Abstract
We introduce the notion of a fractal in an information system and we define a dimension function of a fractal in an information system parallel to the Minkowski dimension in Euclidean spaces. We prove basic properties of this new dimension.
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References
M. F. Barnsley, Fractals Everywhere, Academic Press, 1988.
P. Billingsley, Ergodic Theory and Information, John Wiley, 1985.
C. Carátheodory, Ueber das lineare Mass von Punktmenge eine Verallgemeinerung des Langenbegriffs, Nach.Gessell.Wiss.Göttingen, 1914, 406–426.
K. J. Falconer, The Geometry of Fractal Sets, Cambridge U. Press, 1990.
K. J. Falconer, Fractal Geometry. Mathematical Foundations and Applications, Wiley and Sons, 1990.
F. Hausdor., Dimension und ausseres Mass, Math.Annalen, 79, 1919, 157–179.
W. Hurewicz and H. Wallman, Dimension Theory, Princeton U. Press, 1941.
J. E. Hutchinson, Fractals and self-similarity, Indiana Math. Journal, 30, 1981, 713–747.
B. Mandelbrot, Les Objects Fractals: Forme, Hasard et Dimension, Flammarion, Paris, 1975.
Z. Pawlak, Rough Sets: Theoretical Aspects of Reasoning about Data, Kluwer, 1991.
L. Polkowski, Approximation mathematical morphology. Rough set approach, in: A. Skowron, S. K. Pal (eds.), Rough Fuzzy Hybridization. A New Trend in Decision-Making, Springer Verlag Singapore, 1999, 151–162.
L. Polkowski, Mathematical morphology of rough sets, Bull. Polish Acad. Sci. Math., 41, 1993, 241–273.
L. Polkowski, S. Tsumoto, and T. Y. Lin, (eds.), Rough Set Methods and Applications. New Developments in Knowledge Discovery in Information Systems, Physica Verlag/Springer Verlag, 2000.
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Polkowski, L. (2001). On Fractals in Information Systems: The First Step. In: Terano, T., Ohsawa, Y., Nishida, T., Namatame, A., Tsumoto, S., Washio, T. (eds) New Frontiers in Artificial Intelligence. JSAI 2001. Lecture Notes in Computer Science(), vol 2253. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45548-5_31
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DOI: https://doi.org/10.1007/3-540-45548-5_31
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