  The standard nonlinear Schr\"{o}dinger equation (NLSE) is one of the elegant
equations to find the information about the modulational instability criteria
of dust-ion-acoustic (DIA) waves (DIAWs) and associated DIA rogue waves
(DIARWs) in a three-component dusty plasma medium having inertialess
super-thermal kappa distributed electrons, and inertial warm positive ions and
negative dust grains. It can be seen that under the consideration of inertial
warm ions along with inertial negatively charged dust grains, the plasma system
supports both fast and slow DIA modes. The charge state and number density of
the ion and dust grain are responsible to change the instability conditions of
the DIAWs and the configuration of DIARWs. These results are to be considered
the cornerstone for explaining the real puzzles in space and laboratory dusty
plasmas.
