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.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
References
Aamodt, A., Plaza, E.: Case-based reasoning: Foundational issues, methodological variations, and system approaches. AI Communications 7, 39–59 (1994)
Aït-Kaci, H., Podelski, A.: Towards a meaning of LIFE. J. Logic Programming 16, 195–234 (1993)
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)
Armengol, E., Plaza, E.: Bottom-up induction of feature terms. Machine Learning 41, 259–294 (2002)
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)
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)
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)
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
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)
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)
Carpenter, B.: The Logic of Typed Feature Structures. Tracts in Theoretical Computer Science. Cambridge Univ. Press, Cambridge (1992)
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)
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)
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)
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)
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)
Dubois, D., Prade, H.: What are fuzzy rules and how to use them. Fuzzy Sets and Systems 84, 169–185 (1996)
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)
Filev, D.P., Yager, R.R.: On the issue of obtaining OWA operator weights. Fuzzy Sets and Systems 94, 157–169 (1998)
Grabisch, M., Nguyen, H.T., Walker, E.A.: Fundamentals of Uncertainty Calculi with Applications to Fuzzy Inference. Kluwer, Dordrecht (1995)
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)
Hüllermeier, E., Dubois, D., Prade, H.: Knowledge based extrapolation of cases: a possibilistic approach. In: Proceedings IPMU 2000, Madrid, Spain, pp. 1575–1582 (2000)
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)
Kolodner, J.: Case-Based Reasoning. Morgan Kaufmann Publishers, San Francisco (1993)
López de Mántaras, R.: A distance-based attribute selection measure for decision tree induction. Machine Learning 6, 81–92 (1991)
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)
Miyamoto, S., Suizu, D.: Fuzzy c-Means clustering using transformations into high dimensional spaces. In: Proceedings SCIS&ISIS (CD-ROM), Tsukuba, Japan (2002)
Muggleton, S., De Raedt, L.: Inductive logic programming: Theory and methods. Journal of Logic Programming 19-20, 629–679 (1994)
Luenberger, D.G.: Introduction to Linear and Nonlinear Programming. Addison Wesley, Reading (1973)
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)
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)
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)
Torra, V.: Learning weights for the quasi-weighted means. IEEE Transactions on Fuzzy Systems 10(5), 653–666 (2002)
Vapnik, V.N.: The Nature of the Statistical Learning Theory, 2nd edn. Springer, New York (2000)
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)
Yager, R.R.: On ordered weighted averaging aggregation operators in multi–criteria decision making. IEEE Transactions on SMC 18, 183–190 (1998)
Zadeh, L.A.: Similarity relations and fuzzy orderings. Journal of Information Sciences, 177–200 (1971)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights 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)