Abstract
In this paper, The concepts of fuzzy relation mapping and inverse fuzzy relation mapping are firstly introduced and their properties are studied. Then, the notions of homomorphisms of information systems based on fuzzy relations are proposed, and it is proved that attribute reductions in the original system and image system are equivalent to each other under the condition of homomorphism.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Dubois, D., Prade, H.: Rough Fuzzy Sets and Fuzzy Rough Sets. Internat. J. General Systems 17(2-3), 191–209 (1990)
Graymala-Busse, J.W.: Algebraic Properties of Knowledge Representation Systems. In: Proceedings of the ACM SIGART International Symposium on Methodologies for Intelligent Systems, Knoxville, pp. 432–440 (1986)
Graymala-Busse, J.W., Sedelow Jr., W.A.: On Rough Sets and Information System Homomorphism. Bull. Pol. Acad. Sci. Tech. Sci. 36, 233–239 (1988)
Li, D.Y., Ma, Y.C.: Invariant Characers of Information Systems under Some Homomorphisms. Information Sciences 129, 211–220 (2000)
Lin, T.Y.: Neighborhood Systems and Relational Database. In: Proceedings of 1988 ACM Sixteenth Annual ComputerScience Conference, pp. 23–25 (1988)
Pedrycz, W., Vukovich, G.: Granular Worlds: Representation and Communication Problems. International Journal of Intelligent Systems 15, 1015–1026 (2000)
Pagliani, P.: Transforming Information Systems. In: Proceedings of the 10th International Conference on Rough Sets, Fuzzy Sets, Data Mining and Granular Computing, Canada, pp. 660–670 (2005)
Slezak, D.: Searching for Dynamic Reducts in Inconsistent Decision Tables. In: Proceedings of IPMU 1998, France, pp. 1362–1369 (1998)
Wang, C.Z., Wu, C.X., Chen, D.G.: A Systematic Study on Attribute Reduction with Rough Sets Based on General Binary Relations. Information Sciences 178, 2237–2261 (2008)
Wang, X., Tsang, E.C.C., Zhao, S.Y., Chen, D.G., Yeung, D.S.: Learning Fuzzy Rules from Fuzzy Samples Based on Rough Set Technique. Information Sciences 177, 4493–4514 (2007)
Wang, C., Wu, C., Chen, D., Du, W.: Some Properties of Relation Information Systems under Homomorphisms. Applied Mathematics Letters 21, 940–945 (2008)
Wu, W.Z., Mi, J.S., Zhang, W.X.: Generalized Fuzzy Rough Sets. Information Sciences 151, 263–282 (2003)
Yeung, D.S., Chen, D.G., Tsang, E., Lee, J., Wang, X.Z.: On the Generalization of Fuzzy Rough Sets. IEEE Transactions on Fuzzy Systems 13, 343–361 (2005)
Zadeh, L.A.: The Concept of a Linguistic Variable and its Applications in Approximate Reasoning. Information Sciences 8, 199–251 (1975)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wang, C., Du, W. (2009). Some Invariant Properties of Fuzzy Information Systems under Homomorphism. In: Wen, P., Li, Y., Polkowski, L., Yao, Y., Tsumoto, S., Wang, G. (eds) Rough Sets and Knowledge Technology. RSKT 2009. Lecture Notes in Computer Science(), vol 5589. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02962-2_37
Download citation
DOI: https://doi.org/10.1007/978-3-642-02962-2_37
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02961-5
Online ISBN: 978-3-642-02962-2
eBook Packages: Computer ScienceComputer Science (R0)