Step 1: Understanding the Concept:
The question asks for the title used by the supreme sovereigns of the Vijayanagara Empire.
Step 2: Detailed Explanation:
(1) Rayas: This was the title adopted by the kings of Vijayanagara. The term 'Raya' is a Kannada/Telugu equivalent of the Sanskrit 'Raja' (king). The most famous ruler of the empire, for instance, was Krishnadeva Raya.
(2) Nayakas: The Nayakas were powerful military chiefs or governors who administered territories on behalf of the Rayas. They were subordinates to the central authority, not the supreme rulers themselves.
(3) Kudirais: This is the Tamil word for horses. 'Kudirai chettis' were horse merchants, an important group in the Vijayanagara economy, but it was not a royal title.
(4) Samrajyapatis: While a generic term for 'emperor', 'Raya' was the specific and customary title used by the Vijayanagara monarchs.
Step 3: Final Answer:
The rulers of the Vijayanagara empire called themselves Rayas.