Decision trees using the belief function theory Zied Elouedi LAROID, Institut Supérieur de Gestion de Tunis, 41 rue de la liberté, Le Bardo 2000, Tunisie. zied.elouedi@isg.rnu.tn Khaled Mellouli LAROID, Institut Supérieur de Gestion de Tunis, 41 rue de la liberté, Le Bardo 2000 Tunisie. khaled.mellouli@ihec.rnu.tn Philippe Smets IRIDIA, Université Libre de Bruxelles, 50 av., F.Roosvelt, CP19416, 1050 Bruxelles, Belgique. psmets@ulb.ac.be Abstract This paper presents an algorithm for building decision trees in an uncertain environment. Our algorithm will use the theory of belief functions in order to represent the uncertainty about the parameters of the classification problem. Our method will be concerned with both the decision tree building task and the classification task. Keywords: Belief function theory, Decision tree, Classification. 1 Introduction Decision trees are one of the most widely used classification techniques especially in artificial intelligence. Their popularity is basically due to their ability to express knowledge in a formalism that is often easier to interpret by experts and even by ordinary users. Despite their accuracy when precise and certain data are available, the classical versions of decision tree algorithms are not able to handle the uncertainty in classification problems. Hence, their results are categorical and do not convey the uncertainty that may occur in the attribute values or in the case class. To overcome this limitation, Quinlan has developed probabilistic decision trees [5] where his major objective is to deal with examples characterized by missing or imprecise attribute values. However within his framework, only statistical uncertainty induced by information arisen from random behavior, is taken into account. In this paper, we present a classification method based on the decision tree approach having the objective to cope with the uncertainty that may occur in a classification problem and which is basically related to human thinking, reasoning and cognition. Our algorithm will use the belief function theory as understood in the transferable belief model (TBM) [11, 12] and which seems offering a convenient framework thanks to its ability to represent epistemological uncertainty. Moreover, the TBM allows experts to express partial beliefs in a much more flexible way than probability functions do. It also allows to handle partial or even total ignorance concerning classification parameters. In addition to these advantages, it offers appropriate tools to combine several pieces of evidence. This paper is composed as follows: we start by introducing decision trees, then we give an overview of the basic concepts of the belief function theory. In the main part of the paper, we present our decision tree algorithm based on the evidence theory. The two major phases will be detailed: the building of a decision tree and the classification task. Our algorithm will be illustrated by an example in order to understand its real unfolding. 2 Decision trees Decision trees present a system using a top-down strategy based on the divide and conquer approach where the major aim is to partition the tree in many subsets mutually exclusive. Each subset of the partition represents a classification sub problem.