  This paper aims to introduce a construction technique of set-theoretic
solutions of the Yang-Baxter equation, called strong semilattice of solutions.
This technique, inspired by the strong semilattice of semigroups, allows one to
obtain new solutions. In particular, this method turns out to be useful to
provide non-bijective solutions of finite order. It is well-known braces, skew
braces and semi-braces are closely linked with solutions. Hence, we introduce a
generalization of the algebraic structure of semi-braces based on this new
construction technique of solutions.
