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Uncertain Choices: A Comparison of Fuzzy and Probabilistic Approaches

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Aggregation Functions in Theory and in Practise

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 228))

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Abstract

Choices among alternatives in a set can be expressed in three different ways: by means of choice functions, by means of preference relations or using choice probabilities. The connection between the two first formalizations has been widely studied in the literature, both in the crisp or classical context and in the setting of fuzzy relations. However, the connection between probabilistic choice functions and fuzzy choice functions seems to have been forgotten and as far as we know, no literature can be found about it.

In this contribution we focus on the comparison of both types of choice functions. We provide a way to obtain the fuzzy choice function from the probabilistic choice function and the other way around. Moreover,we can prove that under Luce’s Choice Axiom the fuzzy choice function derived from the probabilistic choice function is G-normal.

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Authors and Affiliations

  1. Dept. of Statistics and Operational Research, University of Oviedo, E-33071, Oviedo, Spain

    Davide Martinetti, Susana Montes & Susana Díaz

  2. Dept. of Mathematical Modelling, Statistics and Bioinformatics, Ghent University, Coupure links 653, B-9000, Ghent, Belgium

    Bernard De Baets

Authors
  1. Davide Martinetti
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  2. Susana Montes
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  3. Susana Díaz
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  4. Bernard De Baets
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Corresponding author

Correspondence to Davide Martinetti .

Editor information

Editors and Affiliations

  1. Department of Automatica y Computacion, Universidad Publica de Navarra, Pamplona, Spain

    Humberto Bustince

  2. Department of Automatica y Computacion, Universidad Publica de Navarra, Pamplona, Spain

    Javier Fernandez

  3. Department of Mathematics and, Slovak University of Technology, Bratislava, Slovakia

    Radko Mesiar

  4. Department of Computer Science, Universidad de Alcalá de Henares, Madrid, Spain

    Tomasa Calvo

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Martinetti, D., Montes, S., Díaz, S., De Baets, B. (2013). Uncertain Choices: A Comparison of Fuzzy and Probabilistic Approaches. In: Bustince, H., Fernandez, J., Mesiar, R., Calvo, T. (eds) Aggregation Functions in Theory and in Practise. Advances in Intelligent Systems and Computing, vol 228. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39165-1_28

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  • DOI: https://doi.org/10.1007/978-3-642-39165-1_28

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39164-4

  • Online ISBN: 978-3-642-39165-1

  • eBook Packages: EngineeringEngineering (R0)

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