Abstract
Decision rules induced from lower approximations of decision classes are certain in the sense of covering the objects which certainly belong to the corresponding decision classes. The definition of rough approximations is originally based on an indiscernibility relation in the set of objects. The indiscernibility relation requiring strict equality of attribute values for the objects being compared is often restrictive in practical applications. This is why, we are proposing to use a more natural similarity relation to define rough approximation of decision classes. The only requirement imposed on this relation is reflexivity. The similarity relation is being derived from data. Decision rules induced from lower approximations of decision classes based on similarity are not only certain but robust in the sense of covering objects which belong to the corresponding decision classes and are not similar to objects from outside. The approach is illustrated by a simple example and it is validated on a set of benchmark examples.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Aha, D.W.: Case-based learning algorithms. In: Proceedings of the Case-Based Reasoning Workshop, Morgan Kaufmann (1991) 147–158
Aha, D.W., Kibler, E., Alberk, M.K.: Instance based learning algorithms. Machine Learning 6 (1991) 37–66
Chan, Ch.-Ch., Grzyma’a-Busse, J.W.: On the two local inductive algorithms: PRISM and LEM2. Foundations of Computing and Decision Sciences 19/3 (1994) 185–204
Chmielewski, M., Grzyma’a-Busse, J.: Global Discretization of Continuous Attributes as Preprocessing for Machine Learning. In: Lin, T. Y., Wildberger, A. M. (eds.), Soft computing: rough sets, fuzzy logic, neural networks, uncertainty management, Simulation Councils, San Diego (1995) 294–301
Dubois, D., Prade, H.: Criteria aggregation and ranking of alternatives in the framework of fuzzy set theory. In: Zimmermann, H.J., Zadeh, L.A., Gaines, B.R. (eds.), Fuzzy sets and decision analysis. Studies in the management sciences 20 North-Holland, Amsterdam (1984) 209–240
Dubois, D., Prade, H.: Putting rough sets and fuzzy sets together. In: Slowiiiski, R. (ed), Intelligent decision support. Handbook of applications and advances of the rough set theory, Kluwer Academic Publishers, Dordrecht (1992) 203–232
Grzyma’a-Busse, J.W.: LERS–a system for learning from examples based on rough sets. In: Slowinski, R. (ed), Intelligent decision support. Handbook of applications and advances of the rough set theory, Kluwer Academic Publishers, Dordrecht (1992) 3–18
Höhle, U.: Quotients with respect to similarity relations. Fuzzy Sets and Systems 27 (1988) 31–44
Jelonek, J.: Generalization capability of homogenous voting classifier based on partially replicated data. In: Integrating Multiple Learned Models for Improving and Scaling Machine Learning Algorithms. Proceedings of Thirteenth National Conference on Artificial Intelligence. Portland, Oregon (1996) 47–52
Krawiec, K., Slowiríski, R., Vanderpooten, D.: Construction of Rough Classifiers based on Application of a Similarity Relation. In: Tsumoto S., Kobayashi, S.
Yokomori, T., Tanaka, H. (eds.), Proceedings of the Fourth International Workshop on Rough Sets, Fuzzy Sets and Machine Discovery (RSFD’96), Tokyo Nov. 6–8, Tokyo Univ. Press (1996) 23–30
Lin, T.: Neighborhood systems and approximation in database and knowledge base systems. In: Proceedings of the 4th International Symposium on Methodologies for Intelligent Systems (1989)
Luce, R.: Semi-orders and a theory of utility discrimination. In: Econometrica 24 1956.
Marcus, S.: Tolerance rough sets, tech topologies, learning processes. Bull. Polish Acad. Sci. Ser. Sci. Tech. 42/3 (1994) 471–484
Merz, C.J., Murphy, P.M.: UCI Repository of machine learning databases http://www.ics.uci.edu/relearn/MLRepository.html]. Irvine, CA: University of California, Department of Information and Computer Science (1996)
Mieko, R., Stefanowski, J., Vanderpooten, D.: Discovery-oriented induction of decision rules. Cahier du LAMSADE 141 Universite de Paris-Dauphine, Paris (Septembre 1996 )
Nieminen, J.: Rough tolerance equality. Fondamenta Informaticae 11/3 (1988) 289–296
Pawlak, Z.: Rough sets. Int. J. Computer and Information Sci. 11 (1982) 341–356
Pawlak, Z.: Rough sets: theoretical aspects of reasoning about data. Kluwer Academic Publishers, Dordrecht (1991)
Polkowski, L., Skowron, A., Zytkow, J.: Tolerance based rough sets. In: Lin, T.Y., Wildberger, A. M. (eds.,) Soft computing: rough sets, fuzzy logic, neural networks, uncertainty management, Simulation Councils, San Diego (1995) 55–58
Quinlan, J.R.: C4.5: Programs for Machine Learning. Morgan Kaufmann Publishers, San Mateo CA (1988)
Rumelhart, D.E., Hinton, G.E., Williams, R.J.: Learning internal representations by error propagation. In: Rumelhart, D.E., McClelland, J.L. and the PDP Research Group (eds.), Parallel distributed processing. Explorations in the microstructure of cognition, MIT Press, Cambridge MA (1986) 318–362
Schreider, J.A.: Equality, Resemblance and Order. Mir Publishers, Moscow (1975)
Shan, N., Ziarko, W.: An incremental learning algorithm for constructing decision rules. In: Ziarko, W. (ed.), Rough sets, fuzzy sets and knowledge discovery, Springer-Verlag, Berlin (1994) 326–334
Skowron, A.: Boolean reasoning for decision rules generation. In: Komorowski, J., Ras, Z.W. (eds.): Methodologies for Intelligent Systems. LNAI 689 Springer Verlag, Berlin (1993) 295–305
Skowron, A., Stepaniuk, J.: Generalized approximation spaces. In: Lin, T.Y., Wild-berger, A.M. (eds.), Soft computing: rough sets, fuzzy logic, neural networks, uncertainty management, Simulation Councils, San Diego (1995) 18–21
Skowron, A., Polkowski, L., Komorowski, J.: Learning tolerance relations by Boolean descriptors: automatic feature extraction from data tables. In: Tsumoto S., Kobayashi, S., Yokomori, T., Tanaka, H. (eds.), Proceedings of the Fourth International Workshop on Rough Sets, Fuzzy Sets and Machine Discovery (RSFD’96), Tokyo Nov. 6–8, Tokyo Univ. Press (1996) 11–17
Slowinski, R., Vanderpooten, D.: Similarity relation as a basis for rough approximations. ICS Research Report 53/95. Institute of Computer Science, Warsaw University of Technology, Warsaw, 1995. Also in: Wang, P. (ed.): Advances in Machine Intelligence & Soft Computing, Bookwrights, Raleigh NC (1997) 17–33
Slowinski, R., Vanderpooten, D.: A generalized definition of rough approximations based on similarity. IEEE Trans. on Data and Knowledge Engineering (to appear)
Stefanowski, J., Vanderpooten, D.: A general two-stage approach to inducing rules from examples. In: Ziarko, W. (ed.), Rough sets, fuzzy sets and knowledge discovery, Springer Verlag, Berlin, British Computer Society, London (1994) 317–325
Tentush, I.: On minimal absorbent sets for some types of tolerance relations. Bull. Polish Acad. Sci. 43/1 (1995) 79–88
31. Tversky, A.: Features of similarity. Psychological Review 84/4 (1977) 327–352
Yao, Y., Wong, S.: Generalization of rough sets using relationships between attribute values. In: Proceedings of the 2nd Annual Joint Conference on Information Sciences, Wrightsville Beach, N.C. (1995) 30–33
Zadeh, L.A.: Similarity relations and fuzzy orderings. Information Sciences 3 (1971) 177–200
Zeeman, E.C.: The topology of brain and visual perception. In: Fort, K.M. (ed.): Topology of 3-manifolds and related topics, Prentice Hall, Englewood Cliffs N.J. (1965) 240–256
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Krawiec, K., Słowiński, R., Vanderpooten, D. (1998). Learning Decision Rules from Similarity Based Rough Approximations. In: Polkowski, L., Skowron, A. (eds) Rough Sets in Knowledge Discovery 2. Studies in Fuzziness and Soft Computing, vol 19. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1883-3_3
Download citation
DOI: https://doi.org/10.1007/978-3-7908-1883-3_3
Publisher Name: Physica, Heidelberg
Print ISBN: 978-3-7908-2459-9
Online ISBN: 978-3-7908-1883-3
eBook Packages: Springer Book Archive