The determination of set-theoretic operations on genuine sets, other than the operations $\subseteq^g$, $=^g$, $^{gc}$, $\cap^g$ and $\cup^g$ presented in the author’s paper Genuine sets (Fuzzy Sets and Systems 105 (1999), 377-384), is proposed as an open question in his paper Some notices on genuine sets (Fuzzy Sets and Systems 110 (2000), 275-278). The present paper gives a desirable answer to this problem, and introduces a general technique for the construction of set-theoretic operations on genuine sets. Furthermore, two examples are designed to demonstrate two significant special classes of set-theoretic operations on genuine sets.