Extremality of collections of sets with respect to general perturbations

The paper proposes another extension of the extremal principle. A new extremality model involving arbitrary families of perturbations (deformations) of the given sets is studied. It generalizes the conventional model based on linear translations of the sets as well as its set-valued extensions. This approach leads to a more general and simpler version of fuzzy separation. We demonstrate the applicability of the new model to set-valued optimization problems, weakening the assumptions of the known results and streamlining their proofs.