Possibilistic networks are important and efficient tools for reasoning under uncertainty. This paper proposes a new graphical model for decision making under uncertainty based on possibilistic networks. In possibilistic decision problems under uncertainty, available knowledge is expressed by means of possibility distribution and preferences are encoded by means another possibility distribution representing the qualitative utility. The first part of the paper proposes a new graphical way to represent such problem, where agent's knowledge and preferences are encoded separately by two distinct possibilistic networks. The first one encodes agent's beliefs and the second one represents the qualitative utility. The second part of the paper proposes a new algorithm for computing optimistic optimal decisions based on merging these two possibilistic networks. In fact, the qualitative possibilistic decision is viewed as a data fusion problem of these two particular possibilistic networks. We show that the computation of optimal decisions comes down to compute a normalization degree of the junction tree associated with the graph representing the fusion of agent's beliefs and preferences. Keywords: Possibilistic decision theory, min-based possibilistic networks, junction trees. Decision making under uncertainty plays an important role in Artificial Intelligence (AI) applications. Several decision making tools have been developed to assist decision makers in their tasks: simulation techniques, dynamic programming, logical decision models and graphical decision models. This paper focuses on graphical decision models which provide efficient decision tools by allowing a compact representation of decision problems under uncertainty [1] . Most of decision graphical models are based on Influence Diagrams (ID) [2] for representing decision maker's beliefs and preferences on sequences of decisions to be made under uncertainty. The evaluation of influence diagrams ensures optimal decisions while maximizing the decision maker's expected utilities. In order to generate optimal decisions, there are two evaluation methods: direct methods [3] that need heavy computations and indirect methods [4] that require a graphical transformation of initial graph into a secondary structure which will be used in different computations. Besides, in many applications, it is easier to express uncertainty in a qualitative way by ranking different states of the world. Similarly, it is more easier to provide a preference relation between different consequences. In these situations, possibility theory [5] is an appropriate framework for representing uncertain knowledge and preferences. Indeed, a qualitative possibilistic decision model [6] allows a gradual expression of both agent's preferences and knowledge. Few works exist on decision making using possibilistic networks. Garcia and Sabbadin [7] have proposed a possibilistic counterpart of standard influence diagrams. Possibilistic Influence Diagrams (PID) offer a compact representation of problems dealing with decision making under uncertainty. The graphical part of possibilistic influence diagrams is exactly the same as the one of standard influence diagrams. Uncertainty is expressed by possibility degrees and preferences are considered as satisfaction degrees. Unlike probabilistic decision theory which is based on one expected utility criteria to evaluate optimal decisions, a qualitative possibilistic decision theory offers several qualitative utility criteria for decision approaches under uncertainty. Among these criteria, one can mention the pessimistic utility and the optimistic one proposed in [6] , the binary utility proposed by Giang and Shenoy [8], etc. In order to evaluate such possibilistic influence diagrams, two ways to accomplish this task, have been proposed in literature: (1) an indirect methods which transform a possibilistic influence diagram either into a decision tree [7] or into a qualitative possibilistic network [9] and (2) a direct methods [7] that use initial structures but require heavy computations in order to update possibility distribution tables. Our aim in this paper is to propose a new graphical model for representing decision making under uncertainty based on the use of possibilistic networks. When agent's knowledge and preferences are expressed in a qualitative way, we suggest to represent them by two distinct qualitative possibilistic networks. The first one encodes a joint possibility distribution representing available knowledge and 8th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT 2013)
In fact, the possibilistic network issued from the fusion phase REF ) is based on more compact representation of the qualitative utility.
A possibilistic graphical model for handling decision problems under uncertainty
EUSFLAT Conf.
Mathematics Computer Science