As we all know, the ALU perform Arithmetic operation, but does the computer understand post-fix notation or not?
Assuming you mean Arithmetic/Logic Unit, no. The ALU does not understand any notation. It only understands instructions. So, for example, the machine code might include an instruction to "add R10 to R11 and store the result in R9," say (disassembled) ADD R9, R10, R11, but the machine code "notation" is understood by the Control Unit, not the ALU.
By the time the ALU receives the information, it is encoded in the form of various control lines being asserted. For instance, in the above example, the CU might assert control lines for "add," "input A is R10," "input B is R11," and "store result in R9." These lines determine how the ALU and the register file behave, and result in the operation desired.
Textual notation, such as 5 + 8 or (+ x 19) or x 19 15 + * or indeed ADD R9, R10, R11, is understood by software, doing processing at a much higher level than the ALU does. It is that software that interprets, say, postfix notation, and issues the instructions that cause the ALU to execute the desired operations.