A user-guided reduction concept lattice and its algebraic structure

Abstract

Concept lattice has been widely studied and it is still attracting researchers in many fields by virtue of its well structured knowledge representation. However, it is more obvious that the number of concept lattice nodes generated from the initial formal context is enormous and results in more storage and lower efficiency of building, especially with the increasing of data to deal with. Meanwhile, users are not interested in the whole intents composed of all the attribute sets and it is a time consuming and troublesome job for them to acquire interesting knowledge. In order to deal with these deficiencies, we propose a constrained concept lattice structure referred to as a reduction concept lattice (RCL) guided by user preferences. This type of lattice structure not only can effectively reduce storage space and construction time, but also help to extract the knowledge that users are interested in. In this study, the definition of RCL is first given based on users’ three types of interesting background knowledge described by predicate logic, together with some RCL’s examples to illustrate this type of structure. Next, an algebraic structure of RCL is defined and its completeness is proved, and accordingly a new way is provided for reduction of concept lattice based on user preferences.