The rulers of Vijayanagara empire called themselves _____.

The correct option is Rayas.

To understand why this is the correct answer, let's look at the historical context of the Vijayanagara Empire:
1. The rulers of the Vijayanagara Empire (established in 1336) referred to themselves as Rayas. For example, famous rulers like Krishnadeva Raya used this title as part of their royal designation.
2. In contrast, the term Nayakas referred to military chiefs or governors who exercised power in specific territories under the control of the empire, rather than the supreme rulers themselves.
3. Kudirais (specifically Kudirai Chettis) refers to horse merchants who were involved in the trade of horses, which was critical for the military strength of the state.
4. Samrajyapatis is not a standard historical title used by the sovereign rulers of the Vijayanagara state.

Therefore, the title that the rulers of the Vijayanagara empire used to address themselves was Rayas.