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Traditional techniques to prove some limit theorems for fuzzy random variables

  • Ana Colubi
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 87)

Abstract

In the last years, some limit theorems for fuzzy random variables have been proven by means of different techniques developed for this purpose. In this work we deal with the cadlag representation of a kind of fuzzy sets to show that these limit results can be also proved by applying well-known techniques in Probability Theory (specifically, the ones which make valid the analogous theorems for D[0, 1]-valued random elements). In this context, we will study a strong law of large numbers (whose proof will suggest a characterization of the uniform convergence) and a strong law of the iterated logarithm. Furthermore, we will check the relationships between these techniques and the ones used by Molchanov to prove a SLLN for the same random elements.

Keywords

Limit Theorem Random Element Iterate Logarithm Fuzzy Random Variable Prove Limit Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Ana Colubi
    • 1
  1. 1.Departamento de Estadística e I.O. y D.M.Universidad de OviedoOviedoSpain

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