A completeness analysis of frequent weighted concept lattices and their algebraic properties

Frequent weighted concept lattice (FWCL) is an interesting version of the WCL (weighted concept lattice), which helps realize knowledge extraction in a more efficient way. One of the open issues is that the completeness of FWCL cannot be ensured (namely, some nodes would be removed since their intent weights are lower than intent importance thresholds specified by the user, so that it can occur that the supremum of their parent nodes or the infimum of their child nodes might not exist). In this study, we first introduce a virtual node into the structure of FWCL to retain the completeness of FWCL. Next, an algebraic system of FWCL is presented by introducing two operations, which form the least frequent upper bound and the greatest frequent lower bound of the FWCL. Finally, we discuss some algebraic properties of FWCL and prove its completeness of knowledge representation in this way providing the theoretical foundations for applications of WCL.