Properties Analysis of Inconsistency-based Possibilistic Similarity Measures

International audienceThis paper deals with the problem of measuring the similarity degree between two normalized possibility distributions encoding preferences or uncertain knowledge. Many exist- ing de nitions of possibilistic similarity indexes aggregate pairwise distances between each situation in possibility distributions. This paper goes one step further, and discusses de nitions of possibilistic similarity measures that include inconsistency degrees between possibility distribu- tions. In particular, we propose a postulate-based analysis of similarity indexes which extends the basic ones that have been recently proposed in a literature

How to preserve the conflict as an alarm in the combination of belief functions?

International audienceIn the belief function framework, a unique function is induced from the use of a combination rule so allowing to synthesize all the knowledge of the initial belief functions. When information sources are reliable and independent, the conjunctive rule of combination, proposed by Smets, may be used. This rule is equivalent to the Dempster rule without the normalization process. The conjunctive combination provides interesting properties, as the commutativity and the associativity. However, it is characterized by having the empty set, called also the conflict, as an absorbing element. So, when we apply a significant number of conjunctive combinations, the mass assigned to the conflict tends to 1 which makes impossible returning the distinction between the problem arisen during the fusion and the effect due to the absorption power of the empty set. The objective of this paper is then to define a formalism preserving the initial role of the conflict as an alarm signal announcing that there is a kind of disagreement between sources. More exactly, that allows to preserve some conflict, after the fusion by keeping only the part of conflict reflecting the opposition between the belief functions. This approach is based on dissimilarity measures and on a normalization process between belief functions. Our proposed formalism is tested and compared with the conjunctive rule of combination on synthetic belief functions

A Pre-Pruning Method in Belief Decision Trees

The belief decision tree approach is a decision tree method adapted in order to handle uncertainty about the actual class of the objects in the training set. The uncertainty is represented by the Transferable Belief Model (TBM). We present two methods to build the tree. In order t

Classification with Belief Decision Trees

Abstract. Decision trees are considered as an efficient technique to express classification knowledge and to use it. However, their most standard algorithms do not deal with uncertainty, especially the cognitive one. In this paper, we develop a method to adapt the decision tree technique to the case where the object’s classes are not exactly known, and where the uncertainty about the class ’ value is represented by a belief function. The adaptation concerns both the construction of the tree and its use to classify new objects characterized by uncertain attribute values.

Modeling Qualitative Assessments under the Belief Function Framework

International audienceThis paper investigates the problem of preference modeling under the belief function framework. In this work, we introduce a new model that is able to generate quantitative information from qualitative assessments. Therefore, we suggest to represent the decision maker preferences in different levels where the indifference, strict preference, weak preference and incompleteness relations are considered. Introducing the weak preference relation separates the preference area from the indifference one by inserting an intermediate zone