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International Conference on Modeling Decisions for Artificial Intelligence

MDAI 2019: Modeling Decisions for Artificial Intelligence pp 52–63Cite as

Fuzzy Confirmation Measures (a)symmetry Properties

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11676))

Abstract

While Bayesian Confirmation Measures assess the degree to which an antecedent \(E\) supports a conclusion \(H\) in a rule \(E\Rightarrow H\) by means of probabilities, Fuzzy Confirmation Measures evaluate the quality of fuzzy association rules between the fuzzy antecedent \(A\) and fuzzy consequence \(B\). Fuzzy Confirmation Measures defined in terms of confidence can be compared in different ways, among them symmetry properties evaluations play an important role. We first focus on symmetry properties for Fuzzy Confirmation Measures and then on the evaluation of possible levels of asymmetry. We suggest a way to measure the level of asymmetry and we also provide some examples to illustrate its possible use.

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Notes

  1. 1.

    Throughout the paper, the formulas are assumed to be well defined, i.e. we assume as granted that denominators do not vanish.

  2. 2.

    Here T is the totally true constant, that is \(T(x)=1\,\forall x \in X\).

  3. 3.

    The IFC definition recalls the analogous class of BCMs that can be written as functions of \(Pr(H|E)\) and \(Pr(H)\) only, which are called IFPD (Initial Final Probability Dependence) confirmation measures [11].

  4. 4.

    Inversion Symmetry (IS) is also called Commutativity Symmetry (see e.g. [12]).

  5. 5.

    Asymmetry degree computations were performed with Wolfram’s software Mathematica (version 11.0.1.0).

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Author information

Authors and Affiliations

  1. Department of Management, Ca’ Foscari University of Venice, Venice, Italy

    Emilio Celotto & Andrea Ellero

  2. Department of Economics, Ca’ Foscari University of Venice, Venice, Italy

    Paola Ferretti

Authors
  1. Emilio Celotto
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  2. Andrea Ellero
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  3. Paola Ferretti
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Corresponding author

Correspondence to Paola Ferretti .

Editor information

Editors and Affiliations

  1. Maynooth University, Maynooth, Ireland

    Vicenç Torra

  2. Tamagawa University, Machida, Tokyo, Japan

    Yasuo Narukawa

  3. University of Milano-Bicocca, Milan, Italy

    Gabriella Pasi

  4. University of Milano-Bicocca, Milan, Italy

    Marco Viviani

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Celotto, E., Ellero, A., Ferretti, P. (2019). Fuzzy Confirmation Measures (a)symmetry Properties. In: Torra, V., Narukawa, Y., Pasi, G., Viviani, M. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2019. Lecture Notes in Computer Science(), vol 11676. Springer, Cham. https://doi.org/10.1007/978-3-030-26773-5_5

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  • DOI: https://doi.org/10.1007/978-3-030-26773-5_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-26772-8

  • Online ISBN: 978-3-030-26773-5

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