Reduced typed angularly decorated planar rooted trees and generalized tridendriform algebras

We introduce a generalization of tridendriform algebras, where each of the three products are replaced by a family of products indexed by a set $\mathrm{\Omega }$. We study the needed structure on $\mathrm{\Omega }$ for free $\mathrm{\Omega }$-tridendriform algebras to be built on Schr{"o}der trees (as it is the case in the classical case), with convenient decorations on their leaves. We obtain in this way extended triassociative semigroups. We describe commutative $\mathrm{\Omega }$-tridendriform algebras in terms of typed words. We also study links with generalizations of Rota-Baxter algebras and describe the Koszul duals of the corresponding operads.