We investigate the structure and properties of $TL$-sub-semihypergroups, where $T$ is an arbitrary triangular norm on a given complete lattice $L$. We study its structure under the direct product and with respect to the fundamental relation. In particular, we consider $L=[0,1]$ and $T=\min $, and investigate the connection between $TL$-sub-semihypergroups and the probability space.