A non-frame valued Cartesian closed category of liminf complete fuzzy orders

Let H={0,12,1} with the natural order and p&q=max⁡{p+q−1,0} for all p,q∈H. It is proved that the category of liminf complete H-ordered sets is Cartesian closed. It reveals that there exists a Cartesian closed category consisting of non-frame valued liminf complete fuzzy ordered sets.