Many-Valued Context Analysis Using Descriptions

Abstract

We propose an approach to many-valued contexts using formal descriptions instead of scaling. The underlying idea is the philosphical definition of a concept as a set of objects together with the most precise description.

We introduce a formal description as a mapping from the set of attributes to the power set of the values (which is extended appropriately to empty cells), assigning to each attribute the set of allowed values. Descriptions are naturally ordered by preciseness. Using this, we can introduce extent and intent according to the philosophical idea, and thus we define concepts. We present a way to restrict the amount of concepts for a many-valued context by preselecting some descriptions of interest. Furthermore, we introduce implications on descriptions, allowing to investigate relationships between attributes.

Within this approach, we reformulate the known theory under a different point of view. It certainly does not provide a better analysis than scaling, but it allows to avoid the generation of a huge one-valued context.