Abstract
The approximation theory is studied via rough sets, fuzzy sets and topological spaces (more precisely, Frechet spaces). Rough set theory is a set theory via knowledge bases. This set theory is extended to fuzzy sets and Frechet topological spaces. By these results one can show that the classification preserves the approximation. We also showed that within the approximation theory, fuzzy set and Frechet topology are intrinsically equivalent notions. Finally, we show that even though approximation is a compromised solution, the three theories allow one to draw an exact solution whenever there are adequate approximations. This implies that these three approaches are good approximation theories.
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
Z. Pawlak. Rough sets. - Theoretical aspects of reasoning about data. Kluwer Academic Publishers, 1990.
W. Sierpinski and C. Krieger. General topology. University of Toronto Press, 1956.
Didier Dubois and Henri Prade. Rough fuzzy sets and fuzzy rough sets. In Int. Journal of General Systems, pages 191–209, 1990.
Donlod F. Stanat and David F. McAllister. Discrete Mathematics in Computer Sci ence. Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1977.
Stella Bairamian. Goal search in relational databases. Master’s thesis, California State University, 1989.
T.Y. Lin and S. Bairamian. Neighborhood systems and goal queries. Manuscript, California State University, Northridge, California, 1987.
Z. Pawlak, S.K.M. Wong, and W. Ziarko. Rough sets: Probabilistic versus deterministic approach. In Int. J. Man-Machine Studies, pages 81–95, 1988. Vol. 29.
T.Y. Lin. Neighborhood systems and relational database. In Proceedings of CSC ‘88, 1988.
T.Y. Lin. Topological data models and approximate retrieval and reasoning. Annual ACM Conference, 1989.
T.Y. Lin. Neighborhood systems and approximation in database and knowledge base systems. In Proceedings of the Fourth International Symposium on Methodologies of Intelligent Systems, Poster Session, 1989.
T.Y. Lin, Q. Liu, K.J. Huang, and W. Chen. Rough sets, neighborhood systems and approximation. In Fifth International Symposium on Methodologies of Intelligent Systems,1990. Selected Papers.
T.Y. Lin, Qing Liu, and K.J. Huang. A model of topological reasoning expert system with application to an expert system for computer-aided diagnosis and treatment in acupuncture and moxibustion. In International Symposium on Expert Systems and Neural Network Theory and Application, 1990.
John Kelly. General topology, 1955.
Abraham Kandel. Fuzzy Mathematical Techniques with Applications. Addison - Wesley, Reading, Massachusetts, 1986.
L.A. Zadeh. Fuzzy sets. Information and Control, 8: pages 338–353, 1965.
T.Y. Lin. Probabilistic measure on aggregation. In Proceedings of the 6th Annual Computer Security Application Conference, pages 286–294, Tucson, Arizona, 1990.
T.Y. Lin. “Inference” free multilevel database system. In Proceedings of the Fourth RADC Database Security Workshop, Little Compton, Rhode Island, 1991.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1992 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Lin, T.Y. (1992). Topological and Fuzzy Rough Sets. In: Słowiński, R. (eds) Intelligent Decision Support. Theory and Decision Library, vol 11. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-7975-9_18
Download citation
DOI: https://doi.org/10.1007/978-94-015-7975-9_18
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4194-4
Online ISBN: 978-94-015-7975-9
eBook Packages: Springer Book Archive