Hi I just want to know how to assign a unique address for each member of a website to identify if they already paid the website's membership fee.
You can use bitcoin api to generate any amount of adresses from your public key (see this example
https://github.com/weex/addrgen)
Now generate unique address for each of your users and store it as an additional field in your database
After this is done - you can easily check if payment have been received if selected address was credited.
Profit!
What if the generated address belongs to other wallet or it is impossible for it to generate an address that belongs to others?
If you use same public key to generate addresses there is no way to generate "wrong" address - all of them will be controlled by a single private key.
There is no specific open source solution that does exactly what you ask for out of the box, but this is very popular solution and you should be able to find code snippets by doing quick google (like the one I linked above).
Just remember to
try everything on testnet before going live! You don't want your users to send their BTC to the void.
Also make sure accepting BTC is legal in country you accept it. Otherwise you may attract unwanted attention. Paying taxes from BTC income can be tricky.