Uniform Mixture Convergence of Continuously Transformed Fuzzy Systems

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.