They will not be able to make an application simply based on the fact that you are a naturalised British citizen. That is not to say that they would be unsuccessful in applying for a family visitor visa (maximum stay of 6 months). They could also apply for an extended family visitor visa (of 1,2,5 or 10 years) they will only be able to stay in the UK for up to 6 months at a time but can make repeated visits.
I am afraid that your parents will struggle to obtain a visa to reside in the UK permanently. They will not be able to make an application simply based on the fact that you are a naturalised British citizen. That is not to say that they would be unsuccessful in applying for a family visitor visa (maximum stay of 6 months). They could also apply for an extended family visitor visa (of 1,2,5 or 10 years) they will only be able to stay in the UK for up to 6 months at a time but can make repeated visits.