Step 1: Understanding Purification.
Purification is the process of separating impurities or unwanted components, commonly involving methods like thermal annealing, acid treatment, or filtration, which are listed under (II).
Step 2: De-agglomeration.
De-agglomeration involves breaking down clusters into smaller particles using methods such as ultrasonication, electric field manipulation, and polymer wrapping, which matches with (IV).
Step 3: Chemical Functionalization.
Chemical functionalization involves modifying the surface of materials, which can be done using various controlled processes like carbon arc burning, where oxygen supply plays a crucial role, matching with (I).
Step 4: Fullerenes.
Fullerenes are molecules made from carbon, and they require specific controlled processes for their creation, which are described by (III).
Final Answer:
\[
\boxed{(4) \, (A) - (II), (B) - (IV), (C) - (I), (D) - (III)}
\]