Combining multi-criteria decision analysis and trend reversal discovery make it possible to extract globally optimal, or non-dominated, data in relation to several criteria, and then to observe their evolution according to a decision-making property. Thus, we introduce Emerging Skycube, a concept associating Skycube and emerging datacube. As far as we know, no DBMS-integrated solution exists to compute an emerging Skycube, and hence taking advantage of ROLAP analysis tools. An emerging datacube has only one measure: we propose to use several to comply to multi-criteria decision analysis constraints which requires multiple attributes. A datacube is expensive to compute. An emerging datacube is about twice as expensive. On the other hand, an emerging Skycube is cheaper as the trend reversal is computed after two Skycube calculations, which considerably reduces the relation volume in comparison with the initial one. It is possible to save even more computing time and storage space. To this end, we propose two successive reductions. First, a Skycube lossless partial materialisation using Skylines concepts lattice, based on the agree concepts lattice and partitions lattice. Then, either the closed emerging Skycube for an information-loss reduction, or the closed emerging L-Skycube for a smaller but lossless reduction.