Abstract
In the framework of classification, the rough fuzzy set (RFS) deal with the fuzzy decision tables with discrete conditional attributes and fuzzy decision attribute. However, in many applications, the conditional attributes are often real-valued. In order to deal with this problem, this paper extends the RFS model to tolerance RFS, The definitions of the tolerance rough fuzzy set approximation operators are given, and their properties are investigated.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
References
Zadeh, L.A.: Fuzzy sets. Inform. Control 8, 338–353 (1965)
Pawlak, Z.: Rough sets. International Journal of Information and Computer Sciences 11(5), 341–356 (1982)
Zimmermann, H.J.: Fuzzy set theory. Journal of Advanced Review 2, 317–332 (2010)
Shen, Q., Jensen, R.: Rough Sets, their Extensions and Applications. International Journal of Automation and Computing 4(1), 1–12 (2007)
Dubois, D., Prade, H.: Rough fuzzy sets and fuzzy rough sets. International Journal of General Systems 17, 191–208 (1990)
Kuncheva, L.I.: Fuzzy rough sets: application to feature selection. Fuzzy Sets and Systems 51(2), 147–153 (1992)
Nanda, S.: Fuzzy rough sets. Fuzzy Sets and Systems 45, 157–160 (1992)
Yao, Y.Y.: Combination of rough and fuzzy sets based on \(\alpha \)-level sets. In: Lin, T.Y., Cercone, N. (eds.) Rough Sets and Data Mining: Analysis for Imprecise Data, pp. 301–321. Kluwer Academic Publishers, Boston (1997)
Yeung, D.S., Chen, D.G., Tsang, E.C.C., et al.: On the generalization of fuzzy rough sets. IEEE Transactions on Fuzzy Systems 13(3), 343–361 (1992)
Skowron, A.: Tolerance approximation spaces. Fundamenta Informaticae 27(2–3), 245–253 (1996)
Parthaláin, N.M., Shen, Q.: Exploring the boundary region of tolerance rough sets for feature selection. Pattern Recognition 42, 655–667 (2009)
Parthaláin, N.M., Shen, Q., Jensen, R.: A distance measure approach to exploring the rough set boundary region for attribute reduction. IEEE Transactions on Knowledge and Data Engineering 22, 306–317 (2010)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Zhang, Y., Zhai, J., Zhang, S. (2014). Tolerance Rough Fuzzy Approximation Operators and Their Properties. In: Wang, X., Pedrycz, W., Chan, P., He, Q. (eds) Machine Learning and Cybernetics. ICMLC 2014. Communications in Computer and Information Science, vol 481. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-45652-1_38
Download citation
DOI: https://doi.org/10.1007/978-3-662-45652-1_38
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-45651-4
Online ISBN: 978-3-662-45652-1
eBook Packages: Computer ScienceComputer Science (R0)