Abstract
The paper discusses mathematical concept of granular model for data and knowledge manipulation. In order to overcome the difficulties caused by extensive data representation a new model based on granular sets and granular relations is put forward. The key idea is that the notion of set may consist of basic elements grouped into bigger granules. A granular set is formed from a universe set and a semi-partition defining granules of its elements. Formal definition of granular sets and some basic algebraic operations on granular sets are introduced in the paper. Further, the concept of granular relation is also defined and some possibilities of application of granular sets and relations to knowledge representation are put forward.
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Järvinen, J., Kortelainen, J.: A Note on Definability in Rough Set Theory. In: De Baets, B., De Caluwe, R., De Tré, G., Fodor, J., Kacprzyk, J., Zadrożny, S. (eds.): Current Issues in Data and Knowledge Engineering, Akademicka Oficyna Wydawnicza EXIT, Warsaw, Poland (2004)
Peters, J.F., Pawlak, Z., Skowron, A.: A rough set approach to measuring information granules. In: COMPSAC’02. Proc. of the 26th International Computer Software and Applications Conference on Prolonging Software Life: Development and Redevelopment, Oxford, pp. 1135–1139 (2002)
Klir, G.J., Yuan, B.: Fuzzy Sets and Fuzzy Logic. In: Theory and Applications, Prentice-Hall, Englewood Cliffs (1995)
Ligȩza, A.: Intelligent data and knowledge analysis and verification; towards a taxonomy of specific problems. In: Vermesan, A., Coenen, F. (eds.) Validation and Verification of Knowledge Based Systems: Theory, Tools and Practice, pp. 313–325. Kluwer Academic Publishers, Boston (1999)
Ligȩza, A.: Granular sets and granular relations: Towards a higher abstraction level in knowledge representation. In: Intelligent Information Systems 2002, pp. 331–340. Physica-Verlag, Heidelberg (2002)
Ligêza, A.: Granular sets and granular relations for algebraic knowledge management. In: ANNiE 2003. Smart engineering system design: neural networks, fuzzy logic, evolutionary programming, complex systems and artificial life: Proc. of the Artificial Neural Networks in Engineering Conference, St. Louis, Missouri. ASME Press Series on Intelligent Engineering Systems Through Artificial Neural Networks, vol. 13, pp. 169–174 (2003)
Ligȩza, A.: Logical foundations of rule-based systems. In: Studies in Computational Intelligence, vol. 11, Springer, Berlin (2006)
Ligȩza, A., Nalepa, G.J.: Knowledge Representation with Granular Attributive Logic for XTT-based Expert Systems. In: Prof. of the 20th International FLAIRS Conference, Key West, Florida (to appear)
Pawlak, Z.: Rough Sets. Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dordrecht, The Netherlands (1991)
Peters, J.F., Skowron, A., Suraj, Z., Rząsa, W., Borkowski, M.: Clustering: A rough set approach to constructing information granules. In: SCDP’02. Proceedings of the 6th International Conference on Soft Computing and Distributed Processing, Rzeszów, pp. 57–61 (2002)
Peters, J.F., Pawlak, Z., Skowron, A.: A rough set approach to measuring information granules. In: Proc. of the 26th International Computer Software and Applications Conference on Prolonging Software Life: Development and Redevelopment, Oxford, pp. 1135–1139 (2002)
Skowron, A., Stepaniuk, J.: Tolerance approximation spaces. Fundamenta Informaticae 27, 245–253 (1996)
Zadeh, L.A.: Fuzzy sets. Information and Control 8, 338–353 (1965)
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Ligęza, A., Szpyrka, M. (2007). A Note on Granular Sets and Their Relation to Rough Sets. In: Kryszkiewicz, M., Peters, J.F., Rybinski, H., Skowron, A. (eds) Rough Sets and Intelligent Systems Paradigms. RSEISP 2007. Lecture Notes in Computer Science(), vol 4585. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73451-2_27
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DOI: https://doi.org/10.1007/978-3-540-73451-2_27
Publisher Name: Springer, Berlin, Heidelberg
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