Founder of Tughlaq Dynasty

The Tughlaq Dynasty, a prominent Muslim dynasty of Turkic origin, established its rule over the Delhi Sultanate in the 14th century. Its foundation marked a new era in Indian history, following the decline of the Khilji dynasty.

• Ghiyasuddin Tughlaq (also known as Ghazi Malik) is accurately recognized as the founder. He ascended to power in 1320 AD, initiating the Tughlaq rule after a period of political instability. His reign focused on restoring order and consolidating the sultanate.
• Firoz Shah Tughlaq was a later and notable ruler of the dynasty, known for his extensive public works and administrative reforms, but he was not the founder.
• Muhammad bin Tughlaq was Ghiyasuddin's son and successor, infamous for his ambitious but often ill-fated administrative experiments. He did not establish the dynasty.

Thus, Ghiyasuddin Tughlaq is the correct answer for founding this influential dynasty.