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Connections between Statistical Depth Functions and Fuzzy Sets

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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

We show that two probabilistic interpretations of fuzzy sets via random sets and large deviation principles have a common feature: they regard the fuzzy set as a depth function of a random object. Conversely, some depth functions in the literature can be regarded as the fuzzy sets of central points of appropriately chosen random sets.

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Authors and Affiliations

  1. Escuela de Ingeniería Técnica Industrial, Departamento de Estadística, e Investigación Operativa y Didáctica de la Matemática, Universidad de Oviedo, E-33071, Gijón, Spain

    Pedro Terán

Authors
  1. Pedro Terán
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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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Terán, P. (2010). Connections between Statistical Depth Functions and Fuzzy Sets. 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_75

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  • DOI: https://doi.org/10.1007/978-3-642-14746-3_75

  • 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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