Binary Naive Possibilistic Classifiers: Handling Uncertain Inputs Salem Benferhat, ∗ Karim Tabia † CRIL-CNRS UMR8188, Universit ´ e d’Artois, Rue Jean Souvraz SP 18 62307 Lens, Cedex, France Possibilistic networks are graphical models particularly suitable for representing and reasoning with uncertain and incomplete information. According to the underlying interpretation of possi- bilistic scales, possibilistic networks are either quantitative (using product-based conditioning) or qualitative (using min-based conditioning). Among the multiple tasks, possibilitic models can be used for, classification is a very important one. In this paper, we address the problem of handling uncertain inputs in binary possibilistic-based classification. More precisely, we propose an effi- cient algorithm for revising possibility distributions encoded by a naive possibilistic network. This algorithm is suitable for binary classification with uncertain inputs since it allows classification in polynomial time using several efficient transformations of initial naive possibilistic networks. C  2009 Wiley Periodicals, Inc. 1. INTRODUCTION Graphical models 1−6 are powerful tools for representing and reasoning un- der uncertainty conditions. They are suitable for handling uncertain, imprecise, and incomplete data. Like probabilistic networks, possibilistic ones 7,8 are graphical models but use possibility theory to handle imprecise and incomplete knowledge. They factor a global joint possibility distribution into a set of local possibility distri- butions that can be combined according to the network structure. This factorization allows interesting inference capabilities. Handling imprecise and incomplete (miss- ing) data are main advantages of possibilistic models. In fact, in many real-world problems, it is needed to handle and reason with missing data. For instance, intru- sion detection systems (IDSs) 9,10 classify audit events (system log records, network packets/connections, etc.) into normal activities or attacks. However, it is required to detect attacks in real-time, which implies detecting attacks with the minimum This is a revised and a long extended version of a conference paper “An efficient algorithm for naive possibilistic classifiers with uncertain inputs” by the authors appeared in SUM’08 Conference (The Second International Conference on Scalable Uncertainty Management). ∗ Author to whom all correspondence should be addressed: e-mail: benfer benferhat@ cril.uniw-artois.fr. † e-mail: tabia@cril.univ-artois.fr. INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, VOL. 24, 1203–1229 (2009) C  2009 Wiley Periodicals, Inc. Published online in Wiley InterScience (www.interscience.wiley.com). • DOI 10.1002/int.20381