  In this paper, three semilinear substructural logics ULw, IULw and HpsUL*w
are constructed. Then the completeness of ULw and IULw with respect to classes
of finite UL and IUL-algebras, respectively, is proved. Algebraically,
non-integral ULw and IULw-algebras have the finite embeddability property,
which gives a characterization for finite UL and IUL-algebras. Furthermore, the
standard completeness of ULw, IULw and HpsUL*w is proved, which shows that they
are substructural fuzzy logics.
