Here, Mr denotes the number of known input-output data pairs contained within the test set. It is important to note that the input-output data pairs (x, y)contained in r may not be contained in G, or vice versa. It also might be the case that the test set is equal to the training set (G=r) however, this choice is not al ways a good one. Most often you will want to test the system with at least some data that were not used to construct f(re) since this will often provide a more realistic assessment of the quality of the approximation We see that evaluation of the error in approximation between g and a fuzzy system f(lo) based on a test set F may or may not be a true measure of the error between g and f for every xEX, but it is the only evaluation we can make based on known information. Hence you can use measures like ∑(g(x)-f(x) (3.6) or sup ig(x)-f(re (3.7) (r, her to measure the approximation error. Accurate function approximation requires that some expression of this nature be small; however, this clearly does not guarantee perfect representation of g with f since most often we cannot test that f matches g over all possible input points We would like to emphasize that the type of function that youHere, MΓ denotes the number of known input-output data pairs contained within the test set. It is important to note that the input-output data pairs (, ) i i x y contained in Γ may not be contained in G, or vice versa. It also might be the case that the test set is equal to the training set (G = ) Γ ; however, this choice is not always a good one. Most often you will want to test the system with at least some data that were not used to construct f ( ) x θ since this will often provide a more realistic assessment of the quality of the approximation. We see that evaluation of the error in approximation between g and a fuzzy system f (x θ) based on a test set F may or may not be a true measure of the error between g and f for every x∈X, but it is the only evaluation we can make based on known information. Hence, you can use measures like ( ( ) ( )) 2 (,) i i i i x y gx f x θ ∈Γ ∑ − (3.6) or { } (,) sup () ( ) i i x y gx f x θ ∈Γ − (3.7) to measure the approximation error. Accurate function approximation requires that some expression of this nature be small; however, this clearly does not guarantee perfect representation of g with f since most often we cannot test that f matches g over all possible input points. We would like to emphasize that the type of function that you