Qualitative possibilistic influence diagrams based on qualitative possibilistic utilities

This paper proposes a new approach for decision making under uncertainty based on influence diagrams and possibility theory. The so-called qualitative possibilistic influence diagrams extend standard influence diagrams in order to avoid difficulties attached to the specification of both probability distributions relative to chance nodes and utilities relative to value nodes. In fact, generally, it is easier for experts to quantify dependencies between chance nodes qualitatively via possibility distributions and to provide a preferential relation between different consequences. In such a case, the possibility theory offers a suitable modeling framework. Different combinations of the quantification between chance and utility nodes offer several kinds of possibilistic influence diagrams. This paper focuses on qualitative ones and proposes an indirect evaluation method based on their transformation into possibilistic networks. The proposed approach is implemented via a possibilistic influence diagram toolbox (PIDT).