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Uncertainty Invariance Transformation in Continuous Case

  • Conference paper
Combining Soft Computing and Statistical Methods in Data Analysis

Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 77))

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Abstract

In this work, a general procedure for transforming a possibility distribution into a probability density function, in the continuous case, is proposed, in a way that the resulting distribution contains the same uncertainty as the original distribution. A significant aspect of this approach is that it makes use of Uncertainty Invariance Principle which is itself a general procedure for going from an initial representation of uncertainty to a new representation.

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References

  1. Baudrit, C., Dubois, D.: Practical representations of incomplete probabilistic knowledge. Comput. Stat. Data An. 51, 86–108 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  2. Chanas, S., Nowakowski, M.: Single value simulation of fuzzy variable. Fuzzy Set Syst. 25, 43–57 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  3. Cover, T., Thomas, J.A.: Elements of Information Theory. John Wiley and Sons, New York (1991)

    Book  MATH  Google Scholar 

  4. De Luca, A., Termini, S.: A definition on a nonprobabilistic entropy in the setting of fuzzy sets theory. Inform. Contr. 20, 301–312 (1972)

    Article  MATH  Google Scholar 

  5. Dubois, D., Prade, H.: On several representations of an uncertain body of evidence. In: Gupta, M.M., Sanchez, E. (eds.) Fuzzy Information and Decision Processes. North-Holland, New York (1982)

    Google Scholar 

  6. Dubois, D., Prade, H., Sandri, S.: On possibility/probability transformations. In: Lowen, R., Roubens, M. (eds.) Fuzzy Logic. Kluwer Academic Publishers, Dordrecht (1993)

    Google Scholar 

  7. Florea, M.C., Jousselme, A.L., Grenier, D., Bossé, E.: Approximation techniques for the transformation of fuzzy sets into random sets. Fuzzy Set Syst. 159, 270–288 (2008)

    Article  MATH  Google Scholar 

  8. Geer, J.F., Klir, G.J.: A mathematical analysis of information preserving transformations between probabilistic and possibilistic formulations of uncertainty. Int. J. Gen. Syst. 20, 143–176 (1992)

    Article  MATH  Google Scholar 

  9. Gupta, C.P.: A note on the transformation of possibilistic information into probabilistic information for investment decision. Fuzzy Set Syst. 56, 175–182 (1993)

    Article  Google Scholar 

  10. Higashi, M., Klir, G.J.: Measures of uncertainty and information based on possibility distributions. Int. J. Gen. Syst. 9, 43–58 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  11. Kapur, J.N.: Measures of information and their applications. John Wiley and Sons, New Delhi (1994)

    MATH  Google Scholar 

  12. Klir, G.J.: A principle of uncertainty and information invariance. Int. J. Gen. Syst. 17, 249–275 (1990)

    Article  MATH  Google Scholar 

  13. Klir, G., Wierman, M.: Uncertainty-Based Information: Elements of Generalized Information Theory. Physica-Verlag, New York (1999)

    MATH  Google Scholar 

  14. Lee, E.S., Li, R.J.: Comparison of fuzzy numbers based on the probability measure of fuzzy events. Comput. Math. Appl. 15, 887–896 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  15. Lee, K.D., Llinas, J.: Hybrid model for intent estimation. In: Proceedings of the Sixth International Conference of Information Fusion, FUSION 2003, Queensland Australia, vol. 1(2), pp. 1215–1222 (2003)

    Google Scholar 

  16. Lee, K.D., Llinas, J., Adleson, R.: Hybrid framework for fusion 2+ in multi-multi air engagement. In: Dasarathy, B.V. (ed.) Proceedings of SPIE Multisensor, Multisource Information Fusion: Architectures, Algorithms and Applications 2005, vol. 5813, pp. 86–95 (2005)

    Google Scholar 

  17. Li, X., Liu, B.: Maximum entropy principle for fuzzy variables. Int. J. Uncertain. Fuzz. 15, 43–52 (2007)

    Article  Google Scholar 

  18. Negi, D.S., Lee, E.S.: Analysis and simulation of fuzzy queues. Fuzzy Set Syst. 46, 321–330 (1992)

    Article  MATH  Google Scholar 

  19. Nuñez, J., Kutalik, Z., Cho, K.H., Wolkenhauer, O.: Level sets and minimum volume sets of probability density functions. Int. J. Approx. Reason. 34, 25–47 (2003)

    Article  MATH  Google Scholar 

  20. Oussalah, M.: On the probability/possibility transformations: a comparative analysis. Int. J. Gen. Syst. 29, 671–718 (2000)

    Article  MATH  Google Scholar 

  21. Rebiasz, B.: Fuzziness and randomness in investment project risk appraisal. Comput. Oper. Res. 34, 199–210 (2007)

    Article  MATH  Google Scholar 

  22. Shannon, C.E.: The mathematical theory of communication. Bell Syst. Tech. J. 27, 379–423 (1948)

    MATH  MathSciNet  Google Scholar 

  23. Wonneberger, S.: Generalization of an invertible mapping between probability and possibility. Fuzzy Set Syst. 64, 229–240 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  24. Yager, R.R.: Entropy and especificity in a mathematical theory of evidence. Int. J. Gen. Syst. 9, 249–260 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  25. Zadeh, L.A.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Set Syst. 1, 3–28 (1978)

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Applied Economic IV, University of the Basque Country, 48015, Bilbao, Spain

    María José Pardo

  2. Department of Business Administration, University of Oviedo, 33204, Gijón, Spain

    David de la Fuente

Authors
  1. María José Pardo
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  2. David de la Fuente
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Editor information

Editors and Affiliations

  1. Research Unit on Intelligent Data Analysis and Graphical Models, European Centre for Soft Computing Edificio Científico-Tecnológico. 3a Planta, C/ Gonzalo Gutiérrez Quirós s/n, 33600, Mieres, Spain

    Christian Borgelt , Gil González-Rodríguez  & Wolfgang Trutschnig ,  & 

  2. Departamento de Estadística e I.O. y D.M., Universidad de Oviedo, Facultad de Ciencias, C/ Calvo Sotelo s/n, 33007, Oviedo, Spain

    María Asunción Lubiano

  3. Departamento de Estadística e I.O. yD.M., Universidad de Oviedo, Facultad de Ciencias, C/ Calvo Sotelo s/n, 33007, Oviedo, Spain

    María Ángeles Gil

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

    Przemysław Grzegorzewski

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

    Olgierd Hryniewicz

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Pardo, M.J., de la Fuente, D. (2010). Uncertainty Invariance Transformation in Continuous Case. In: Borgelt, C., et al. Combining Soft Computing and Statistical Methods in Data Analysis. Advances in Intelligent and Soft Computing, vol 77. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14746-3_61

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  • DOI: https://doi.org/10.1007/978-3-642-14746-3_61

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14745-6

  • Online ISBN: 978-3-642-14746-3

  • eBook Packages: EngineeringEngineering (R0)

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