Rough ideal statistical convergence for complex uncertain double sequences

Abstract In this paper, we introduce the notion of rough ℐ 2 {\mathscr{I}_{2}} -statistical convergence (denoted as r ⁢ - ⁢ 𝒮 ⁢ ( ℐ 2 ) {r\text{-}\mathcal{S}(\mathscr{I}_{2})} -convergence) of complex uncertain double sequences in four fundamental aspects of uncertainty, namely almost sure, measure, mean, and distribution. This framework extends the existing notion of rough ℐ {\mathscr{I}} -convergence for complex uncertain sequences to the broader setting of double sequences. In addition, we investigate r ⁢ - ⁢ 𝒮 ⁢ ( ℐ 2 ) {r\text{-}\mathcal{S}(\mathscr{I}_{2})} -convergence in p -distance and r ⁢ - ⁢ 𝒮 ⁢ ( ℐ 2 ) {r\text{-}\mathcal{S}(\mathscr{I}_{2})} -convergence in metric for complex uncertain double sequences. Overall, this study provides a comprehensive diagrammatic illustration of the interrelationships among the various r ⁢ - ⁢ 𝒮 ⁢ ( ℐ 2 ) {r\text{-}\mathcal{S}(\mathscr{I}_{2})} -convergence concepts and offers some significant observations highlighting their distinctions, supported by illustrative examples.