The Importance of the Study of Algebras of Fuzzy Logic

In this paper I begin a sistematic algebraic investigation of some algebras of fuzzy logic: BL-algebras and DRl-monoids; BL-algebras are particular residuated lattices; The origin of; BL-algebras is in Mathematical; LogicBL-algebras, introduced by P.Hajek, form an algebraic counterpart of the basc fuzzy logic.In the paper it is shown that BL-algebras are the duals of bounded representable DRI-monoids. This duality enables us to describe some structure properties of BL-algebras.