In format preserving encryption an attacker knows the format and data type of the plain text. The format of the plain text and cipher text are same. usually cipher text are unreadable form. then how FPE is secure?what are all the possible attacks on FPE cipher?
Usually FPE is $Rank-LPE-DeRank$ Where LPE is length preserving encryption. The advantages of FPE schemes Preserving Formats and Lengths could be used against it too.
There are two attack vectors specific to FPE (but they are by design !)
Length Preserving This might aide to brute force attacks if the domain is too small. For example encrypting an IP Address using FPE , the Cipher text is just $32$ bits, Where as encrypting with traditional AES would result in $128$ bits.
Inferences FPE ciphers may reveal more inferences about the underlying data. For example encrypting an IP Address still looks like an IP Address, this leaks inference that the underlying data types are. An attacker getting access to encrypted logs might find it difficult to guess what the underlying data is if it looks random strings but if the encrypted logs have format preserving data this might leak the nature of the data is. One could argue this to be advantage too data that does not look random might not raise any suspicion etc.
It also depends on the over all system design what additional layers of security exist.
Also this particular paper explains in much detail in theoretical jargon.