Probabilist, possibilist and belief objects for knowledge analysis

The main aim of the symbolic approach in data analysis is to extend problems, methods and algorithms used on classical data to more complex data called ‘symbolic objects’ which are well adapted to representing knowledge and which are ‘generic’ unlike usual observations which characterize ‘individual things’. The paper introduces several kinds of symbolic objects: Boolean, possibilist, probabilist and belief. It briefly presents some of their qualities and properties; three theorems show how Probability, Possibility and Evidence theories may be extended on these objects. Finally, four kinds of data analysis problems including the symbolic extension are illustrated by several algorithms which induce knowledge from classical data or from a set of symbolic objects.