Skip to main content

Possibilistic Graphical Models for Uncertainty Modeling

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9858))

Abstract

Belief graphical models, especially the probabilistic ones, have now a long history and they are successfully used in a wide range of tasks and applications. Thanks to independence relations, they allow a compact representation of complex and uncertain information and they greatly simplify the critical tasks of information elicitation, representation and inference. Many alternative belief graphical models have been proposed to overcome the limits of probability theory and take advantage of the decomposability property. This paper surveys most of the works dealing with belief graphical models based on possibility theory, an alternative uncertainty theory particularly suited for dealing with incomplete and qualitative uncertain knowledge.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Ajroud, A., Benferhat, S.: An approximate algorithm for min-based possibilistic networks. Int. J. Intell. Syst. 29, 615–633 (2014)

    Article  Google Scholar 

  2. Amor, N.B., Benferhat, S.: Graphoid properties of qualitative possibilistic independence relations. Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 13(1), 59–96 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  3. Amor, N.B., Benferhat, S., Dubois, D., Geffner, H., Prade, H.: Independence in qualitative uncertainty frameworks. In: KR 2000, Principles of Knowledge Representation and Reasoning Proceedings of the Seventh International Conference, Breckenridge, Colorado, USA, 11–15 April 2000, pp. 235–246 (2000)

    Google Scholar 

  4. Amor, N.B., Dubois, D., Gouider, H., Prade, H.: Possibilistic conditional preference networks. In: Destercke, S., Denoeux, T. (eds.) ECSQARU 2015. LNCS, vol. 9161, pp. 36–46. Springer, Heidelberg (2015)

    Chapter  Google Scholar 

  5. Ayachi, R., Amor, N.B., Benferhat, S.: Inference using compiled min-based possibilistic causal networks in the presence of interventions. Fuzzy Sets Syst. 239, 104–136 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  6. Ayed, R., Bounhas, I., Elayeb, B., Evrard, F., Bellamine-Bensaoud, N.: A possibilistic approach for the automatic morphological disambiguation of Arabic texts. In: International Conference on Software Engineering, Artificial Intelligence, Networking and Parallel/Distributed Computing, Kyoto, Japan. IEEE Computer Society (2012)

    Google Scholar 

  7. Ben Amor, N., Benferhat, S., Mellouli, K.: Anytime propagation algorithm for min-based possibilistic graphs. Soft Comput. 8, 150–161 (2003)

    Article  MATH  Google Scholar 

  8. Benferhat, S., Delobelle, J., Tabia, K.: Three-valued possibilistic networks: semantics & inference. In: 2013 IEEE 25th International Conference on Tools with Artificial Intelligence, Herndon, VA, USA, 4–6 November 2013, pp. 38–45 (2013)

    Google Scholar 

  9. Benferhat, S., Dubois, D., Garcia, L., Prade, H.: On the transformation between possibilistic logic bases and possibilistic causal networks. Int. J. Approximate Reasoning 29(2), 135–173 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  10. Benferhat, S., Khellaf, F., Zeddigha, I.: Negated min-based possibilistic networks. In: Florida Artificial Intelligence Research Society Conference (2016)

    Google Scholar 

  11. Benferhat, S., Lagrue, S., Tabia, K.: Interval-based possibilistic networks. In: Straccia, U., Calì, A. (eds.) SUM 2014. LNCS, vol. 8720, pp. 37–50. Springer, Heidelberg (2014)

    Google Scholar 

  12. Benferhat, S., Levray, A., Tabia, K.: On the analysis of probability-possibility transformations: changing operations and graphical models. In: Destercke, S., Denoeux, T. (eds.) ECSQARU 2015. LNCS, vol. 9161, pp. 279–289. Springer, Heidelberg (2015)

    Chapter  Google Scholar 

  13. Benferhat, S., Levray, A., Tabia, K.: Probability-possibility transformations: application to credal networks. In: Beierle, C., Dekhtyar, A. (eds.) SUM 2015. LNCS, vol. 9310, pp. 203–219. Springer, Heidelberg (2015)

    Chapter  Google Scholar 

  14. Benferhat, S., Smaoui, S.: Hybrid possibilistic networks. Int. J. Approx. Reasoning 44(3), 224–243 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  15. Benferhat, S., Smaoui, S.: Inferring interventions in product-based possibilistic causal networks. Fuzzy Sets Syst. 169(1), 26–50 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  16. Benferhat, S., Tabia, K.: Inference in possibilistic network classifiers under uncertain observations. Ann. Math. Artif. Intell. 64(2–3), 269–309 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  17. Benferhat, S., Tabia, K.: Reasoning with uncertain inputs in possibilistic networks. In: Principles of Knowledge Representation, Reasoning: Proceedings of the Fourteenth International Conference, KR 2014, Vienna, Austria, 20–24 July 2014 (2014)

    Google Scholar 

  18. Borgelt, C., Gebhardt, J., Kruse, R.: Graphical models. In: Proceedings of International School for the Synthesis of Expert Knowledge (ISSEK 98), pp. 51–68. Wiley (2002)

    Google Scholar 

  19. Borgelt, C., Kruse, R.: Graphical Models - Methods for Data Analysis and Mining. Wiley, New York (2002)

    MATH  Google Scholar 

  20. Borgelt, C., Kruse, R.: Learning possibilistic graphical models from data. IEEE Trans. Fuzzy Syst. 11(2), 159–172 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  21. Borgwardt, S., Fazzinga, B., Lukasiewicz, T., Shrivastava, A., Tifrea-Marciuska, O.: Preferential query answering over the semantic web with possibilistic networks. In: Kambhampati, S. (ed.) Proceedings of the 25th International Joint Conference on Artificial Intelligence, IJCAI 2016, New York, NY, USA, 9–15 July 2016. AAAI Press (2016)

    Google Scholar 

  22. Bouchon-Meunier, B., Coletti, G., Marsala, C.: Independence and possibilistic conditioning. Ann. Math. Artif. Intell. 35(1–4), 107–123 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  23. Boughanem, M., Brini, A., Dubois, D.: Possibilistic networks for information retrieval. Int. J. Approx. Reasoning 50(7), 957–968 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  24. Bounhas, M., Hamed, M.G., Prade, H., Serrurier, M., Mellouli, K.: Naive possibilistic classifiers for imprecise or uncertain numerical data. Fuzzy Sets Syst. 239, 137–156 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  25. Cayrol, C., Dubois, D., Touazi, F.: Symbolic possibilistic logic: completeness and inference methods. In: Destercke, S., Denoeux, T. (eds.) ECSQARU 2015. LNCS, vol. 9161, pp. 485–495. Springer, Berlin (2015)

    Chapter  Google Scholar 

  26. Chavira, M., Darwiche, A.: Compiling bayesian networks with local structure. In: Proceedings of the 19th International Joint Conference on Artificial Intelligence (IJCAI), pp. 1306–1312 (2005)

    Google Scholar 

  27. De Campos, C.P.: New complexity results for map in bayesian networks. In: Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence, IJCAI 2011, vol. 3, pp. 2100–2106. AAAI Press (2011)

    Google Scholar 

  28. Destercke, S., Dubois, D., Chojnacki, E.: Transforming probability intervals into other uncertainty models. In: EUSFLAT 2007 Proceedings, vol. 2, pp. 367–373. Universitas Ostraviensis, Ostrava (2007)

    Google Scholar 

  29. Druzdzel, M.J., Van Der Gaag, L.C.: Elicitation of probabilities for belief networks: combining qualitative and quantitative information. In: Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence, UAI 1995, pp. 141–148. Morgan Kaufmann Publishers Inc., San Francisco (1995)

    Google Scholar 

  30. Dubois, D., Foulloy, L., Mauris, G., Prade, H.: Probability-possibility transformations, triangular fuzzy sets, and probabilistic inequalities. Reliable Comput. 10(4), 273–297 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  31. Dubois, D., Fusco, G., Prade, H., Tettamanzi, A.: Uncertain logical gates in possibilistic networks. An application to human geography. In: Beierle, C., Dekhtyar, A. (eds.) SUM 2015. LNCS, vol. 9310, pp. 249–263. Springer, Heidelberg (2015)

    Chapter  Google Scholar 

  32. Dubois, D., Prade, H., Theory, P.: An Approach to Computerized Processing of Uncertainty. Plenum Press, New York (1988)

    Google Scholar 

  33. Dubois, D., Prade, H.: The logical view of conditioning and its application to possibility and evidence theories. Int. J. Approx. Reasoning 4(1), 23–46 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  34. Dubois, D., Prade, H.: Inference in possibilistic hypergraphs. In: Bouchon-Meunier, B., Zadeh, L.A., Yager, R.R. (eds.) IPMU 1990. LNCS, vol. 521, pp. 250–259. Springer, Heidelberg (1991)

    Chapter  Google Scholar 

  35. Dubois, D., Prade, H.: Possibilistic logic: a retrospective and prospective view. Fuzzy Sets Syst. 144(1), 3–23 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  36. Dubois, D., Prade, H.: Practical methods for constructing possibility distributions. Int. J. Intell. Syst. 31(3), 215–239 (2016)

    Article  MathSciNet  Google Scholar 

  37. Fonck, P.: Conditional independence in possibility theory. In: Proceedings of the Tenth International Conference on Uncertainty in Artificial Intelligence, UAI 1994, pp. 221–226. Morgan Kaufmann Publishers Inc., San Francisco (1994)

    Google Scholar 

  38. Fonck, P.: A comparative study of possibilistic conditional independence and lack of interaction. Int. J. Approximate Reasoning 16(2), 149–171 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  39. Garcia, L., Sabbadin, R.: Complexity results and algorithms for possibilistic influence diagrams. Artif. Intell. 172(8), 1018–1044 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  40. Gasse, M., Aussem, A., Elghazel, H.: A hybrid algorithm for bayesian network structure learning with application to multi-label learning. Expert Syst. Appl. 41(15), 6755–6772 (2014)

    Article  Google Scholar 

  41. Gebhardt, J., Kruse, R.: Learning possibilistic networks from data. In: Proceedings 5th International Workshop on Artificial Intelligence and Statistics, Fort Lauderdale, pp. 233–244 (1996)

    Google Scholar 

  42. Guezguez, W., Amor, N.B., Mellouli, K.: Qualitative possibilistic influence diagrams based on qualitative possibilistic utilities. Eur. J. Oper. Res. 195(1), 223–238 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  43. Haddad, M., Leray, P., Amor, N.B.: Learning possibilistic networks from data: a survey. In: 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology (IFSA-EUSFLAT-15), Gijón, Spain, 30 June 2015 (2015)

    Google Scholar 

  44. Heni, A., Amor, N.B., Benferhat, S., Alimi, A.: Dynamic possibilistic networks: representation and exact inference. In: 2007 IEEE International Conference on Computational Intelligence for Measurement Systems and Applications, pp. 1–8, June 2007

    Google Scholar 

  45. Hisdal, E.: Conditional possibilities independence and non interaction. Fuzzy Sets Syst. 1(4), 283–297 (1978)

    Article  MATH  Google Scholar 

  46. Howard, R.A., Matheson, J.E.: Influence diagrams. Principles Appl. Decis. Anal. 2, 720–761 (1984)

    Google Scholar 

  47. Joslyn, C.: Towards an empirical semantics of possibility through maximum uncertainty. In: Fourth World Congress of the International Fuzzy Systems Association: Artificial Intelligence, pp. 86–89 (1991)

    Google Scholar 

  48. Klir, G.J., Geer, J.F.: Information-preserving probability-possibility transformations: recent developments. In: Lowen, R., Roubens, M. (eds.) Fuzzy Logic, pp. 417–428. Kluwer Academic Publishers, Dordrecht (1993)

    Chapter  Google Scholar 

  49. Lang, J.: Possibilistic logic: complexity and algorithms. In: Kohlas, J., Moral, S. (eds.) Algorithms for Uncertainty and Defeasible Reasoning, vol. 5, pp. 179–220. Kluwer Academic Publishers (2001)

    Google Scholar 

  50. Lauritzen, S.L., Spiegelhalter, D.J.: Local computations with probabilities on graphical structures and their application to expert systems. In: Readings in Uncertain Reasoning, pp. 415–448. Morgan Kaufmann Publishers Inc., San Francisco (1990)

    Google Scholar 

  51. De Campos, L.M., Huete, J.F., Moral, S.: Possibilistic independence. In: Proceedings of EUFIT 1995, vol. 1, pp. 69–73 (1995)

    Google Scholar 

  52. Masson, M.-H., Denoeux, T.: Inferring a possibility distribution from empirical data. Fuzzy Sets Syst. 157(3), 319–340 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  53. Nilsson, N.J.: Probabilistic logic. Artif. Intell. 28(1), 71–88 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  54. Pearl, J.: Reverend bayes on inference engines: a distributed hierarchical approach. In: Proceedings of the American Association of Artificial Intelligence National Conference on AI, Pittsburgh, PA, pp. 133–136 (1982)

    Google Scholar 

  55. Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann Publishers Inc., San Francisco (1988)

    MATH  Google Scholar 

  56. Sangesa, R., Cabs, J., Corts, U.: Possibilistic conditional independence: a similarity-based measure and its application to causal network learning. Int. J. Approximate Reasoning 18(1), 145–167 (1998)

    Article  MathSciNet  Google Scholar 

  57. Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press, Princeton (1976)

    MATH  Google Scholar 

  58. Slimen, Y.B., Ayachi, R., Amor, N.B.: Probability-possibility transformation: application to Bayesian and possibilistic networks. In: Masulli, F. (ed.) WILF 2013. LNCS, vol. 8256, pp. 122–130. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  59. Zadeh, L.A.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst. 100, 9–34 (1999)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Karim Tabia .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Tabia, K. (2016). Possibilistic Graphical Models for Uncertainty Modeling. In: Schockaert, S., Senellart, P. (eds) Scalable Uncertainty Management. SUM 2016. Lecture Notes in Computer Science(), vol 9858. Springer, Cham. https://doi.org/10.1007/978-3-319-45856-4_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-45856-4_3

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-45855-7

  • Online ISBN: 978-3-319-45856-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics