On the Use of Guaranteed Possibility Measures in Possibilistic Networks

Possibilistic networks are useful tools for reasoning under uncertainty. Uncertain pieces of information can be described by different measures: possibility measures, necessity measures and more recently, guaranteed possibility measures, denoted by Δ. This paper first proposes the use of guaranteed possibility measures to define a so-called Δ-based possibilistic network. This graphical representation tries to express and to deal with the minimal (lower-bound) possibility degree guaranteed for each variable. We then establish relationships between graphical and logical-based representations of uncertain information encoded by guaranteed possibility measures. We show that possibilistic networks based on guaranteed possibility measures can be easily transformed, in a polynomial time, in Δ-based knowledge bases. Then we analyze propagation algorithms in Δbased possibilistic networks. In fact, standard possibilistic propagation algorithms can be re-used since we show that a simple rewriting of the chain rule allows the transformation of the initial Δ-based possibilistic networks into standard min-based possibilistic networks.