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Random Fuzzy Sets: Theory and Application to Machine Learning

Tutorial at FUZZ-IEEE 2023, Songdo Incheon, Korea, August 13, 2023

Instructor: Thierry Denoeux

Objective: The theory of epistemic random fuzzy sets has been recently proposed as a very general formalism for uncertain reasoning, encompassing both the Dempster-Shafer theory of evidence and possibility theory as special cases. This tutorial is intended to provide an introduction to this new framework and to demonstrate its application to uncertainty quantification in machine learning.

Outline: The tutorial will consist in three main parts. The classical frameworks – random sets and belief functions on the one hand, fuzzy sets and possibility theory on the other hand will first be recalled. The general theory will then be introduced, and two important practical models will be described: Gaussian random fuzzy numbers, which constitute a convenient model to represent and combine belief functions on the real line, and Gaussian random fuzzy vectors, a multidimensional extension allowing one to define belief functions on R^p. Finally, the third part of the tutorial will be devoted to machine learning. The problem of evidential regression (quantifying the uncertainty on the prediction of a quantitative response variable using a belief function) will first be discussed. A neural network model for evidential regression based on Gaussian random fuzzy numbers will then be described, and its advantages as compared to purely fuzzy or probabilistic models will be discussed.



Related papers

  1. Thierry Denoeux. Reasoning with fuzzy and uncertain evidence using epistemic random fuzzy sets: general framework and practical models. Fuzzy Sets and Systems, Vol. 453, Pages 1-36, 2023. pdf
  2. Thierry Denoeux. Parametric families of continuous belief functions based on generalized Gaussian random fuzzy numbers. Fuzzy Sets and Systems (accepted for publication), 2023. hal-04060251
  3. Thierry Denoeux. Belief Functions on the Real Line defined by Transformed Gaussian Random Fuzzy Numbers. 2023 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2023), Songdo Incheon, Korea, August 13-17, 2023. pdf
  4. Thierry Denoeux. Quantifying Prediction Uncertainty in Regression using Random Fuzzy Sets: the ENNreg model. IEEE Transactions on Fuzzy Systems (to appear), 2023. pdf
  5. Thierry Denoeux. Belief functions induced by random fuzzy sets: A general framework for representing uncertain and fuzzy evidence. Fuzzy Sets and Systems, Vol. 424, pages 63-91, 2021. pdf


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