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Erschienen in:
General Chebyshev Type Inequality for Seminormed Fuzzy Integral Kapitel lesen Erstes Kapitel lesen

2019 | OriginalPaper | Buchkapitel

Fuzzy Confirmation Measures (a)symmetry Properties

verfasst von : Emilio Celotto, Andrea Ellero, Paola Ferretti

Erschienen in: Modeling Decisions for Artificial Intelligence

Verlag: Springer International Publishing

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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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Vorheriges Kapitel Set-Based Extended Functions
Nächstes Kapitel Fake News Detection in Microblogging Through Quantifier-Guided Aggregation
Fußnoten
1
Throughout the paper, the formulas are assumed to be well defined, i.e. we assume as granted that denominators do not vanish.
 
2
Here T is the totally true constant, that is \(T(x)=1\,\forall x \in X\).
 
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
Inversion Symmetry (IS) is also called Commutativity Symmetry (see e.g. [12]).
 
5
Asymmetry degree computations were performed with Wolfram’s software Mathematica (version 11.0.1.0).
 
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Metadaten
Titel
Fuzzy Confirmation Measures (a)symmetry Properties
verfasst von
Emilio Celotto
Andrea Ellero
Paola Ferretti
Copyright-Jahr
2019
Buch
Modeling Decisions for Artificial Intelligence

Print ISBN: 978-3-030-26772-8

Electronic ISBN: 978-3-030-26773-5

Copyright-Jahr: 2019

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

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