Possibilistic Graphical Models

Abstract

Graphical modeling is an important method to efficiently represent and analyze uncertain information in knowledge-based systems. Its most prominent representatives are Bayesian networks and Markov networks for probabilistic reasoning, which have been well-known for over ten years now. However, they suffer from certain deficiencies, if imprecise information has to be taken into account. Therefore possibilistic graphical modeling has recently emerged as a promising new area of research. Possibilistic networks are a noteworthy alternative to probabilistic networks whenever it is necessary to model both uncertainty and imprecision. Imprecision, understood as set-valued data, has often to be considered in situations in which information is obtained from human observers or imprecise measuring instruments. In this paper we provide an overview on the state of the art of possibilistic networks w.r.t. to propagation and learning algorithms.

On the connection between probability boxes and possibility measures

“…As future lines of research, we point out the generalisation of a number of properties of possibility measures to p-boxes, such as the connection with fuzzy logic [1] or the representation by means of graphical structures [29], and the study of the connection of p-boxes with other uncertainty models, such as clouds and random sets.…”

Anytime propagation algorithm for min-based possibilistic graphs

“…This is due to the existence of two definitions of possibilistic conditioning : product-based and min-based conditioning [5,7,14]. When we use the product form of conditioning, we get a possibilistic network close to the probabilistic one sharing the same features and having the same theoretical and practical results [4]. However, this is not the case with min-based networks [10,12].…”

“…For more details see [4]. The principle of this propagation method is to transform the initial DAG into a junction tree and then to perform the propagation on this new graph.…”

Possibility Theory and Its Applications: Where Do We Stand?

“…Other applications of possibility theory can be found in fields such as data analysis [137,132,24], database querying [25], diagnosis [27,26], belief revision [18], argumentation [4,3], case-based reasoning [56,101], learning [120,121], and information merging [19] (taking advantage of the bipolar representation setting which distinguishes between positive information of the form ∆(φ) ≥ α and negative information expressing impossibility under the form N (φ) ≥ α ⇔ 1 − Π(¬φ) ≥ α [20]). …”