Abstract
We discuss the problem of measuring the quality of decision support (classification) system that involves granularity. We put forward the proposal for such quality measure in the case when the underlying granular system is based on rough and fuzzy set paradigms. We introduce the notion of approximation, loss function, and empirical risk functional that are inspired by empirical risk assessment for classifiers in the field of statistical learning.
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.
Similar content being viewed by others
References
Warwick, B. (ed.): The Handbook of Risk. John Wiley & Sons, New York (2003)
Bostrom, A., French, S., Gottlieb, S. (eds.): Risk Assessment, Modeling and Decision Support. Risk, Governance and Society, vol. 14. Springer, Heidelberg (2008)
Vapnik, V.: Statisctical Learning Theory. John Wiley & Sons, New York (1998)
Berger, J.O.: Statistical Decision Theory and Bayesian Analysis, 2nd edn. Springer, New York (1985)
Szczuka, M.: Towards approximation of risk. In: Chan, C.-C., Grzymala-Busse, J.W., Ziarko, W.P. (eds.) RSCTC 2008. LNCS (LNAI), vol. 5306, pp. 320–328. Springer, Heidelberg (2008)
Szczuka, M.S.: Approximation of loss and risk in selected granular systems. In: Sakai, H., Chakraborty, M.K., Hassanien, A.E., Slezak, D., Zhu, W. (eds.) RSFDGrC 2009. LNCS, vol. 5908, pp. 168–175. Springer, Heidelberg (2009)
Skowron, A., Szczuka, M.S.: Toward interactive computations: A rough-granular approach. In: Advances in Machine Learning II. SCI, vol. 263, pp. 23–42. Springer, Heidelberg (2010)
Pedrycz, W., Skowron, A., Kreinovich, V. (eds.): Handbook of Granular Computing. John Wiley & Sons, New York (2007)
Zadeh, L.: Fuzzy sets and information granularity. In: Gupta, M., Ragade, R., Yager, R. (eds.) Advances in Fuzzy Set Theory and Application, pp. 3–18. North-Holland Publishing Co., Amsterdam (1979)
Vapnik, V.: Principles of risk minimization for learning theory. In: Proceedings of NIPS, pp. 831–838 (1991)
Pawlak, Z.: Rough Sets. Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dordrecht (1991)
Pawlak, Z.: Rough sets, rough functions and rough calculus. In: Pal, S.K., Skowron, A. (eds.) Rough Fuzzy Hybridization: A New Trend in and Decision Making, pp. 99–109. Springer, Singapore (1999)
Halmos, P.: Measure Theory. Springer, Berlin (1974)
Höeppner, F., Klawonn, F.: Systems of information granules. In: [8], pp. 187–203
Yager, R.R., Filev, D.P.: Essentials of fuzzy modeling and control. John Wiley & Sons, Chichester (1994)
Skowron, A., Synak, P.: Complex patterns. Fundamenta Informaticae 60(1-4), 351–366 (2004)
Jankowski, A., Peters, J.F., Skowron, A., Stepaniuk, J.: Optimization in discovery of compound granules. Fundamenta Informaticae 85, 249–265 (2008)
Kleinberg, J., Papadimitriou, C., Raghavan, P.: A microeconomic view of data mining. Data Mining and Knowledge Discovery 2, 311–324 (1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Szczuka, M. (2011). Risk Assessment in Granular Environments. In: Peters, J.F., Skowron, A., Chan, CC., Grzymala-Busse, J.W., Ziarko, W.P. (eds) Transactions on Rough Sets XIII. Lecture Notes in Computer Science, vol 6499. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18302-7_8
Download citation
DOI: https://doi.org/10.1007/978-3-642-18302-7_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-18301-0
Online ISBN: 978-3-642-18302-7
eBook Packages: Computer ScienceComputer Science (R0)