I have a class that retrieves its memeber (more or less 10 members) from a database.
My question is: is it more efficient to fetch them every time from the db (MySQL
Depends what you mean by 'efficient'. One's time-efficient, one's disk-space-efficient. And it's very difficult to judge the two against each other, unless your requirements are at either extreme end of the spectrum. You'd probably do OK just flipping a coin, measuring performance over time, and adjusting based on any observed problems.
Premature optimisation is the root of all evil.