Abstract
This chapter elaborates on the conceptual and algorithmic framework of information granulation. We provide a detailed algorithm of information granulation that is cast as an optimization problem reconciling two conflicting design criteria namely a specificity of information granules and their experimental relevance (coverage of numeric data). The resulting information granules are formalized in the language of set theory (interval analysis) and maximize local information density. The uniform treatment of data points and data intervals (hyperboxes) allows for a recursive application of the algorithm. We assess the quality of information granules through the application of FCM clustering (Fuzzy C-Means) algorithm. The algorithm is applied to two-dimensional synthetic data and experimental traffic data.
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
Bargiela, A. (2001), Interval and Ellipsoidal Uncertainty Models, in W. Pedrycz (ed.) Granular Computing, Springer Verlag, 23–57.
Bargiela, A., Pedrycz, W. (2002), Recursive information granulation: Aggregation and interpretation issues, IEEE Trans, on Syst. Man and Cybernetics, to appear.
Berthold, M., Huber, K.-P. (1999), Constructing fuzzy graphs from examples, Intelligent Data Analysis, 3(1), pp.37–54.
Bezdek, J.C. (1981), Pattern Recognition with Fuzzy Objective Function Algorithms, Plenum Press, N. York.
Box, G.E., Jenkins, G.M. (1970), Time Series Analysis: Forecasting and Control, Holden Day, San Francisco.
Chiu, S. (1996), Method and software for extracting fuzzy classification rules by subtractive clustering, NAFIPS, 1996, pp. 461–465.
Cios, K., Pedrycz, W., Swiniarski, R. 1998), Data Mining Techniques, Kluwer Academic Publishers, Boston.
Claramunt, C., Jiang, B., Bargiela, A. (2000), A new framework for the integration, analysis and visualization of urban traffic data within geographic information systems, Transportation Research-Part C, 167–184.
Das, et al., (1998), Rule discovery from time series, Proc. of 4 th Int. Conf. on Knowledge Discovery and Data Mining, 16–22.
Davis, E. (1987), Constraint propagation with interval labels, Artificial Intelligence, 24, 347–410.
Everitt, B.S. (1974), Cluster Analysis, Heinemann, Berlin.
Gabrys, B., Bargiela, A. (2000), General fuzzy min-max neural network for clustering and classification, IEEE Trans. on Neural Networks, vol.11, no.3, 769–783.
Hata, Y., Mukaidono, M. (1999), On some classes of fuzzy information granularity and their representations, ISMVL′99, Japan, 288–293.
Herera, F., Martinez, L. (2001), A model based on linguistic 2-tuples for dealing with multigranular hierarchical linguistic contexts in multi-expert decision making, IEEE Trans. on Systems Man and Cybernetics, SMC-B, vol. 31, 2, 227–234.
Hoppner, F., Klawonn, F., Kruse, R., Runkler, T. (1999), Fuzzy Cluster Analysis, J. Wiley, Chicester.
Huber, P.J. (1981), Robust Statistics, J. Wiley, New York.
Kandel, A. (1986), Fuzzy Mathematical Techniques with Applications, Addison-Wesley, Reading, MA.
Kenneth, D.L., Jeffrey, L.A. (1990), Robust Regression. Analysis and Applications, Marcel Dekker, New York.
Kosonen, I., Bargiela, A., Claramunt, C. (1998), A distributed information system for traffic control, Proc. l0th European Simulation Symposium (ESS), 355–361.
Kosonen, I., Bargiela, A. (2001), Real-time environment for micro-simulation of urban traffic, European simulation Symposium ESS′2001, Marseille, Oct. 2001, 382–386.
Kuipers, B.J. (1984), Qualitative Reasoning, MIT Press, Cambridge, MA.
Madisetti, V.K., Williams, D.B. (1998), The Digital Signal Processing Handbook, CRC Press/IEEE Press, Boca Raton.
Mani, I., Maybury M.T. (eds.) (1999), Advances in Automatic Text Summarization, MIT Press, Cambridge, MA.
Moore, R.E. (1966), Interval Analysis, Prentice Hall, Englewood Cllifs, NJ.
Moore, R.E. (ed.) (1988), Reliability in Computing: The Role of Interval Methods, Academic Press, N. York.
Pawlak, Z., (1991), Rough Sets: Theoretical Aspects of Reasoning about Data, Kluwer Academic, Dordrecht.
Oppenheim, A.V., Wilsky, A.S. (1983), Signals and Systems, Prentice Hall, Englewood Cliffs, NJ.
Oppenheim, A.V., Schafer, R.W. (1989), Discrete-Time Signal Processing, Englewood Cliffs.
Pedrycz, W. (1997), Computational Intelligence: An Introduction, CRC Press, Boca Raton.
Pedrycz, W., Gomide, F. (1998), An Introduction to Fuzzy Sets, Cambridge, MIT Press, Cambridge, MA.
Pedrycz, W. (2001), Fuzzy equalization in the construction of fuzzy sets, Fuzzy Sets and Systems, 119(2), 321–327.
Pedrycz, W., Bargiela, A. (2001), Information granulation: A search for data structures, Knowledge-based Engineering Systems KES 2001, Osaka, October 2001, 1147–1151.
Sowa, J.F. (2000), Knowledge Representation. Logical, Philosophical and Computational Foundations, Brooks/Cole, Pacific Grove.
Thiele, H. (2000), On algebraic foundations of information granulation III, Investigating the HATA-MUKAIDONO approach, ISMVL 2000, USA, 2000.
Zadeh, LA. (1979), Fuzzy sets and information granularity, In: M.M. Gupta, R.K. Ragade, R.R. Yager, eds., Advances in Fuzzy Set Theory and Applications, North Holland, Amsterdam, 3–18.
Zadeh, LA. (1996), Fuzzy logic = Computing with words, IEEE Trans. on Fuzzy Systems, vol. 4, 2, 103–111.
Zadeh, L.A. (1997), Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic, Fuzzy Sets and Systems, 90, 111–117.
Zadeh, LA. (1999), From computing with numbers to computing with words-from manipulation of measurements to manipulation of perceptions, IEEE Trans. on Circuits and Systems, 45, 105–119.
Zadeh, LA., Kacprzyk, J. (1999), Computing with words in Information/Intelligent Systems, Studies in Fuzziness and Soft Computing series, Vol. 33 & 34, Physica-Verlag.
Zimmermann, HJ. (1985), Fuzzy Set Theory and Its Applications, Kluwer Academic Publishers, Dordrecht.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer Science+Business Media New York
About this chapter
Cite this chapter
Bargiela, A., Pedrycz, W. (2003). Recursive Information Granulation. In: Granular Computing. The Springer International Series in Engineering and Computer Science, vol 717. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-1033-8_7
Download citation
DOI: https://doi.org/10.1007/978-1-4615-1033-8_7
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-5361-4
Online ISBN: 978-1-4615-1033-8
eBook Packages: Springer Book Archive