Finding Frequent and Infrequent Elements of Partial Orders Product and the Problem of Two-Valued Monotone Function Decoding

Two equivalent data analysis problems are considered: the problem of finding maximal frequent and minimal infrequent elements of a Cartesian product of partial orders P using database transactions, and the problem of finding upper zeros and lower units for a two-valued monotone function defined on the elements of the set P and taking the value 0 and 1, respectively, on frequent and infrequent elements of this set. The authors propose and experimentally investigate an original approach to solving these problems.