Boutheina Ben Yaghlane

Belief function independence

In this paper, we study the notion of marginal independence between two sets of variables when uncertainty is expressed by belief functions as understood in the context of the transferable belief model (TBM). We define the concepts of non-interactivity and irrelevance, that are not equivalent. Doxastic independence for belief functions is defined as irrelevance and irrelevance preservation under Dempsters rule of combination. We prove that doxastic independence and non-interactivity are equivalent.

Belief function independence: II. The conditional case

Abstract In the companion paper [Int. J. Approx. Reasoning 29 (1) (2002) 47], we have emphasized the distinction between non-interactivity and doxastic independence in the context of the transferable belief model. The first corresponds to decomposition of the belief function, whereas the second is defined as irrelevance preserved under Dempster’s rule of combination. We had shown that the two concepts are equivalent in the marginal case. We proceed here with the conditional case. We show how the definitions generalize themselves, and that we still have the equivalence between conditional non-interactivity and conditional doxastic independence.

Inference in directed evidential networks based on the transferable belief model

Inference algorithms in directed evidential networks (DEVN) obtain their efficiency by making use of the represented independencies between variables in the model. This can be done using the disjunctive rule of combination (DRC) and the generalized Bayesian theorem (GBT), both proposed by Smets [Ph. Smets, Belief functions: the disjunctive rule of combination and the generalized Bayesian theorem, International Journal of Approximate Reasoning 9 (1993) 1-35]. These rules make possible the use of conditional belief functions for reasoning in directed evidential networks, avoiding the computations of joint belief function on the product space. In this paper, new algorithms based on these two rules are proposed for the propagation of belief functions in singly and multiply directed evidential networks.

Directed evidential networks with conditional belief functions

The main question addressed in this paper is how to represent belief functions independencies by graphical model. Directed evidential networks (DEVNs) with conditional belief functions are then proposed. These networks are directed acyclic graphs (DAGs) similar to Bayesian networks but instead of using probability functions, we use belief functions. Directed evidential network with conditional belief functions has the advantage of providing an appropriate representation of the knowledge that can be produced as conditional relationships.

Independence concepts for belief functions

In this paper, we try to study the independence concept for belief functions theory, as applied to one interpretation of this theory called the transferable belief model (TBM). In this context, two new results are given in this paper : first, the concept of belief function independence has different intuitive meaning which are non-interactivity, irrelevance and doxastic independence, second, the concepts of non-interactivity and independence are identical under a new property called irrelevance preservation under Dempsters rule of combination.

Comparing evidential graphical models for imprecise reliability

This paper presents a comparison of two evidential networks applied to the reliability study of complex systems with uncertain knowledge. This comparison is based on different aspects. In particular, the original structure, the graphical structures for the inference, the messagepassing schemes, the storage efficiencies, the computational efficiencies and the exactness of the results are studied.

Classification of Message Spreading in a Heterogeneous Social Network

Nowadays, social networks such as Twitter, Facebook and LinkedIn become increasingly popular. In fact, they introduced new habits, new ways of communication and they collect every day several information that have different sources. Most existing research works focus on the analysis of homogeneous social networks, i.e. we have a single type of node and link in the network. However, in the real world, social networks offer several types of nodes and links. Hence, with a view to preserve as much information as possible, it is important to consider social networks as heterogeneous and uncertain. The goal of our paper is to classify the social message based on its spreading in the network and the theory of belief functions. The proposed classifier interprets the spread of messages on the network, crossed paths and types of links. We tested our classifier on a real word network that we collected from Twitter, and our experiments show the performance of our belief classifier.

Incremental Maintenance of Frequent Itemsets in Evidential Databases

In the last years, the problem of Frequent Itemset Mining (FIM) from imperfect databases has been sufficiently tackled to handle many kinds of data imperfection. However, frequent itemsets discovered from databases describe only the current state of the data. In other words, when data are updated, the frequent itemsets could no longer reflect the data, i.e., the data updates could invalidate some frequent itemsets and vice versa, some infrequent ones could become valid. In this paper, we try to resolve the problem of Incremental Maintenance of Frequent Itemsets (IMFI) in the context of evidential data. We introduce a new maintenance method whose experimentations show efficiency compared to classic methods.

An Intelligent Flexible Querying Approach for Temporal Databases

Time is a crucial dimension in many application domains. This paper proposes an intelligent approach to querying temporal databases using fuzzy temporal criteria. Relying on fuzzy temporal Allen relations, a particular class of criteria are studied. First, a query language that supports flexible temporal query is discussed. Then, the architecture and the interface of the system developed are explicitly described. To evaluate intelligently temporal queries, our system is endowed with some reasoning capabilities.

Updating Directed Belief Networks

This paper deals with the knowledge representation and reasoning in directed belief networks. These networks are similar to those defined by Pearl (causal networks), but instead of probability functions, we use belief functions. Based on the work of Cano et al. [1992] in which they have presented an axiomatic framework for propagating valuations in directed acyclic graph using Shafer-Shenoys axioms of valuation-based system (VBS), we show how the Dempster-Shafer theory fits in this framework. Then, we present a propagation algorithm in directed belief networks that is extended from Pearls algorithm, but it is expressed in terms of belief functions.