Question regarding approximation property of fuzzy systems

Hi group, I am currently doing research on adaptive fuzzy control of
nonlinear systems. In my work, I need to show that there exist fuzzy
systems with the same antecedent parts(and different conseqences) to
approximate a number of continuous functions with arbitrary accuracies.


Wang [L.X. Wang. Adaptive Fuzzy Systems and Control: Design and
Stability Analysis. Prentice-Hall, Englewood Cliff, NJ, 1994] showed in
the Universal Approximation Theorem that zero-order Takagi-Sugeno fuzzy
systems with Gaussian membership functions for input, center-average
defuzzifier, and product-type inference are universal approximators.
That is for any given continuous function f(x) in a compact set U,
there exist a fuzzy system F of the above form to approximate it with
arbitrary accuracy.

My question is: for any given continuous functions f(x) and g(x) in a
compact set U, can we show that there exist 3 fuzzy systems F1, F2, and
F3 with the same antecedent parts to approximate f(x), g(x), and
f(x)*g(x) respectively with arbitrary accuracies?

Thank you for your help

.