The “Increased Melee Attack Speed” value shows a sum of all your increases to melee attack speed, and intentionally does not factor in your base attack rate. This is for the sake of effects such as Void Knight’s Rot Grip, which cares about the sum of increased melee attack speed and does not consider your base attack rate.
The “Melee Attack Speed” value factors in both your base attack rate and all modifiers to your melee attack speed.