Reasoning with Uncertain Inputs in Possibilistic Networks

2009

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 ∆. This paper first proposes the use of guaranteed possibility measures to define a so-called ∆-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 ∆-based knowledge bases. Then we analyze propagation algorithms in ∆based 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 ∆-based possibilistic networks into standard min-based possibilistic networks.

International Journal of Approximate Reasoning, 2002

Possibilistic logic bases and possibilistic graphs are two different frameworks of interest for representing knowledge. The former ranks the pieces of knowledge (expressed by logical formulas) according to their level of certainty, while the latter exhibits relationships between variables. The two types of representation are semantically equivalent when they lead to the same possibility distribution (which rank-orders the possible interpretations). A possibility distribution can be decomposed using a chain rule which may be based on two different kinds of conditioning that exist in possibility theory (one based on the product in a numerical setting, one based on the minimum operation in a qualitative setting). These two types of conditioning induce two kinds of possibilistic graphs. This article deals with the links between the logical and the graphical frameworks in both numerical and quantitative settings. In both cases, a translation of these graphs into possibilistic bases is provided. The converse translation from a possibilistic knowledge base into a min-based graph is also described.

2013 IEEE 25th International Conference on Tools with Artificial Intelligence, 2013

Possibilistic networks are belief graphical models based on possibility theory. This paper deals with a special kind of possibilistic networks called three-valued possibilistic networks where only three possibility levels are used to encode uncertain information. The paper analyzes different semantics of three-valued networks and provides precise relationships relating the different semantics. More precisely, the paper analyzes two categories of methods for deriving a three-valued joint possibility distribution from a three-valued possibilistic network. The first category of methods is based on viewing the three-valued possibilistic network as a family of compatible networks and defining combination rules for deriving the threevalued joint distribution. The second category is based on three-valued chain rules using three-valued operators inspired from some three-valued logics. Finally, the paper shows that the inference using the well-known Junction tree algorithm cannot be extended to all the three-valued chain rules.

Possibilistic networks are belief graphical models based on possibility theory. This paper deals with a special kind of possibilistic networks called three-valued possibilistic networks where only three possibility levels are used to encode uncertain information. The paper analyzes different semantics of three-valued networks and provides precise relationships relating the different semantics. More precisely, the paper analyzes two categories of methods for deriving a three-valued joint possibility distribution from a three-valued possibilistic network. The first category of methods is based on viewing the three-valued possibilistic network as a family of compatible networks and defining combination rules for deriving the threevalued joint distribution. The second category is based on three-valued chain rules using three-valued operators inspired from some three-valued logics. Finally, the paper shows that the inference using the well-known Junction tree algorithm cannot be extended to all the three-valued chain rules.

2020

Many real world problems and applications require to exploit incomplete, complex and uncertain information. Belief graphical models encompass a wide range of graphical formalisms for representing and reasoning with uncertain and complex information. They generally involve a graphical component which can be directed or undirected and a numerical one depending on the considered uncertainty setting. The graphical component encodes a set of independence statements while the numerical one quantifies the uncertainty regarding variables. The main use of belief graphical models is knowledge representation, reasoning and decision making for multivariate problems. Belief graphical models can be built either by eliciting the uncertain knowledge of an expert or automatically learnt from data using machine learning techniques. Many types of inference algorithms exist and many platforms are now available allowing modeling and reasoning with belief graphical models in many application areas such a...

Possibilistic logic bases and possibilistic graphs are two different frameworks of interest for representing knowledge. The former stratifies the pieces of knowledge (expressed by logical formulas) accor?i � g to their level of certainty, while the latter exhibits relationships between variables. The two types of representations are semantically equivalent when they lead to the same possibility distribution (which rank orders the possible interpretations). A possibility distribution can be decomposed using a chain rule which may be based on two different kinds of conditioning which exist in possibility theory (one based on product in a numerical setting, one based on minimum operation in a qualitative setting). These two types of conditioning induce two ki n_ ds of possibilistic graphs. In both cases, a translatiOn of these graphs into possibilistic bases is provided. The converse translation from a possibilistic knowledge base into a min-based graph is also described.

Proceedings of the 8th conference of the European Society for Fuzzy Logic and Technology, 2013

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.

1993

Abstract In this paper some initial work towards a new approach to qualitative reasoning under uncertainty is presented. This method is not only applicable to qualitative probabilistic reasoning, as is the case with other methods, but also allows the qualitative propagation within networks of values based upon possibility theory and Dempster-Shafer evidence theory. The method is applied to two simple networks from which a large class of directed graphs may be constructed.

Lecture Notes in Computer Science, 2012

Directed evidential graphical models are important tools for handling uncertain information in the framework of evidence theory. They obtain their efficiency by compactly representing (in)dependencies between variables in the network and efficiently reasoning under uncertainty. This paper presents a new dynamic evidential network for representing uncertainty and managing temporal changes in data. This proposed model offers an alternative framework for dynamic probabilistic and dynamic possibilistic networks. A complexity study of representation and reasoning in the proposed model is also presented in this paper.

1990

We describe how to combine probabilistic logic and Bayesian networks to obtain a new framework (\Bayesian logic") for dealing with uncertainty and causal relationships in an expert system. Probabilistic logic, invented by Boole, is a technique for drawing inferences from uncertain propositions for which there are no independence assumptions. A Bayesian network is a \belief net" that can represent complex conditional independence assumptions. We show how to solve inference problems in Bayesian logic by applying Benders decomposition to a nonlinear programming formulation. We also show that the number of constraints grows only linearly with the problem size for a large class of networks.