2013Hadamard inequalities (HH-inequalities) for convex fuzzy-IVF via fuzzy interval Riemann\u2013Liouville fractional integrals. These outcomes are a generalization of a number of previously known results, and many new outcomes can be deduced as a result of appropriate parameter \u201c\u03b3\u201d and real valued function \u201c\u03a9\u201d selections. We hope that our fuzzy order relations results can be used to evaluate a number of mathematical problems related to real-world applications.<\/jats:p>","DOI":"10.3390\/sym13040673","type":"journal-article","created":{"date-parts":[[2021,4,13]],"date-time":"2021-04-13T22:55:09Z","timestamp":1618354509000},"page":"673","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":60,"title":["New Hermite\u2013Hadamard Inequalities in Fuzzy-Interval Fractional Calculus and Related Inequalities"],"prefix":"10.3390","volume":"13","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"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6837-8075","authenticated-orcid":false,"given":"Pshtiwan Othman","family":"Mohammed","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Education, University of Sulaimani, Sulaimani, 46001, Kurdistan Region, Iraq"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6105-2435","authenticated-orcid":false,"given":"Muhammad Aslam","family":"Noor","sequence":"additional","affiliation":[{"name":"Department of Mathematics, COMSATS University Islamabad, Islamabad 44000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0365-0282","authenticated-orcid":false,"given":"Y. S.","family":"Hamed","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,4,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1007\/s00041-012-9223-8","article-title":"On the Gagliardo-Nirenberg type inequality in the critical Sobolev-Morrey space","volume":"19","author":"Sawano","year":"2013","journal-title":"J. Fourier Anal. Appl."},{"key":"ref_2","first-page":"33","article-title":"On some Ostrowski type inequalities","volume":"18","author":"Gavrea","year":"2010","journal-title":"Gen. 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