A Theoretical Framework for Optimality Conditions of Nonlinear Type-2 Interval-Valued Unconstrained and Constrained Optimization Problems Using Type-2 Interval Order Relations

In the traditional nonlinear optimization theory, Karush-Kuhn-Tucker (KKT) optimality conditions for constrained problems with inequality constraints play an essential role. The situation becomes challenging when theory of is discussed under uncertainty. Several researchers have interval approach to tackle uncertainty and derived conditions. However, there are several realistic situations in which not suitable. This study aims introduce Type-2 overcome limitation classical approach. introduces order relation interval-valued function concepts derive generalized KKT uncertain environments. Then, unconstrained problem after that, using these conditions, derived. Finally, proposed demonstrated by numerical examples.