Is it logical to use “Proof-of-Authority” for a “public” blockchain?
What is the reason? And Is it logical to use "Proof-of-Authority" for a "public" blockchain, in sense of keeping decentralization?


Proof of Authority is, by definition, centralised. If the authority nodes go rogue, or fail to reach consensus, the network is useless. 

You could use it in public networks (some of the ethereum testnets are PoA), but it would not be a decentralized network. The value of a PoA mainnet would have to come from some benefit of its centralization, and a very high level of trust in the trusted authorities.