{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T15:12:47Z","timestamp":1774624367402,"version":"3.50.1"},"reference-count":24,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2023,11,13]],"date-time":"2023-11-13T00:00:00Z","timestamp":1699833600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Due to various unpredictable factors, a decision maker frequently experiences uncertainty and hesitation when dealing with real-world practical optimization problems. At times, it\u2019s necessary to simultaneously optimize a number of non-linear and competing objectives. Linear Diophantine fuzzy numbers are used to address the uncertain parameters that arise in these circumstances. The objective of this manuscript is to present a method for solving a linear Diophantine fuzzy multi-objective nonlinear programming problem (LDFMONLPP). All the coefficients of the nonlinear multi-objective functions and the constraints are linear Diophantine fuzzy numbers (LDFNs). Here we find the solution of the nonlinear programming problem by using Karush-Kuhn-Tucker condition. A numerical example is presented.<\/jats:p>","DOI":"10.3390\/axioms12111048","type":"journal-article","created":{"date-parts":[[2023,11,14]],"date-time":"2023-11-14T02:20:37Z","timestamp":1699928437000},"page":"1048","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Multi-Objective Non-Linear Programming Problems in Linear Diophantine Fuzzy Environment"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-2896-7408","authenticated-orcid":false,"given":"Salma","family":"Iqbal","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, Riphah International University, Sector I-14, Islamabad 44000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5362-9916","authenticated-orcid":false,"given":"Naveed","family":"Yaqoob","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Riphah International University, Sector I-14, Islamabad 44000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0314-876X","authenticated-orcid":false,"given":"Muhammad","family":"Gulistan","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB T6G 2R3, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,11,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1016\/0165-0114(78)90031-3","article-title":"Fuzzy programming and linear programming with several objective functions","volume":"1","author":"Zimmermann","year":"1978","journal-title":"Fuzzy Sets Syst."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"B-141","DOI":"10.1287\/mnsc.17.4.B141","article-title":"Decision-making in a fuzzy environment","volume":"17","author":"Bellman","year":"1970","journal-title":"Manag. 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