The authors study a fuzzy propositional logic which extends the well-known Łukasiewicz, product and Gödel logics; see, for instance, the paper of P. Hájek and the authors [Arch. Math. Logic 35, 191-208 (1996; Zbl 0848.03005)]. The corresponding algebras are defined and a related completeness theorem is established. Further it is proved that the linearly ordered algebras of this logic are embeddable in the related linearly ordered abelian rings with strong unit and cancellation law.