I don't think so, because fuzzy logic deals with degrees of truth between 0 (false) and 1 (true). Instead, this is a probability problem that deals with degrees of likelihood between 0 and 1 that the truth of a specific condition (two people have the same birthday) is either there or it's not, i.e. not fuzzy at all, just true or false. Fuzzy logic would only be involved if two people sort of had the same birthday, but not really, but kind of, except not, yet they do.