{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T00:58:12Z","timestamp":1760230692390,"version":"build-2065373602"},"reference-count":73,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2022,8,9]],"date-time":"2022-08-09T00:00:00Z","timestamp":1660003200000},"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>Many fields of mathematics rely on convexity and nonconvexity, especially when studying optimization issues, where it stands out for a variety of practical aspects. Owing to the behavior of its definition, the idea of convexity also contributes significantly to the discussion of inequalities. The concepts of symmetry and convexity are related and we can apply this because of the close link that has grown between the two in recent years. In this study, harmonic convexity, also known as harmonic s-convexity for fuzzy number valued functions (F-NV-Fs), is defined in a more thorough manner. In this paper, we extend harmonically convex F-NV-Fs and demonstrate Hermite\u2013Hadamard (H.H) and Hermite\u2013Hadamard Fej\u00e9r (H.H. Fej\u00e9r) inequalities. The findings presented here are summaries of a variety of previously published studies.<\/jats:p>","DOI":"10.3390\/sym14081639","type":"journal-article","created":{"date-parts":[[2022,8,10]],"date-time":"2022-08-10T09:47:06Z","timestamp":1660124826000},"page":"1639","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Some Fuzzy Inequalities for Harmonically s-Convex Fuzzy Number Valued Functions in the Second Sense Integral"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7580-7533","authenticated-orcid":false,"given":"Jorge E.","family":"Mac\u00edas-D\u00edaz","sequence":"first","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"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7450-8067","authenticated-orcid":false,"given":"Muhammad Bilal","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, COMSATS University Islamabad, Islamabad 44000, Pakistan"}]},{"given":"Hleil","family":"Alrweili","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Art and Science, Northern Border University, Rafha, Saudi Arabia"}]},{"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. Box 11099, Taif 21944, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,9]]},"reference":[{"key":"ref_1","unstructured":"Dragomir, S.S., and Pearce, V. (2000). Selected Topics on Hermite-Hadamard Inequalities and Applications. RGMIA Monographs, Victoria University."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"274","DOI":"10.1016\/j.cam.2018.10.022","article-title":"New Hermite\u2013Hadamard type integral inequalities for convex functions and their applications","volume":"350","author":"Mehrez","year":"2019","journal-title":"J. Comput. Appl. Math."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Mitrinovi\u0107, D.S., Pe\u010dari\u0107, J.E., and Fink, A.M. (1993). 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