Implementing imperfect information in fuzzy databases

Information in real-world applications is often vague, imprecise and uncertain. Ignoring the inherent imperfect nature of real-world will undoubtedly introduce some deformation of human perception of real-world and may eliminate several substantial information, which may be very useful in several data-intensive applications. In database context, several fuzzy database models have been proposed. In these works, fuzziness is introduced at different levels. Common to all these proposals is the support of fuzziness at the attribute level. This paper proposes first a rich set of data types devoted to model the different kinds of imperfect information. The paper then proposes a formal approach to implement these data types. The proposed approach was implemented within a relational object database model but it is generic enough to be incorporated into other database models.ou

Uncertainty Analysis of the Adequacy Assessment Model of a Distributed Generation System

Due to the inherent aleatory uncertainties in renewable generators, the reliability/adequacy assessments of distributed generation (DG) systems have been particularly focused on the probabilistic modeling of random behaviors, given sufficient informative data. However, another type of uncertainty (epistemic uncertainty) must be accounted for in the modeling, due to incomplete knowledge of the phenomena and imprecise evaluation of the related characteristic parameters. In circumstances of few informative data, this type of uncertainty calls for alternative methods of representation, propagation, analysis and interpretation. In this study, we make a first attempt to identify, model, and jointly propagate aleatory and epistemic uncertainties in the context of DG systems modeling for adequacy assessment. Probability and possibility distributions are used to model the aleatory and epistemic uncertainties, respectively. Evidence theory is used to incorporate the two uncertainties under a single framework. Based on the plausibility and belief functions of evidence theory, the hybrid propagation approach is introduced. A demonstration is given on a DG system adapted from the IEEE 34 nodes distribution test feeder. Compared to the pure probabilistic approach, it is shown that the hybrid propagation is capable of explicitly expressing the imprecision in the knowledge on the DG parameters into the final adequacy values assessed. It also effectively captures the growth of uncertainties with higher DG penetration levels

The PITA System: Tabling and Answer Subsumption for Reasoning under Uncertainty

Many real world domains require the representation of a measure of uncertainty. The most common such representation is probability, and the combination of probability with logic programs has given rise to the field of Probabilistic Logic Programming (PLP), leading to languages such as the Independent Choice Logic, Logic Programs with Annotated Disjunctions (LPADs), Problog, PRISM and others. These languages share a similar distribution semantics, and methods have been devised to translate programs between these languages. The complexity of computing the probability of queries to these general PLP programs is very high due to the need to combine the probabilities of explanations that may not be exclusive. As one alternative, the PRISM system reduces the complexity of query answering by restricting the form of programs it can evaluate. As an entirely different alternative, Possibilistic Logic Programs adopt a simpler metric of uncertainty than probability. Each of these approaches -- general PLP, restricted PLP, and Possibilistic Logic Programming -- can be useful in different domains depending on the form of uncertainty to be represented, on the form of programs needed to model problems, and on the scale of the problems to be solved. In this paper, we show how the PITA system, which originally supported the general PLP language of LPADs, can also efficiently support restricted PLP and Possibilistic Logic Programs. PITA relies on tabling with answer subsumption and consists of a transformation along with an API for library functions that interface with answer subsumption

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

Possibilistic networks for uncertainty knowledge processing in student diagnosis

In this paper, a possibilistic network implementation for uncertain knowledge modeling of the diagnostic process is proposed as a means to achieve student diagnosis in intelligent tutoring system. This approach is proposed in the object oriented programming domain for diagnosis of students learning errors and misconception. In this expertise domain dependencies between data exist that are encoded in the structure of network. Also, it is available qualitative information about these data which are represented and interpreted with qualitative approach of possibility theory. The aim of student diagnosis system is to ensure an adapted support for the student and to sustain the student in personalized learning process and errors explanation

Possibilistic Conditional Preference Networks

International audienceThe paper discusses the use of product-based possibilistic networks for representing conditional preference statements on discrete variables. The approach uses non-instantiated possibility weights to define conditional preference tables. Moreover, additional information about the relative strengths of symbolic weights can be taken into account. It yields a partial preference order among possible choices corresponding to a symmetric form of Pareto ordering. In the case of Boolean variables, this partial ordering coincides with the inclusion between the sets of preference statements that are violated. Furthermore, this graphical model has two logical counterparts in terms of possibilistic logic and penalty logic. The flexibility and the representational power of the approach are stressed. Besides, algorithms for handling optimization and dominance queries are provided

Possibilistic networks parameter learning: Preliminary empirical comparison

International audienceLike Bayesian networks, possibilistic ones compactly encode joint uncertainty representations over a set of variables. Learning possibilistic networks from data in general and from imperfect or scarce data in particular, has not received enough attention. Indeed, only few works deal with learning the structure and the parameters of a possibilistic network from a dataset. This paper provides a preliminary comparative empirical evaluation of two approaches for learning the parameters of a possibilistic network from empirical data. The first method is a possibilistic approach while the second one first learns imprecise probability measures then transforms them into possibility distributions by means of probability-possibility transformations. The comparative evaluation focuses on learning belief networks on datasets with missing data and scarce datasets