Rough Ideal Convergence of Double Sequences in Probabilistic Normed Space

In this work, we study the notions of rough I 2 -Cauchy and rough I * 2 -Cauchy for double sequences in the setting of random 2-normed space.The notions of rough I 2 -convergence, rough I * 2 -convergence, rough I 2 -limit points, and rough I 2 -cluster points of probabilistic normed double sequences are also developed and investigated.By proving that rough I2 * -convergence implies rough I2-convergence in probabilistic normed space, we discuss the connection between rough I 2 -and rough I * 2 -convergence.Additionally, we have demonstrated by an example that rough I 2 -convergence in probabilistic normed space does not imply rough I * 2convergence.The significance of condition (AP2) in summability analysis utilizing ideals is supported by our findings.