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The modulational instability (MI) criteria of dust-ion-acoustic (DIA) waves(DIAWs) have been investigated in a four-component pair-ion plasma havinginertial pair-ions, inertialess non-thermal non-extensive electrons, andimmobile negatively charged massive dust grains. A nonlinear Schr\"{o}dingerequation (NLSE) is derived by using reductive perturbation method. Thenonlinear and dispersive coefficients of the NLSE can predict themodulationally stable and unstable parametric regimes of DIAWs and associatedfirst and second order DIA rogue waves (DIARWs). The MI growth rate and theconfiguration of the DIARWs are examined, and it is found that the MI growthrate increases (decreases) with increasing the number density of the negativelycharged dust grains in the presence (absence) of the negative ions. It is alsoobserved that the amplitude and width of the DIARWs increase (decrease) withthe negative (positive) ion mass. The implications of the results to laboratoryand space plasmas are briefly discussed.

Modulational instability of dust-ion-acoustic waves in pair-ion plasma having non-thermal non-extensive electrons