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Soft Methods for Integrated Uncertainty Modelling pp 129–135Cite as

A Note on Random Upper Semicontinuous Functions

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Part of the book series: Advances in Soft Computing ((AINSC,volume 37))

Abstract

This note aims at presenting the most general framework for a class U of random upper semicontinuous functions, namely random elements whose sample paths are upper semicontinuous (u.s.c.) functions, defined on some locally compact, Hausdorff and second countable base space, extending Matheron’s framework for random closed sets. It is shown that while the natural embedding process does not provide compactness for U, the Lawson topology does.

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References

  1. Beer, G. (1993), Topologies on Closed and Closed Convex Sets, Kluwer Academic, Dordrecht.

    MATH  Google Scholar 

  2. Billingsley, P. (1968), Convergence of Probability Measures, J.Wiley, New York.

    MATH  Google Scholar 

  3. Colubi, A., Dominguez-Menchero, Lopez-Diaz, M. and Ralescu, D. (2002), A D[0,1] representation of random upper semicontinuous functions, Proc. Amer. Math. Soc. 130(11), 3237–3242.

    Article  MATH  MathSciNet  Google Scholar 

  4. Dudley, R. (1989), Real Analysis and Probability,Wadsworth and Brooks/Cole, Belmon.

    MATH  Google Scholar 

  5. Gierz, G., Hofmann, K. H., Keimeil, K., Lawson, J. D., Mislove, M.W. and Scott, D. S. (2003), Continuous Lattices and Domains. Cambridge Univ. Press, Cambridge, UK.

    MATH  Google Scholar 

  6. Li, S., Ogura, Y. and Kreinovich, V. (2002), Limit Theorems and Applications of Set-Valued and Fuzzy Set-Valued Random Variables, Kluwer Academic, Dordreccht.

    Google Scholar 

  7. Matheron, G. (1975), Random Sets and Integral Geometry, J.Wiley, New York.

    MATH  Google Scholar 

  8. Molchanov, I. (2005), Theory of Random Sets, Springer-Verlag.

    Google Scholar 

  9. Nguyen, H. T. (2005), On modeling of perception-based information for intelligent technology and statistics, J. of Taiwan Intelligent Technology and Applied Statistics 3(2), 25–43.

    Google Scholar 

  10. Nguyen, H. T. (2006), An Introduction to Random Sets, Chapman and Hall/CRC.

    Google Scholar 

  11. Norberg, T. (1992), On the existence of ordered coupling of random sets-with applications, Israel Journal of Mathematics (77), 241–264.

    Google Scholar 

  12. Ogura, Y. and Li, S. (2005), On limit theorems for random fuzzy sets including large deviation principles, In Soft Methodology and Random Information Systems (Lopez-Dias, M. et al, eds.), Springer-Verlag, 32–44.

    Google Scholar 

  13. Teran, P. (2005), A large deviation principle for random upper semicontinuous functions, Proc. Amer. Math. Soc. 134(2), 571–580.

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, New Mexico State University Las Cruces, 88003-8001, NM, USA

    Hung T. Nguyen & Yukio Ogura

Authors
  1. Hung T. Nguyen
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  2. Yukio Ogura
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  3. Santi Tasena
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  4. Hien Tran
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Editor information

Editors and Affiliations

  1. AI Group Department of Engineering Mathematics, University of Bristol, BS8 1TR, Bristol, UK

    Jonathan Lawry

  2. Statistics and Operations Research, Rey Juan Carlos University, C-Tulip˙n s/n MÛstoles28933, Spain

    Enrique Miranda

  3. Intelligent Systems Group Department of Electronics & Computer Science, University of Santiago de Compostela Santiago de Compostela, Spain

    Alberto Bugarin

  4. Department of Applied Mathematics, Beijing University of Technology, 100022, Beijing, P.R. China

    Shoumei Li

  5. Dpto. Estadistica e I.O y D.M. Calle Calvo Sotelo s/n, Universiad de Oviedo Fac. Ciencias, 33071, Oviedo, Spain

    Maria Angeles Gil

  6. Systems Research Institute Polish Academy of Sciences, Newelska 6, 01-447, Warsaw, Poland

    Przemys aw Grzegorzewski

  7. Systems Research Institute Polish Academy of Sciences, Newelska 6, 01-447, Warsaw, Poland

    Olgierd Hyrniewicz

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© 2006 Springer

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Nguyen, H.T., Ogura, Y., Tasena, S., Tran, H. (2006). A Note on Random Upper Semicontinuous Functions. In: Lawry, J., et al. Soft Methods for Integrated Uncertainty Modelling. Advances in Soft Computing, vol 37. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-34777-1_17

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  • DOI: https://doi.org/10.1007/3-540-34777-1_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-34776-7

  • Online ISBN: 978-3-540-34777-4

  • eBook Packages: EngineeringEngineering (R0)

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