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Combination of dependent and partially reliable Gaussian random fuzzy numbers

Published: 18 October 2024 Publication History

Abstract

Gaussian random fuzzy numbers are random fuzzy sets generalizing Gaussian random variables and possibility distributions. They define belief functions on the real line that can be conveniently combined by the product-intersection rule under the independence assumption. In this paper, we introduce various extensions of this rule to account for dependence and partial reliability of the pieces of evidence. We first provide formulas for the combination of an arbitrary number of Gaussian random fuzzy numbers whose dependence is described by a correlation matrix, and we introduce a minimum-conflict combination operation. To account for partially reliable evidence, we then introduce two discounting operations called possibilistic and evidential discounting, as well as several combination operators based on different assumptions, each one parameterized by a correlation matrix and a vector of discounting coefficients. We demonstrate the application of these operators to the combination of predictions with different sets of inputs in machine learning, and show that performance can be enhanced by optimizing the parameters of the combination operators.

Highlights

Gaussian random fuzzy numbers (GRFNs) represent evidence about real variables.
We address the combination of dependent GRFNs with an arbitrary correlation matrix.
We propose two discounting mechanisms for GRFNs.
We introduce combination rules for combining dependent and partially reliable GRFNs.
We demonstrate an application of these rules in machine learning.

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    Information & Contributors

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    Published In

    cover image Information Sciences: an International Journal
    Information Sciences: an International Journal  Volume 681, Issue C
    Oct 2024
    1022 pages

    Publisher

    Elsevier Science Inc.

    United States

    Publication History

    Published: 18 October 2024

    Author Tags

    1. Evidence theory
    2. Dempster-Shafer theory
    3. Belief functions
    4. Random fuzzy sets
    5. Discounting
    6. Information fusion
    7. Machine learning
    8. Regression

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