  We construct certain monoids, called tied monoids. These monoids result to be
semidirect products finitely presented and commonly built from braid groups and
their relatives acting on monoids of set partitions. The nature of our monoids
indicate that they should give origin to new knot algebras; indeed, our tied
monoids include the tied braid monoid and the tied singular braid monoid, which
were used, respectively, to construct new polynomial invariants for classical
links and singular links. Consequently, we provide a mechanism to attach an
algebra to each tied monoid. To build the tied monoids it is necessary to have
presentations of set partition monoids of types A, B and D, among others. For
type A we use a presentation due to FitzGerald and for the other type it was
necessary to built them.
