Cartesian closedness of the category of real-valued sets, I

Let $[0,1{]}_{\ast }$ be the unit interval $[0,1]$ equipped with a continuous t-norm $\ast$. It is shown that the category of $[0,1{]}_{\ast }$-sets is cartesian closed if, and only if, $\ast$ is the minimum t-norm on $[0,1]$.