Abstract

As is well known, any preorder R on a set U induces an Alexandrov topology on U. In some interesting cases related to data mining an Alexandrov topology can be transformed into different types of logico-algebraic models. In some cases, (pre)topological operators provided by Pointless Topology may define a topological space on U even if R is not a preorder. If this is the case, then we call R a crypto-preorder. The paper studies the conditions under which a relation R is a crypto-preorder and how to transform a crypto-preorder into a proper preorder.