{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:11:44Z","timestamp":1760145104711,"version":"build-2065373602"},"reference-count":43,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2024,6,16]],"date-time":"2024-06-16T00:00:00Z","timestamp":1718496000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Russian Science Foundation","award":["23-11-00164","TU-DSPP-2024-66"],"award-info":[{"award-number":["23-11-00164","TU-DSPP-2024-66"]}]},{"name":"Taif University, Saudi Arabia","award":["23-11-00164","TU-DSPP-2024-66"],"award-info":[{"award-number":["23-11-00164","TU-DSPP-2024-66"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Both theoretical and applied mathematics depend heavily on integral inequalities with generalized convexity. Because of its many applications, the theory of integral inequalities is currently one of the areas of mathematics that is evolving at the fastest pace. In this paper, based on fuzzy Aumann\u2019s integral theory, the Hermite\u2013Hadamard\u2019s type inequalities are introduced for a newly defined class of nonconvex functions, which is known as\u00a0U\u00b7D preinvex fuzzy number-valued mappings (U\u00b7D preinvex\u00a0F\u00b7N\u00b7V\u00b7Ms) on coordinates. Some Pachpatte-type inequalities are also established for the product of two\u00a0U\u00b7D preinvex\u00a0F\u00b7N\u00b7V\u00b7Ms, and some Hermite\u2013Hadamard\u2013Fej\u00e9r-type inequalities are also acquired via fuzzy Aumann\u2019s integrals. Additionally, several new generalized inequalities are also obtained for the special situations of the parameters. Additionally, some of the interesting remarks are provided to acquire the classical and new exceptional cases that can be considered as applications of the main outcomes. Lastly, a few suggested uses for these inequalities in numerical integration are made.<\/jats:p>","DOI":"10.3390\/axioms13060404","type":"journal-article","created":{"date-parts":[[2024,6,17]],"date-time":"2024-06-17T08:48:31Z","timestamp":1718614111000},"page":"404","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A New Class of Coordinated Non-Convex Fuzzy-Number-Valued Mappings with Related Inequalities and Their Applications"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7862-4743","authenticated-orcid":false,"given":"Aleksandr","family":"Rakhmangulov","sequence":"first","affiliation":[{"name":"Department of Logistics and Transportation Systems Management, Nosov Magnitogorsk State Technical University, Magnitogorsk 455000, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9758-5591","authenticated-orcid":false,"given":"A. F.","family":"Aljohani","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 47512, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ali","family":"Mubaraki","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"}]},{"given":"Saad","family":"Althobaiti","sequence":"additional","affiliation":[{"name":"Department of Sciences and Technology, Ranyah University College, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,6,16]]},"reference":[{"key":"ref_1","unstructured":"Hardy, G.H., Littlewood, J.E., and P\u00f3lya, G. (1952). 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