The correct answer for this question is option 3, which is to carry out an anti-piracy role. The Indian Navy has indeed deployed its fleet ships to patrol near the Gulf of Aden, which is a region known for piracy activities. By doing so, the Indian Navy aims to protect Indian merchant vessels and ensure the safety of maritime trade routes in the area.

Option 1, which suggests that the deployment is to show off naval might, is not the primary objective of the Indian Navy`s operation near the Gulf of Aden. While it may indirectly demonstrate the Navy`s capabilities, the main focus is to address the piracy issue.

Similarly, option 2, which implies dominant intentions in the Indian Ocean region, is not the primary reason for the deployment. The Indian Navy`s presence in the Gulf of Aden serves a specific purpose of combating piracy, rather than asserting dominance.

Option 4, exercise operational readiness in international water, is partially correct. The Indian Navy`s operations near the Gulf of Aden do enhance its operational readiness, but the primary objective remains the anti-piracy role rather than general training exercises.

Overall, option 3 provides the most accurate explanation for the deployment of the Indian Navy`s fleet ships near the Gulf of Aden