Abstract
Frequently, knowledge systems represent information crisply. That is, for a given object in the database, and a given property (attribute-value pair), there is no uncertainty whether or not the object has that property. This certainty restricts expressive power. Therefore, we present here an approach to knowledge representation and rough set-based inductive learning using a fuzzy set representation of information. Specifically, we introduce the Fuzzy Property Set model, which is an enhancement of the Property Set model in which each object is represented by a collection of properties. In this fuzzy enhancement, it is possible to denote the degree to which an object has a particular property. Fuzzy rough set upper and lower approximations are defined using this model, as a basis for the inductive learning of concepts. Various similarity and distance measures can then be used to rank objects according their similarity to the upper or lower concept approximations.
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References
M. Hadjimichael, S.K.M. Wong, “Quantifying Inductive Learning Generalization,” submitted for publication, 1993.
R. S. Michalski, J. B. Larson, “Selection of most representative training examples and incremental generation of VL1 hypothesis: the underlying methodology and the description of programs ESEL and AQ11,” Report No. 867, Department of Computer Science, University of Illinois, Urbana, Illinois, 1978.
A. Motro, “Accommodating Imprecision in Database Systems: Issues and Solutions,” SIGMOD Record,19, n4, 69–74, 1990
Z. Pawlak, “Rough Sets,” International Journal of Computer and Information Sciences, 11, 341–356, 1984.
X.T. Peng, A. Kandel, “Concepts, Rules, and Fuzzy Reasoning: A Factor Space Approach,” IEEE Trans. Syst., Man, and Cyber., 21, nl, 194–205, 1991.
H. Prade, C. Testemale, “Generalizing Database Relational Algebra for the Treatment of Incomplete or Uncertain Information and Vague Queries,” Information Sciences, 34, 115–143, 1984.
J.R. Quinlan, “Learning efficient classification procedures and the application to chess end-games,” Machine Learning, an Artificial Intelligence Approach. (eds. Michalski, Carbonell, Mitchell), Tioga Publishing Co., Palo Alto, 1983.
L. Wang, J.M. Mandel, “Generating Fuzzy Rules by Learning from Examples,” IEEE Trans. Syst., Man, and Cyber., 2, n6, 1414–1427, 1992.
S.K.M. Wong, Y. Yao, “A Statistical Similarity Measure,” Proc. 10th Annual International ACM SIGIR Conference on Research and Development in Information Retrieval, New Orleans, 3–12, 1987.
L. A. Zadeh, “Fuzzy Sets,” Inf. Control, 8, 338–353, 1965.
M. Zemankova, A. Kandel, “Implementing Imprecision in Information Systems,” Information Sciences, 37, 107–141, 1985.
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© 1994 British Computer Society
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Hadjimichael, M., Wong, S.K.M. (1994). Fuzzy Representations in Rough Set Approximations. In: Ziarko, W.P. (eds) Rough Sets, Fuzzy Sets and Knowledge Discovery. Workshops in Computing. Springer, London. https://doi.org/10.1007/978-1-4471-3238-7_41
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DOI: https://doi.org/10.1007/978-1-4471-3238-7_41
Publisher Name: Springer, London
Print ISBN: 978-3-540-19885-7
Online ISBN: 978-1-4471-3238-7
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