Abstract
The probability mixture structure of additive fuzzy systems allows uniform convergence of the generalized probability mixtures that represent the if-then rules of one system or of many combined systems. A new theorem extends this result and shows that it still holds uniformly for any continuous function of such fuzzy systems if the underlying functions are bounded. This allows fuzzy rule-based systems to approximate a far wider range of nonlinear behaviors for a given set of sample data and still produce an explainable probability mixture that governs the rule-based proxy system.
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Kosko, B. (2022). Uniform Mixture Convergence of Continuously Transformed Fuzzy Systems. In: Rayz, J., Raskin, V., Dick, S., Kreinovich, V. (eds) Explainable AI and Other Applications of Fuzzy Techniques. NAFIPS 2021. Lecture Notes in Networks and Systems, vol 258. Springer, Cham. https://doi.org/10.1007/978-3-030-82099-2_19
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