We examine double successive approximations on a set, which we denote by L2L1, U2U1, U2L1, L2U1 where L1, U1 and L2, U2 are based on generally non-equivalent equivalence relations E1 and E2 respectively, on a finite non-empty set V. We consider the case of these operators being given fully defined on its powerset P(V ). Then, we investigate if we can reconstruct the equivalence relations which ...

We present the PowerSetViewer visualization system for the lattice-based mining of powersets. Searching for items within the powerset of a universe occurs in many large dataset knowledge discovery contexts. Using a spatial layout based on a powerset provides a unified visual framework at three different levels: data mining on the filtered dataset, browsing the entire dataset, and comparing mult...

The nested relational algebra is often inadequate as a tool to handle nested relations, since several important queries, such as transitive closure, cannot expressed by it. On the other hand, the powerset algebra does allow the expression of transitive closure, but in a too expensive way. Therefore, we consider various other extensions to the nested algebra, such as least tixpoint and programmi...

We study the orbits under natural action of a permutation group G≤Sn on powerset

An algorithm for the uniform random generation of the powerset construction is presented. Given a combinatorial class I, together with a counting procedure and an unranking procedure (or simply a random generation procedure) for I, this algorithm provides counting and unranking (or random generation) procedures for P = powerset(I). For most combi-natorial structures, each random powerset of siz...