Lukasiewicz-based merging possibilistic networks. (English) Zbl 1433.68457

Summary: Possibility theory provides a good framework for dealing with merging problems when information is pervaded with uncertainty and inconsistency. Many merging operators in possibility theory have been proposed. This paper develops a new approach to merging uncertain information modeled by possibilistic networks. In this approach we restrict our attention to show how a “triangular norm” establishes a lower bound on the degree to which an assessment is true when it is obtained by a set of initial hypothesis represented by a joint possibility distribution. This operator is characterized by its high effect of reinforcement. A strongly conjunctive operator is suitable to merge networks that are not involved in conflict, especially those supported by both sources. In this paper, the Lukasiewicz t-norm is first applied to a set of possibility measures to combine networks having the same and different graphical structures. We then present a method to merge possibilistic networks dealing with cycles.


68T37 Reasoning under uncertainty in the context of artificial intelligence
Full Text: DOI


[1] Baral, C.; Kraus, S.; Minker, J.; Subrahmanian, V. S., Combining knowledge bases consisting in first order theories, Comput. Intell., 8, 45-71, (1992)
[2] Barra, V.; Boire, J. Y., Quantification of brain tissue volumes using mr/mr fusion, (Proceedings of the World Congress on Medical Physics and Biomedical Engineering, (2000)), 1404-1410
[3] Ben Amor, N.; Benferhat, S.; Mellouli, K., A two steps algorithm for MIN-based possibilistic causal networks, (Proceedings of 6th European Conference on Symbolic and Quantitative Approaches to Reasoning With Uncertainty (ECSQARU’01), (2001)), 266-277 · Zbl 1001.68532
[4] Benferhat, S.; Dubois, D.; Kaci, S.; Prade, H., Possibilistic merging and distance-based fusion of propositional information, Ann. Math. Artif. Intell., 34, 217-252, (2002) · Zbl 1001.68032
[5] Benferhat, S.; Dubois, D.; Kaci, S.; Prade, H., Possibilistic merging and distance-based fusion of propositional information, Ann. Math. Artif. Intell., 34, 217-252, (2002) · Zbl 1001.68032
[6] Benferhat, S.; Dubois, D.; Prade, H., From semantic to syntactic approaches to information combination in possibilistic logic, (Aggregation and Fusion of Imperfect Information, (1997), Physica-Verlag), 141-151 · Zbl 0898.68079
[7] Benferhat, S.; Smaoui, S., Hybrid possibilistic networks, Int. J. Approx. Reason., 44, 224-243, (2007) · Zbl 1116.68094
[8] Benferhat, S.; Titouna, F., Aggregating quantitative possibilistic networks, (Proceedings of the 9th International Florida Artificial Intelligence Research (Flairs’06), (2006)), 800-805
[9] Benferhat, S.; Titouna, F., Fusion and normalization of quantitative networks, Appl. Intell., 31, 135-160, (2009)
[10] Benferhat, S.; Titouna, F., On the fusion of probabilistic networks, (24th International Conference on Industrial Engineering and Other Applications of Applied Intelligent Systems, IEA/AIE 2011, (2011)), 49-58
[11] Borgelt, C.; Gebhardt, J.; Kruse, R., Possibilistic graphical models, (Proceedings of International School for the Synthesis of Expert Knowledge (ISSEK’98), (1998)), 51-68 · Zbl 0979.68106
[12] Butz, C. J.; Chen, J.; Konkel, K.; Lingras, P., A comparative study of variable elimination and arc reversal in Bayesian network inference, (Proceedings of the Twenty-Second International FLAIRS Conference, (2009))
[13] Calvo, T.; Mayor, G.; Mesiar, R., Aggregation operators: new trends and applications, (Studies in Fuzziness and Soft Computing, vol. 97, (2002), Physica-Verlag Heidelberg) · Zbl 0983.00020
[14] Cholvy, L., Reasoning about merging information, (Handbook of Defeasible Reasoning and Uncertainty Management Systems, vol. 3, (1998)), 233-263 · Zbl 0928.03017
[15] Damarla, T.; Mehmood, A.; Sabatier, J., Detection of people and animals using non-imaging sensors, (Proceedings of the 14th International Conference on Information Fusion, (2011)), 1-6
[16] De Cooman, G., Possibility theory - part I: measure and integral theoretics groundwork; part II: conditional possibility; part III: possibilistic independence, Int. J. Gen. Syst., 25, 291-371, (1997)
[17] De Mouzon, O.; El Faouzi, N.; Nowtny, B.; Morin, J. M.; Chung, E., Data fusion for traffic and safety indicators, (The Intelligent Roads Perspectives. ITS World Congress, (2006))
[18] de Oude, P.; Ottens, B.; Pavlin, G., Information fusion with distributed probabilistic networks, (Artificial Intelligence and Applications, (2005)), 195-201
[19] Dubois, D., Possibility theory and statistical reasoning, Comput. Stat. Data Anal., 51, 47-69, (2006) · Zbl 1157.62309
[20] Dubois, D.; Prade, H., Possibility theory: an approach to computerized processing of uncertainty, (1988), Plenum Press New York
[21] Dubois, D.; Prade, H., Possibility theory: qualitative and quantitative aspects, (Handbook of Defeasible Reasoning and Uncertainty Managment Systems, vol. 1, (1998)), 169-226 · Zbl 0924.68182
[22] Dubois, D.; Prade, H., Possibility theory and its applications: where do we stand?, Eusflat, (2011)
[23] Fahim, M.; Siddiqi, M. H.; Sungyoung, L.; Young-Koo, L., A multi-strategy Bayesian model for sensor fusion in smart environments, (5th International Conference on Computer Sciences and Convergence Information Technology (ICCIT), (2010)), 52-57
[24] Fonck, P., Propagating uncertainty in a directed acyclic graph, (Proceedings of International Conference on Information Processing of Uncertainty in Knowledge Based Systems (IPMU’92), (1992)), 17-20
[25] Garci, J.; Guerrero, J. L.; Luis, A.; Molina, J. M., Robust sensor fusion in real maritime surveillance scenarios, (13th Conference on Information Fusion (FUSION), (2010)), 1-8
[26] Hilletofth, P.; Ujvari, S.; Johansson, R., Agent-based simulation fusion for improved decision making for service operations, (12th International Conference on Information Fusion, FUSION ’09, (2009)), 998-1005
[27] Jensen, F. V., Introduction to Bayesian networks, (1996), UCL Press, University College London
[28] JoseDel, S.; Moral, S., Qualitative combination of Bayesian networks, Int. J. Intell. Syst., 18, 237-249, (2003) · Zbl 1028.68165
[29] Klir, G.; Yan, B., Fuzzy sets and fuzzy logics: theory and applications, (1995), Book of Fuzzy Sets, Uncertainty, and Information
[30] Koller, D.; Friedman, N., Probabilistic graphical models: principles and techniques, (2009), MIT Press
[31] Konieczny, S.; Perez, R., On the logic of merging, (Proceedings of the 6th International Conference on Principles of Knowledge Representation and Reasoning (KR’98), (1998)), 488-498
[32] Lin, J., Integration of weighted knowledge bases, Artif. Intell., 83, 363-378, (1996)
[33] Lin, J.; Mendelzon, A. O., Merging databases under constraints, Int. J. Coop. Inf. Syst., 7, 55-76, (1998)
[34] Maaref, H.; Oussalah, M.; Barret, C., Fusion de données capteurs en vue de la localisation absolue d’un robot mobile par une méthode basée sur la théorie des possibilités. comparaison avec le filtre de Kalman, Trait. Signal, 16, 345-359, (1999) · Zbl 1002.93545
[35] Matzkevich, I.; Abramson, B., The topological fusion of Bayes nets, (Proceedings of the 8th Conference on Uncertainty in Artificial Intelligence (UAI’92), Stanford, CA, USA, (1992)), 191-198
[36] Matzkevich, I.; Abramson, B., Some complexity considerations in the combination of belief networks, (Proceedings of the 9th Conference on Uncertainty in Artificial Intelligence (UAI’93), San Fransisco, CA, (1993)), 152-158
[37] Nguyen, H. T.; Kreinovich, V.; Wojciechowskic, P., Strict Archimedean t-norms and t-conorms as universal approximators, Int. J. Approx. Reason., 18, 239-249, (1998) · Zbl 0955.68108
[38] Pearl, J., Probabilistic reasoning in intelligent systems: networks of plausible inference, (1988), Morgan Kaufmann San Fransisco (California)
[39] Raptis, S. N.; Tzafestas, S. G., Object hypothesis support in the context of knowledge based fuzzy/possibilistic fusion of image descriptions, (3rd International Conference on Information Fusion, vol. 1, (2000)), 3-8
[40] Soleimanpour, S.; Ghidary, S. S.; Meshgi, K., Sensor fusion in robot localization using ds-evidence theory with conflict detection using Mahalanobis distance, (7th IEEE International Conference on Cybernetic Intelligent Systems, (2008)), 1-6
[41] Sossai, C.; Chemello, G., Coherent functions in autonomous systems, J. Mult.-Valued Log. Soft Comput., 9, 171-194, (2002)
[42] Zadeh, L., Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets Syst., 1, 13-28, (1978) · Zbl 0377.04002
[43] Zhou, Y., Intelligent processing research for target fusion recognition system based on multi-agents, (International Conference on Computational Intelligence and Software Engineering (CiSE), (2010)), 1-4
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.