IEEE Systems, Man and Cybernetics Magazine - April 2021 - 19

embedded in an AMN as a fine-tuning stage. If the last
layer of an ANN has more than one neuron, then MLR must
be used. This triple-hybrid computing system, which is
called mathematical neural regression (MNR), is presented in Figure 11.

Note that the new dimension is v instead of n. This
means that the actual dimension can be reduced if
(v 1 n) and vice versa if (v 2 n). To clarify how this
hybrid computing system works, let's consider the preceding illustrative example. First, v (= 3) 1 n (= 4), so the
new dimension of the regression model will be less. Using
(18) yields
yt = b 0 + b 1 g 1 + b 2 g 2 + b 3 g 3, (19)

which ends up with the final mathematical expression:
yt (X ) =
a 3,1 $ x b3 c
nF
b 0 + b 1 $