Abstract
Ever since the first hybrid fuzzy rough set model was proposed in the early 1990’s, many researchers have focused on the definition of the lower and upper approximation of a fuzzy set by means of a fuzzy relation. In this paper, we review those proposals which generalize the logical connectives and quantifiers present in the rough set approximations by means of corresponding fuzzy logic operations. We introduce a general model which encapsulates all of these proposals, evaluate it w.r.t. a number of desirable properties, and refine the existing axiomatic approach to characterize lower and upper approximation operators.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Zadeh, L.A.: Fuzzy sets. Information and Control 8, 338–353 (1965)
Pawlak, Z.: Rough sets. International Journal of Computer and Information Sciences 11(5), 341–356 (1982)
Dubois, D., Prade, H.: Rough fuzzy sets and fuzzy rough sets. International Journal of General Systems 17, 191–209 (1990)
Jensen, R., Shen, Q.: Fuzzy-rough sets assisted attribute selection. IEEE Transactions on Fuzzy Systems 15(1), 73–89 (2007)
Tsang, E., Chen, D., Yeung, D., Wang, X., Lee, J.: Attributes reduction using fuzzy rough sets. IEEE Transactions on Fuzzy Systems 16(5), 1130–1141 (2008)
Cornelis, C., Hurtado Martín, G., Jensen, R., Ślęzak, D.: Attribute selection with fuzzy decision reducts. Information Sciences 180(2), 209–224 (2010)
Verbiest, N., Cornelis, C., Herrera, F.: FRPS: A fuzzy rough prototype selection method. Pattern Recognition 46(10), 2770–2782 (2013)
Morsi, N., Yakout, M.: Axiomatics for fuzzy rough set. Fuzzy Sets Systems 100, 327–342 (1998)
Radzikowska, A., Kerre, E.: A comparative study of fuzzy rough sets. Fuzzy Sets and Systems 126, 137–155 (2002)
Wu, W., Mi, J., Zhang, W.: Generalized fuzzy rough sets. Information Sciences 151, 263–282 (2003)
Mi, J., Zhang, W.: An axiomatic characterization of a fuzzy generalization of rough sets. Information Sciences 160, 235–249 (2004)
Wu, W., Zhang, W.: Constructive and axiomatic approaches of fuzzy approximation operators. Information Sciences 159, 233–254 (2004)
Wu, W., Leung, Y., Mi, J.: On characterizations of (I, T)-fuzzy rough approximation operators. Fuzzy Sets and Systems 154, 76–102 (2005)
Pei, D.: A generalized model of fuzzy rough sets. International Journal of General Systems 34(5), 603–613 (2005)
Yeung, D., Chen, D., Tsang, E., Lee, J., Xizhao, W.: On the generalization of fuzzy rough sets. IEEE Transactions on Fuzzy Systems 13(3), 343–361 (2005)
De Cock, M., Cornelis, C., Kerre, E.: Fuzzy rough sets: the forgotten step. IEEE Transactions on Fuzzy Systems 15(1), 121–130 (2007)
Mi, J., Leung, Y., Zhao, H., Feng, T.: Generalized fuzzy rough sets determined by a triangular norm. Information Sciences 178, 3203–3213 (2008)
Hu, Q., Zhang, L., Chen, D., Pedrycz, W., Yu, D.: Gaussian kernel based fuzzy rough sets: model, uncertainty measures and applications. International Journal of Approximate Reasoning 51, 453–471 (2010)
Slowinski, R., Vanderpooten, D.: Similarity relations as a basis for rough approximations. In: Wang, P. (ed.) Advances in Machine Intelligence and Soft Computing, pp. 17–33 (1997)
Slowinski, R., Vanderpooten, D.: Generalized rough set models. In: Polkowski, L., Skowron, A. (eds.) Rough Sets in Knowledge Discovery, pp. 286–318 (1998)
Fodor, J.: Left-continuous t-norms in fuzzy logic: an overview. Journal of Applied Sciences at Budapest Tech Hungary 1(2) (2004)
Radzikowska, A., Kerre, E.: Characterisation of main classes of fuzzy relations using fuzzy modal operators. Fuzzy Sets and Systems 152, 223–247 (2005)
Salido, J.M.F., Murakami, S.: Rough set analysis of a general type of fuzzy data using transitive aggregations of fuzzy similarity relations. Fuzzy Sets and Systems 139, 635–660 (2003)
Mieszkowicz-Rolka, A., Rolka, L.: Fuzzy rough approximations of process data. International Journal of Approximate Reasoning 49, 301–315 (2008)
Cornelis, C., De Cock, M., Radzikowska, A.M.: Vaguely quantified rough sets. In: An, A., Stefanowski, J., Ramanna, S., Butz, C.J., Pedrycz, W., Wang, G. (eds.) RSFDGrC 2007. LNCS (LNAI), vol. 4482, pp. 87–94. Springer, Heidelberg (2007)
Zhao, S., Tsang, E.C.C., Chen, D.: The model of fuzzy variable precision rough sets. IEEE Transactions on Fuzzy Systems 17(2), 451–467 (2009)
Hu, Q., An, S., Yu, D.: Soft fuzzy rough sets for robust feature evaluation and selection. Information Sciences 180, 4384–4400 (2010)
Cornelis, C., Verbiest, N., Jensen, R.: Ordered weighted average based fuzzy rough sets. In: Yu, J., Greco, S., Lingras, P., Wang, G., Skowron, A. (eds.) RSKT 2010. LNCS, vol. 6401, pp. 78–85. Springer, Heidelberg (2010)
Hu, Q., Zhang, L., An, S., Zhang, D., Yu, D.: On robust fuzzy rough set models. IEEE Transactions on Fuzzy Systems 20(4), 636–651 (2012)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
D’eer, L., Verbiest, N., Cornelis, C., Godo, L. (2013). Implicator-Conjunctor Based Models of Fuzzy Rough Sets: Definitions and Properties. In: Ciucci, D., Inuiguchi, M., Yao, Y., Ślęzak, D., Wang, G. (eds) Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing. RSFDGrC 2013. Lecture Notes in Computer Science(), vol 8170. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41218-9_18
Download citation
DOI: https://doi.org/10.1007/978-3-642-41218-9_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-41217-2
Online ISBN: 978-3-642-41218-9
eBook Packages: Computer ScienceComputer Science (R0)