Possibility Theory and Formal Concept Analysis: Context Decomposition and Uncertainty Handling

Abstract

Formal Concept Analysis uses a simple representation framework called 'formal context'. In the classical setting, a formal context specifies existing Boolean relationships between a set of objects and their corresponding properties. Formal concepts are then defined as pairs consisting of a set of objects and a set of properties that mutually characterize each other through a Galois connection. Another Galois connection is also introduced in this setting on the basis of operators induced by a recent possibility theory reading of Formal Concept Analysis. It is shown that this second Galois connection enables us to characterize independent sub-contexts inside the formal context. The second part of the paper discusses an extension of Formal Concept Analysis that has not been much studied, namely the situation where one may be uncertain on the fact that an object possesses or not a Boolean property. Uncertainty is here represented in the possibilistic representation framework.