Cuts or thresholds, what is the best reduction method in fuzzy formal concept analysis?

Recently α-cut irreducible and δ1δ2-multi-adjoint concept lattices have been introduced as two different methodologies focus on reducing the size of a given fuzzy concept lattice. The philosophy of both methodologies is completely different and so, the obtained lattices too. This paper analyzes the differences and proposes that the best is to combine both methodologies in order to obtain new procedures to reduce the information retrieval, only considering the important information for the user and with the advantages of both philosophies.