New Graphical Model for Computing Optimistic Decisions in Possibility Theory Framework

This paper first proposes a new graphical model for decision making under uncertainty based on min-based possibilistic networks. A decision problem under uncertainty is described by means of two distinct min-based possibilistic networks: the first one expresses agent's knowledge while the second one encodes agent's preferences representing a qualitative utility. We then propose an efficient algorithm for computing optimistic optimal decisions using our new model for representing possibilistic decision making under uncertainty. We show that the computation of optimal decisions comes down to compute a normalization degree of the junction tree associated with the graph resulting from the fusion of agent's beliefs and preferences. This paper also proposes an alternative way for computing optimal optimistic decisions. The idea is to transform the two possibilistic networks into two equivalent possibilistic logic knowledge bases, one representing agent's knowledge and the other represents agent's preferences. We show that computing an optimal optimistic decision comes down to compute the inconsistency degree of the union of the two possibilistic bases augmented with a given decision

A Relationship Between the Probabilistic and the Possibilistic Logic

This paper points out that there exists a relationship between the principle of Maximal Entropy (ME) in probability theory and the principle of minimal Specificity (mS) in possibility theory via consistent transformations on sets of probability and possibility distributions. By using these transformations, the paper investigates the possibilities to apply methods of probabilistic logic for possibility knowledge bases and conversely, reasoning methods of possibilistic logic for probability knowledge bases