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Relaxed upper stability of Ekeland's variational principle for fuzzy-valued functions | ||
| Iranian Journal of Fuzzy Systems | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 25 شهریور 1405 اصل مقاله (3.79 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2026.55132.9782 | ||
| نویسنده | ||
| Vo Minh Tam* | ||
| Dong Thap University | ||
| چکیده | ||
| We study the relaxed upper stability of Ekeland's variational principle for fuzzy functions under fuzzy order relations induced by the lower and upper set orders of $\alpha$-level sets. Under a D-convergence assumption for fuzzy-valued functions, we prove that every Painleve--Kuratowski outer limit point of exact fuzzy Ekeland variational points for perturbed problems belongs to the relaxed variational set of the limit problem. We also clarify the relation between exact and relaxed variational sets by explicit examples, show that exact upper stability fails in general and prove that it can be recovered under an additional separation condition on the limit problem. Several open questions concerning lower and exact upper stability are discussed. | ||
| کلیدواژهها | ||
| Ekeland's variational principle؛ fuzzy-valued function؛ relaxed upper stability؛ fuzzy order relation؛ Painlev\'e--Kuratowski outer limit | ||
| مراجع | ||
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