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We define Aeppli and Bott-Chern cohomology for bi-generalized complexmanifolds and show that they are finite dimensional for compact bi-generalizedHermitian manifolds. For totally bounded double complexes $(A, d', d'')$, weshow that the validity of $d'd''$-lemma is equivalent to having the samedimension of several cohomology groups. Some calculations of Bott-Cherncohomology groups of some bi-generalized Hermitian manifolds are given.

Aeppli and Bott-Chern cohomology for bi-generalized Hermitian manifolds and $d'd''$-lemma