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

Reduced typed angularly decorated planar rooted trees and generalized tridendriform algebras