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Fractal Analysis Approaches to Granular Computing

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Rough Sets (IJCRS 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10313))

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Abstract

Granular computing has emerged as one of the fastest growing information processing paradigms in computational intelligence and human-centric systems. Fractal analysis has equally gained ground in understanding complex phenomena. This article examines and analyzes fractal analysis and its close relationship with granular computing. We argue that fractal analysis can be viewed as special granular computing approaches especially from methodology and mechanism point of views. In this article, we also bring out the granular structure existing in a fractal analysis application. The aim of this research is to demonstrate fractal analysis as a granular computing approach based on these findings.

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References

  1. Addison, P.S.: Fractals and Chaos: An Illustrated Course. CRC Press, Boca Raton (1997)

    MATH  Google Scholar 

  2. Al-Akaidi, M.: Fractal Speech Processing. Cambridge University Press, Cambridge (2004)

    Book  Google Scholar 

  3. Bargiela, A., Pedrycz, W.: Granular Computing: An introduction. Springer Science and Business Media, Heidelberg (2002)

    MATH  Google Scholar 

  4. Bargiela, A., Pedrycz, W.: Towards a theory of granular computing for human-centered information processing. IEEE Trans. Fuzzy Syst. 16(2), 320–330 (2008)

    Article  Google Scholar 

  5. Barnsley, M.: Fractals Everywhere. UK Academic Press, Cambridge (1998)

    MATH  Google Scholar 

  6. Boeing, G.: Visual analysis of nonlinear dynamical systems: chaos, fractals, self-similarity and the limits of prediction. Systems 4(4), 37 (2016)

    Article  Google Scholar 

  7. Feder, J.: Fractals. Springer Science & Business Media, Heidelberg (2013)

    MATH  Google Scholar 

  8. Kinsner, W.: A unified approach to fractal dimensions. Int. J. Cogn. Inf. Nat. Intell. 1(4), 26–46 (2007)

    Article  Google Scholar 

  9. Klinkenberg, B.: A review of methods used to determine the fractal dimension of linear features. Math. Geosci. 26(1), 23–46 (1994)

    Google Scholar 

  10. Mandelbrot, B.B.: How long is the coast of britain? Statistical self-similarity and fractional dimension. Science 156(3775), 636–638 (1967)

    Article  Google Scholar 

  11. Mandelbrot, B.B., Pignoni, R.: The Fractal Geometry of Nature. WH freeman, New York (1983)

    Book  Google Scholar 

  12. Pedrycz, W., Bargiela, A.: Fuzzy fractal dimensions and fuzzy modeling. Inf. Sci. 153, 199–216 (2003)

    Article  Google Scholar 

  13. Peitgen, H.O., Jürgens, H., Saupe, D.: Chaos and Fractals: New Frontiers of Science. Springer Science & Business Media, Heidelberg (2006)

    MATH  Google Scholar 

  14. Polkowski, L.: On asymptotic properties of rough—set—theoretic approximations. fractal dimension, exact sets, and rough inclusion in potentially infinite information systems. In: Alpigini, J.J., Peters, J.F., Skowron, A., Zhong, N. (eds.) RSCTC 2002. LNCS, vol. 2475, pp. 167–174. Springer, Heidelberg (2002). doi:10.1007/3-540-45813-1_21

    Chapter  MATH  Google Scholar 

  15. Polkowski, L.: On fractal dimension in information systems. Toward exact sets in infinite information systems. Fundamenta Informaticae 50(3–4), 305–314 (2002)

    MathSciNet  MATH  Google Scholar 

  16. Squarcina, L., DeLuca, A., Bellani, M., Brambilla, P., Turkheimer, F., Bertoldo, A.: Fractal analysis of MRI data for the characterization of patients with schizophrenia and bipolar disorder. J. Theor. Biol. 60(4), 1697 (2015)

    Google Scholar 

  17. Vuduc, R.: Image segmentation using fractal dimension. Report on GEOL 634 (1997)

    Google Scholar 

  18. Yao, J.T.: Recent developments in granular computing: a bibliometrics study. In: IEEE International Conference on Granular Computing, pp. 74–79 (2008)

    Google Scholar 

  19. Yao, J.T.: Novel Developments in Granular Computing: Applications for Advanced Human Reasoning and Soft Computation: Applications for Advanced Human Reasoning and Soft Computation. IGI Global, Hershey (2010)

    Google Scholar 

  20. Yao, J.T., Vasilakos, A.V., Pedrycz, W.: Granular computing: perspectives and challenges. IEEE Trans. Cybern. 43(6), 1977–1989 (2013)

    Article  Google Scholar 

  21. Yao, Y.Y.: Three perspectives of granular computing. J. Nanchang Inst. Technol. 25(2), 16–21 (2006)

    Google Scholar 

  22. Zadeh, L.A.: Towards a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic. Fuzzy Sets Syst. 90(2), 111–127 (1997)

    Article  MathSciNet  Google Scholar 

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Acknowledgement

This research was partially supported by an NSERC discovery grant.

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Correspondence to JingTao Yao .

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Yao, J., Oladimeji, O.A., Zhang, Y. (2017). Fractal Analysis Approaches to Granular Computing. In: Polkowski, L., et al. Rough Sets. IJCRS 2017. Lecture Notes in Computer Science(), vol 10313. Springer, Cham. https://doi.org/10.1007/978-3-319-60837-2_18

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  • DOI: https://doi.org/10.1007/978-3-319-60837-2_18

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-60836-5

  • Online ISBN: 978-3-319-60837-2

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