zbMATH — the first resource for mathematics

Binary naive possibilistic classifiers: handling uncertain inputs. (English) Zbl 1192.68667
Summary: Possibilistic networks are graphical models particularly suitable for representing and reasoning with uncertain and incomplete information. According to the underlying interpretation of possibilistic 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 efficient 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.

68T30 Knowledge representation
68T10 Pattern recognition, speech recognition
Full Text: DOI
[1] Darwiche, Modeling and reasoning with Bayesian networks (2009) · Zbl 1231.68003 · doi:10.1017/CBO9780511811357
[2] Borgelt, Graphical models: Methods for data analysis and mining (2002) · Zbl 1017.62002
[3] Jensen, An introduction to Bayesian networks (1996)
[4] Pearl, Probabilistic reasoning in intelligent systems: Networks of plausible inference (1988) · Zbl 0746.68089
[5] JordanMI. editor. Learning in graphical models. Cambridge, MA: MIT Press; 1999.
[6] KassimA, MittalA. editor. Bayesian network technologies: Applications and graphical models. Hershey, PA: IGI Publishing; 2007.
[7] Benferhat, Hybrid possibilistic networks, Int J Approx Reason 44 (3) pp 224– (2007) · Zbl 1116.68094
[8] Kruse, Possibilistic graphical models. In: Proc Int School for the Synthesis of Expert Knowledge (ISSEK’98) pp 51– (1998) · Zbl 0979.68106
[9] Axelsson S. Intrusion detection systems: A survey and taxonomy. Technical Report 99-15, Chalmers University, March 2000.
[10] Patcha, An overview of anomaly detection techniques: Existing solutions and latest technological trends, Comput Netw 51 (12) pp 3448– (2007)
[11] de Cooman, Updating beliefs with incomplete observations, Artif Intell 159 (1-2) pp 75– (2004) · Zbl 1086.68599
[12] Williams, On classification with incomplete data, IEEE Trans Pattern Anal Machine Intell 29 (3) pp 427– (2007)
[13] Borgelt C, Gebhardt J. A naive bayes style possibilistic classifier. In: Proc 7th European Congress on Intelligent Techniques and Soft Computing (EUFIT’99), Aachen, Germany; 1999.
[14] Elouedi Z, Haouari B, Ben Amor N, Mellouli K. Naive possibilistic network classifier. In: Proc 13th Congress of International Association for Fuzzy-Set Management and Economy, SIGEF’06; 2006. · Zbl 1192.68519
[15] Jeffrey, The logic of decision (1965)
[16] Zadeh, Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets Syst 1 (1) pp 3– (1978) · Zbl 0377.04002
[17] Spohn, Causation in decision, belief change, and statistics II pp 105– (1988) · doi:10.1007/978-94-009-2865-7_6
[18] Hisdal, Conditional possibilities independence and non interaction, Fuzzy Sets Syst 1 (4) pp 283– (1978) · Zbl 0393.94050
[19] Bouchon-Meunier, Independence and possibilistic conditioning, Annals Math. Artif. Intell 35 (1-4) pp 107– (2002) · Zbl 1004.60001
[20] Huete JF, De Campos LM, Moral S. Possibilistic independence. In: Proc EUFIT 95; 1995. Vol 1, pp 69-73.
[21] Prade, Possibility theory: An approach to computerized processing of uncertainty (1988) · Zbl 0703.68004
[22] Fonck, A comparative study of possibilistic conditional independence and lack of interaction, Int J Approx Reason 16 (2) pp 149– (1997) · Zbl 0939.68115
[23] Ben Amor N, Benferhat S, Mellouli K. A two-steps algorithm for min-based possibilistic causal networks. In: ECSQARU; 2001. pp 266-277. · Zbl 1001.68532
[24] Dubois D, Prade H. An overview of ordinal and numerical approaches to causal diagnostic problem solving. 2000. pp 231-280. · Zbl 0971.68149
[25] Roubos, Learning fuzzy classification rules from labeled data, Inf Sci Inf Comput Sci 150 (1-2) pp 77– (2003)
[26] Dubois, A synthetic view of belief revision with uncertain inputs in the framework of possibility theory, Int J Approx Reason 17 (2-3) pp 295– (1997) · Zbl 0935.03026
[27] Dubois, Possibility theory and data fusion in poorly informed environments, Control Eng Pract 2 (5) pp 811– (1994)
[28] Benferhat, Aggregation and fusion of imperfect information. Physica-Verlag 12 pp 141– (1988) · doi:10.1007/978-3-7908-1889-5_9
[29] Dubois, Data fusion in robotics and machine intelligence pp 481– (1992)
[30] Benczúr A, Bíró I, Csalogány K, Sarlós T. Web spam detection via commercial intent analysis. In: AIRWeb ’07: Proc 3rd International Workshop on Adversarial Information Retrieval on the Web. New York, USA; 2007. pp 89-92.
[31] van Rijsbergen CJ. Getting into information retrieval. In: Lectures on information retrieval. 2001. pp 1-20.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.