Abstract
In this paper, to deal with practical situations where a fuzzy classification must be approximated by available knowledge expressed in terms of a Pawlak’s approximation space, we investigate an extension of approximation quality measure to a fuzzy classification aimed at providing a numerical characteristic for such situations. Furthermore, extensions of related coefficients such as the precision measure and the significance measure are also discussed. A simple example is given to illustrate the proposed notions.
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
Baldwin, J.F.: The management of fuzzy and probabilistic uncertainties for knowledge based systems. In: Shapiro, S.A. (ed.) The Encyclopaedia of AI, Wiley, New York (1992)
Banerjee, M., Pal, S.K.: Roughness of a fuzzy set. Infor. Sci. 93, 235–246 (1996)
Chen, S.M., Huang, C.M.: Generating weighted fuzzy rules from relational database systems for estimating null values using genetic algorithms. IEEE Transactions on Fuzzy Systems 11, 495–506 (2003)
De Luca, A., Termini, S.: A definition of a nonprobabilistic entropy in the setting of fuzzy set theory. Information and Control 20, 301–312 (1972)
Dubois, D., Jaulent, M.-C.: A general approach to parameter evaluation in fuzzy digital pictures. Pattern Recognition Letters 6, 251–259 (1987)
Dubois, D., Prade, H.: On several representations of an uncertain body of evidence. In: Gupta, M.M., Sanchez, E. (eds.) Fuzzy Information and Decision Processes, pp. 167–181. North-Holland, Amsterdam (1982)
Dubois, D., Prade, H.: Rough fuzzy sets and fuzzy rough sets. Inter. J. of Gen. Sys. 17, 191–209 (1990)
Gediga, G., Düntsch, I.: Rough approximation quality revisited. Artificial Intelligence 132, 219–234 (2001)
Goodman, I.R.: Fuzzy sets as equivalence classes of random sets. In: Yager, R. (ed.) Fuzzy Set and Possibility Theory, pp. 327–342. Pergamon Press, Oxford (1982)
Huynh, V.N., Nakamori, Y.: An approach to roughness of fuzzy sets. In: Proceedings of the FUZZ-IEEE 2004 (2004)
Huynh, V.N., Nakamori, Y.: A roughness measure for fuzzy sets. Infor. Sci. 173, 255–275 (2005)
Pal, S.K., Skowron, A. (eds.): Rough Fuzzy Hybridization: New Trends in Decision Making. Springer, Singapore (1999)
Pawlak, Z.: Rough sets. Inter. J. of Comp. and Infor. Sci. 11, 341–356 (1982)
Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Boston (1991)
Wygralak, M.: Rough sets and fuzzy sets: some remarks on interrelations. Fuzzy Sets and Systems 29, 241–243 (1989)
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 of Imprecise Data, pp. 301–321. Kluwer Academic Publishers, Dordrecht (1997)
Yao, Y.Y.: A comparative study of fuzzy sets and rough sets. Infor. Sci. 109, 227–242 (1998)
Zadeh, L.A.: Fuzzy sets. Information and Control 8, 338–353 (1965)
Zimmermann, H.-J.: Fuzzy Set Theory and Its Applications, 2nd edn. Kluwer Academic Publishers, Dordrecht (1991)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Huynh, VN., Murai, T., Ho, TB., Nakamori, Y. (2005). An Extension of Rough Approximation Quality to Fuzzy Classification. In: Ślęzak, D., Wang, G., Szczuka, M., Düntsch, I., Yao, Y. (eds) Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing. RSFDGrC 2005. Lecture Notes in Computer Science(), vol 3641. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11548669_39
Download citation
DOI: https://doi.org/10.1007/11548669_39
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28653-0
Online ISBN: 978-3-540-31825-5
eBook Packages: Computer ScienceComputer Science (R0)