Data-based adaptive computation technique
International Journal of Information and Communication Technology
Factor analysis latent subspace modeling and robust fuzzy clustering using t-distributions
IEEE Transactions on Fuzzy Systems
From minimum enclosing ball to fast fuzzy inference system training on large datasets
IEEE Transactions on Fuzzy Systems
Fuzzy transform as an additive normal form
Fuzzy Sets and Systems
Fuzzy Sets and Systems
Adaptive non-additive generalized fuzzy systems
Applied Soft Computing
Additive and nonadditive fuzzy hidden Markov models
IEEE Transactions on Fuzzy Systems
A method for training finite mixture models under a fuzzy clustering principle
Fuzzy Sets and Systems
A possibilistic clustering approach toward generative mixture models
Pattern Recognition
Estimation of fuzzy measures using covariance matrices in Gaussian mixtures
Applied Computational Intelligence and Soft Computing
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This work explores how a kind of probabilistic system, namely the Gaussian mixture model (GMM), can be translated to an additive fuzzy system. We will prove the mathematical equivalence between the conditional mean of a GMM, and the defuzzified output of a generalized fuzzy model (GFM). The relationship between a GMM and a GFM, and the conditions for GMM to GFM translation will be made explicit in the form of theorems. The work will then extend to special cases of the GFM, specifically the Mamdani-Larsen and Takagi-Sugeno fuzzy models. The possibility of reverse translation, that is, from a GFM to a GMM will also be discussed. Finally, we will consider the generality of a GMM, specifically how it can approximate other distribution functions.