Skip to main content
SpringerLink
Log in

A Possibility Theory-Oriented Discussion of Conceptual Pattern Structures

  • Conference paper
Scalable Uncertainty Management (SUM 2010)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6379))

Included in the following conference series:

Abstract

A fruitful analogy between possibility theory and formal concept analysis has recently contributed to show the interest of introducing new operators in this latter setting. In particular, another Galois connection, distinct from the classical one that defines formal concepts, has been laid bare which allows for the decomposition of a formal context into sub-contexts when possible. This paper pursues a similar investigation by considering pattern structures which are known to offer a generalization of formal concept analysis. The new operators as well as the other Galois connection are introduced in this framework, where an object is associated to a structured description rather than just to its set of properties. The description may take many different forms. In this paper, we more particularly focus on two important particular cases, namely ordered lists of intervals, and propositional knowledge bases, which both allow for incomplete descriptions. They are then extended to fuzzy and uncertain descriptions by introducing fuzzy intervals and possibilistic logic bases respectively in these two settings.

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

Access this chapter

Log in via an institution
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 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Baader, F., Molitor, R.: Building and structuring description logic knowledge bases using least common subsumers and concept analysis. In: Ganter, B., Mineau, G.W. (eds.) ICCS 2000. LNCS, vol. 1867, pp. 292–305. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  2. Chaudron, L., Maille, N.: Generalized formal concept analysis. In: Ganter, B., Mineau, G.W. (eds.) ICCS 2000. LNCS, vol. 1867, pp. 357–370. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  3. Djouadi, Y., Dubois, D., Prade, H.: Différentes extensions floues de l’analyse formelle de concepts. In: Rencontres Francophones sur la Logique Floue et ses Applications (LFA), Annecy, France, November 5-6, pp. 141–148. Cépadues Editions (2009)

    Google Scholar 

  4. Djouadi, Y., Dubois, D., Prade, H.: Possibility theory and formal concept analysis: Context decomposition and uncertainty handling. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds.) Computational Intelligence for Knowledge-Based Systems Design. LNCS, vol. 6178, pp. 260–269. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  5. Dubois, D., Dupin de Saint  Cyr, F., Prade, H.: A possibilty-theoretic view of formal concept analysis. Fundamenta Informaticae (1-4), 195–213 (2007)

    Google Scholar 

  6. Dubois, D., Lang, J., Prade, H.: Possibilistic logic. In: Gabbay, D.M., Hogger, C.J., Robinson, J.A., Nute, D. (eds.) Handbook of Logic in Artificial Intelligence and Logic Programming, vol. 3, pp. 439–513. Oxford University Press, Oxford (1994)

    Google Scholar 

  7. Dubois, D., Mengin, J., Prade, H.: Possibilistic uncertainty and fuzzy features in description logic. A preliminary discussion. In: Sanchez, E. (ed.) Fuzzy Logic and the Semantic Web, pp. 101–113. Elsevier, Amsterdam (2006)

    Google Scholar 

  8. Dubois, D., Prade, H.: Fuzzy Sets and Systems: Theory and Applications (1980)

    Google Scholar 

  9. Dubois, D., Prade, H.: Possibility Theory. Plenum Press, New York (1988)

    MATH  Google Scholar 

  10. Dubois, D., Prade, H.: Possibility theory as a basis for preference propagation in automated reasoning. In: Proc. 1st IEEE Inter. Conf. on Fuzzy Systems 1992 (FUZZ-IEEE 1992), San Diego, Ca., March 8-12, pp. 821–832 (1992)

    Google Scholar 

  11. Dubois, D., Prade, H.: Possibility theory: qualitative and quantitative aspects. In: Gabbay, D., Smets, P. (eds.) Quantified Representation of Uncertainty and Imprecision. Handbook of Defeasible Reasoning and Uncertainty Management Systems, vol. 1, pp. 169–226. Kluwer Acad. Publ., Dordrecht (1998)

    Google Scholar 

  12. Dubois, D., Prade, H.: Possibility theory and formal concept analysis in information systems. In: Proc. Inter. Fuzzy Systems Assoc. World Congress and Conf. of the Europ. Soc. for Fuzzy Logic and Technology (IFSA-EUSFLAT 2009), Lisbon, July 20-24, pp. 1021–1026 (2009)

    Google Scholar 

  13. Düntsch, I., Gediga, G.: Approximation operators in qualitative data analysis. In: Theory and Application of Relational Structures as Knowledge Instruments, pp. 216–233 (2003)

    Google Scholar 

  14. Düntsch, I., Orlowska, E.: Mixing modal and sufficiency operators. Bulletin of the Section of Logic, Polish Academy of Sciences 28(2), 99–106 (1999)

    MATH  Google Scholar 

  15. Ferré, S.: Complete and incomplete knowledge in logical information systems. In: Benferhat, S., Besnard, P. (eds.) ECSQARU 2001. LNCS (LNAI), vol. 2143, pp. 782–791. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  16. Ferré, S., Ridoux, O.: A logical generalization of formal concept analysis. In: Ganter, B., Mineau, G.W. (eds.) ICCS 2000. LNCS, vol. 1867, pp. 371–384. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  17. Ferré, S., Ridoux, O.: Introduction to logical information systems. Inf. Process. Management 40(3), 383–419 (2004)

    Article  MATH  Google Scholar 

  18. Ganter, B., Kuznetsov, S.O.: Pattern structures and their projections. In: Alexandrov, V.N., Dongarra, J., Juliano, B.A., Renner, R.S., Tan, C.J.K. (eds.) ICCS 2001. LNCS, vol. 2074, pp. 129–142. Springer, Heidelberg (2001)

    Google Scholar 

  19. Ganter, B., Wille, R.: Formal Concept Analysis. Springer, Heidelberg (1999)

    MATH  Google Scholar 

  20. Georgescu, G., Popescu, A.: Non-dual fuzzy connections. Arch. Math. Log. 43(8), 1009–1039 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  21. Kuznetsov, S.O.: Learning of simple conceptual graphs from positive and negative examples. In: Żytkow, J.M., Rauch, J. (eds.) PKDD 1999. LNCS (LNAI), vol. 1704, pp. 384–391. Springer, Heidelberg (1999)

    Google Scholar 

  22. Kuznetsov, S.O.: Pattern structures for analyzing complex data. In: Sakai, H., Chakraborty, M.K., Hassanien, A.E., Ślęzak, D., Zhu, W. (eds.) RSFDGrC 2009. LNCS, vol. 5908, pp. 33–44. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  23. Pawlak, Z.: Rough Sets. Theoretical Aspects of. Reasoning about Data. Kluwer Acad. Publ., Dordrecht (1991)

    MATH  Google Scholar 

  24. Popescu, A.: A general approach to fuzzy concepts. Mathematical Logic Quarterly 50, 265–280 (2004)

    Article  MATH  Google Scholar 

  25. Prade, H., Serrurier, M.: Bipolar version space learning. Inter. J. of Intelligent Systems 23(10), 1135–1152 (2008)

    Article  MATH  Google Scholar 

  26. Benferhat, S., Tabia, K.: An efficient algorithm for naive possibilistic classifiers with uncertain inputs. In: Greco, S., Lukasiewicz, T. (eds.) SUM 2008. LNCS (LNAI), vol. 5291, pp. 63–77. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  27. Yao, Y.Y., Chen, Y.: Rough set approximations in formal concept analysis. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets V. LNCS, vol. 4100, pp. 285–305. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  28. Yao, Y.Y.: A comparative study of formal concept analysis and rough set theory in data analysis. In: Tsumoto, S., Słowiński, R., Komorowski, J., Grzymała-Busse, J.W. (eds.) RSCTC 2004. LNCS (LNAI), vol. 3066, pp. 59–68. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  29. Zadeh, L.A.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems 1, 3–28 (1978)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Campus Scientique, B.P. 235, 54500, Vanduvre-l‘es-Nancy, France

    Zainab Assaghir & Mehdi Kaytoue

  2. IRIT, Université Paul Sabatier, 31062, Toulouse Cedex 09, France

    Henri Prade

Authors
  1. Zainab Assaghir
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mehdi Kaytoue
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Henri Prade
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Maryland, MD 20910, College Park, USA

    Amol Deshpande

  2. Department of Computer Science, University College London, Gower Street, WC1E 6BT, London, UK

    Anthony Hunter

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Assaghir, Z., Kaytoue, M., Prade, H. (2010). A Possibility Theory-Oriented Discussion of Conceptual Pattern Structures. In: Deshpande, A., Hunter, A. (eds) Scalable Uncertainty Management. SUM 2010. Lecture Notes in Computer Science(), vol 6379. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15951-0_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-15951-0_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15950-3

  • Online ISBN: 978-3-642-15951-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation