Skip to main content
SpringerLink
Log in

On Learning Similarity Relations in Fuzzy Case-Based Reasoning

  • Conference paper
Transactions on Rough Sets II

Part of the book series: Lecture Notes in Computer Science ((TRS,volume 3135))

Abstract

Case–based reasoning (CBR) is a problem solving technique that puts at work the general principle that similar problems have similar solutions. In particular, it has been proved effective for classification problems. Fuzzy set–based approaches to CBR rely on the existence of a fuzzy similarity functions on the problem description and problem solution domains. In this paper, we study the problem of learning a global similarity measure in the problem description domain as a weighted average of the attribute–based similarities and, therefore, the learning problem consists in finding the weighting vector that minimizes mis–classification. The approach is validated by comparing results with an application of case–based reasoning in a medical domain that uses a different model.

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. Aamodt, A., Plaza, E.: Case-based reasoning: Foundational issues, methodological variations, and system approaches. AI Communications 7, 39–59 (1994)

    Google Scholar 

  2. Aït-Kaci, H., Podelski, A.: Towards a meaning of LIFE. J. Logic Programming 16, 195–234 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  3. Armengol, E., Palaudaries, A., Plaza, E.: Individual prognosis of diabetes long– term risks: A CBR approach. Methods of Information in Medicine (special issue on prognosis models in medicine: AI and Statistics) 40, 46–51 (2001)

    Google Scholar 

  4. Armengol, E., Plaza, E.: Bottom-up induction of feature terms. Machine Learning 41, 259–294 (2002)

    Article  Google Scholar 

  5. Armengol, E., Plaza, E.: Lazy induction of descriptions for relational case-based learning. In: Flach, P.A., De Raedt, L. (eds.) ECML 2001. LNCS (LNAI), vol. 2167, pp. 13–24. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  6. Bonissone, P., Ayub, S.: Representing cases and rules in plausible reasoning systems. In: Proceedings of the, ARPA/RL Planning Initiative, Tucson, AZ,USA, pp. 305–316 (1994)

    Google Scholar 

  7. Bonissone, P., Cheetman, W.: Applications of fuzzy case–based reasoning to residential property valuation. In: Proceedings of the 6th IEEE Int. Conference on Fuzzy Systems FUZZ-IEEE 1997, Barcelona, Spain, pp. 37–44 (1997)

    Google Scholar 

  8. Bonissone, P., de Mántaras, L.: Fuzzy Case–Based Reasoning Systems. In: Ruspini, E., Bonissone, P.P., Pedrycz, W. (eds.) Handbook of Fuzzy Computing, F 4.3: pp. 1–17. IOS Publishing Ltd., Amsterdam

    Google Scholar 

  9. Burkhard, H.-D., Richter, M.: On the notion of similarity of case–based reasoning and fuzzy theory. In: Pal, S.K., Dillon, T.S., Yeung, D.S. (eds.) Soft Computing in Case Base Reasoning, pp. 29–46. Springer, Berlin (2001)

    Google Scholar 

  10. de Calmès, M., Dubois, D., Hüllermeier, E., Prade, H., Sèdes, F.: Case–based querying and prediction: A fuzzy set approach. In: Proc of the IEEE International Conference on Fuzzy Systems, Hawaii, USA, pp. 735–740 (2002)

    Google Scholar 

  11. Carpenter, B.: The Logic of Typed Feature Structures. Tracts in Theoretical Computer Science. Cambridge Univ. Press, Cambridge (1992)

    Book  MATH  Google Scholar 

  12. Cheetham, B., Cuddihy, P., Goebel, K.: Applications of soft CBR at General Electric. In: Pal, S.K., Dillon, T.S., Yeung, D.S. (eds.) Soft Computing in Case Base Reasoning, pp. 335–365. Springer, Berlin (2001)

    Google Scholar 

  13. Dubois, D., Esteva, F., Garcia, P., Godo, L., Lòpez de Màntaras, R., Prade, H.: Fuzzy modelling of case–based reasoning and decision. In: Leake, D.B., Plaza, E. (eds.) ICCBR 1997. LNCS(LNAI), vol. 1266, pp. 599–610. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  14. Dubois, D., Esteva, F., Garcia, P., Godo, L., Lòpez de Mantaras, R., Prade, H.: Fuzzy set modeling in case-based reasoning. International Journal of Intelligent System 13(4), 345–373 (1998)

    Article  MATH  Google Scholar 

  15. Dubois, D., Hüllermeier, E., Prade, H.: Formalizing case–based inference using fuzzy rules. In: Pal, S.K., So, D.Y., Dillon, T. (eds.) Soft Computing in Case–Based Reasoning, pp. 47–72. Springer, Berlin (2000)

    Google Scholar 

  16. Dubois, D., Hüllermeier, E., Prade, H.: Flexible control of case–based prediction in the framework of possibility theory. In: Blanzieri, E., Portinale, L. (eds.) EWCBR 2000. LNCS (LNAI), vol. 1898, pp. 61–73. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  17. Dubois, D., Prade, H.: What are fuzzy rules and how to use them. Fuzzy Sets and Systems 84, 169–185 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  18. Esteva, F., Garcia, P., Godo, L.: Fuzzy similarity-based models in case-based reasoning. In: Proceedings of the 11th IEEE International Conference on Fuzzy Systems FUZZ-IEEE 2002, Hawaii, USA, pp. 1348–1353 (2002)

    Google Scholar 

  19. Filev, D.P., Yager, R.R.: On the issue of obtaining OWA operator weights. Fuzzy Sets and Systems 94, 157–169 (1998)

    Article  MathSciNet  Google Scholar 

  20. Grabisch, M., Nguyen, H.T., Walker, E.A.: Fundamentals of Uncertainty Calculi with Applications to Fuzzy Inference. Kluwer, Dordrecht (1995)

    Google Scholar 

  21. Hansem, B., Riordan, D.: Fuzzy case-based prediction of ceiling and visibility. In: Proceedings of the 1st Conference on Artificial Intelligence, pp. 118–123. American Metereological Society (1998)

    Google Scholar 

  22. Hüllermeier, E., Dubois, D., Prade, H.: Knowledge based extrapolation of cases: a possibilistic approach. In: Proceedings IPMU 2000, Madrid, Spain, pp. 1575–1582 (2000)

    Google Scholar 

  23. Jaczynski, M., Trousse, B.: Fuzzy logic for the retrieval step of a case-based reasoner. In: Haton, J.-P., Manago, M., Keane, M.A. (eds.) EWCBR 1994. LNCS, vol. 984, pp. 313–321. Springer, Heidelberg (1995)

    Google Scholar 

  24. Kolodner, J.: Case-Based Reasoning. Morgan Kaufmann Publishers, San Francisco (1993)

    Google Scholar 

  25. López de Mántaras, R.: A distance-based attribute selection measure for decision tree induction. Machine Learning 6, 81–92 (1991)

    Google Scholar 

  26. Marichal, J.-L., Roubens, M.: Determination of weights of interacting criteria from a reference set. Papiers de Recherche. Faculté dÉconomie de Gestion et de Sciences Sociales, Groupe d’Etude des Mathematiques du Management et de lÉconomie, N. 9909 (1999)

    Google Scholar 

  27. Miyamoto, S., Suizu, D.: Fuzzy c-Means clustering using transformations into high dimensional spaces. In: Proceedings SCIS&ISIS (CD-ROM), Tsukuba, Japan (2002)

    Google Scholar 

  28. Muggleton, S., De Raedt, L.: Inductive logic programming: Theory and methods. Journal of Logic Programming 19-20, 629–679 (1994)

    Article  Google Scholar 

  29. Luenberger, D.G.: Introduction to Linear and Nonlinear Programming. Addison Wesley, Reading (1973)

    MATH  Google Scholar 

  30. Plaza, E., Esteva, F., Garcia, P., Godo, L., López de M‘antaras, R.: A logical approach to case-based reasoning using fuzzy similarity relations. Information Sciences 106, 105–122 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  31. Tanaka, A., Murofushi, T.: A learning model using fuzzy measure and the Choquet integral. In: Proceedings of the 5th Fuzzy System Symposium, Kobe, Japan, pp. 213–217 (1989) (in Japanese)

    Google Scholar 

  32. Torra, V.: On the learning of weights in some aggregation operators: the weighted mean and OWA operators. Mathematics and Soft Computing 6, 249–265 (2000)

    Google Scholar 

  33. Torra, V.: Learning weights for the quasi-weighted means. IEEE Transactions on Fuzzy Systems 10(5), 653–666 (2002)

    Article  MathSciNet  Google Scholar 

  34. Vapnik, V.N.: The Nature of the Statistical Learning Theory, 2nd edn. Springer, New York (2000)

    MATH  Google Scholar 

  35. Yager, R.R.: Case-based reasoning, fuzzy systems modelling and solution composition. In: Leake, D.B., Plaza, E. (eds.) ICCBR 1997. LNCS, vol. 1266, pp. 633–643. Springer, Heidelberg (1997)

    Google Scholar 

  36. Yager, R.R.: On ordered weighted averaging aggregation operators in multi–criteria decision making. IEEE Transactions on SMC 18, 183–190 (1998)

    Google Scholar 

  37. Zadeh, L.A.: Similarity relations and fuzzy orderings. Journal of Information Sciences, 177–200 (1971)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut d’Investigació en Intel·ligència Artificial CSIC, Campus UAB s/n, 08193, Bellaterra, Catalonia, Spain

    Eva Armengol, Francesc Esteva, Lluís Godo & Vicenç Torra

Authors
  1. Eva Armengol
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Francesc Esteva
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Lluís Godo
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Vicenç Torra
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Manitoba, R3T 5V6, Winnipeg, Manitoba, Canada

    James F. Peters

  2. Institute of Mathematics, Warsaw University, Banacha 2, 02-097, Warsaw, Poland

    Andrzej Skowron

  3. Institut de Recherche en Informatique de Toulouse, France

    Didier Dubois

  4. Institute of Computer Science, Polish Academy of Sciences, 01–237, Warsaw, Poland

    Jerzy W. Grzymała-Busse

  5. Department of Systems Innovation, Graduate School of Engineering Science, Osaka University, 1-3, Machikaneyama, Toyonaka, 560-8531, Osaka, Japan

    Masahiro Inuiguchi

  6. Polish-Japanese Institute of Information Technology Warsaw, Poland Department of Mathematics and Computer Science, University of Warmia and Mazury, Olsztyn, Poland

    Lech Polkowski

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Armengol, E., Esteva, F., Godo, L., Torra, V. (2004). On Learning Similarity Relations in Fuzzy Case-Based Reasoning. In: Peters, J.F., Skowron, A., Dubois, D., Grzymała-Busse, J.W., Inuiguchi, M., Polkowski, L. (eds) Transactions on Rough Sets II. Lecture Notes in Computer Science, vol 3135. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27778-1_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-27778-1_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23990-1

  • Online ISBN: 978-3-540-27778-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation