This paper introduces the notions of asymptotic Wijsman \(\mathcal {I}_2\) -deferred statistical equivalence and asymptotic Wijsman strong \(\mathcal {I}_2\) -deferred Cesàro equivalence for double sequences of sets in metric spaces. These concepts provide a unified framework that combines asymptotic equivalence, ideal-statistical convergence and deferred Cesàro summability within the Wijsman setting. We establish fundamental inclusion relations between the corresponding equivalence classes and prove that strong \(\mathcal {I}_2\) -deferred Cesàro equivalence implies \(\mathcal {I}_2\) -deferred statistical equivalence, while the converse holds under boundedness conditions. A counterexample is constructed to demonstrate that the reverse implication fails in general. Furthermore, we analyze the stability of these notions under suitable boundedness and structural constraints.
