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Figure 1. Structure of a distributed neuro-fuzzy model
Level 3: this layer is the generator of production rules, as fuzzy rules are generated here.
Level 4: The implication is made.
Level 5: Outputs of individual ostmodels are plotted against expressions where indicates
the number of ostmodels used.
Level 6: the result of the generalized model is obtained as a sum of individual
submodels.
The partially fuzzy neuro-fuzzy model of the input signals is
expressed as a five-layer
structure with the Takagi-Sugeno logical inference mechanism.
In this case [3;6;7] some input signals are clear (not fuzzy) (Fig. 2), but with their actual
values weighted by the appropriate weight coefficient, they are directly entered into the
third layer, that is, directly into the next part of the Takagi-Sugeno functions. When using
the Takagi-Sugeno logical inference mechanism, the number of fuzzy rules involved in the
process model and the parameters to be determined when training them to the neural
network is reduced. For example, the model under consideration has 4 inputs, and the total
number of rules to be constructed is 9.
Figure 2. Structure of partially fuzzy neuro-fuzzy model of input signals
The total number of parameters to be defined in the training model is 64. In addition, the
considered model is close to the linear model in structure, so it can be called quasi-linear. It
also reduces the computational burden in the process of optimizing control decisions and
makes the considered model suitable for real-time operation. The main difficulty in using
the considered model is to determine which of the input signals should be fuzzy and which
should be directly included in the next part of the fuzzy rules (Fig. 3).
To find a suitable solution to this problem, three distributed neuro-fuzzy models, I-
order, II-order and III-order models are considered and their
modeling efficiency and
accuracy are investigated. In this case, the values of the output data of the object are
pressed and the values of the control effects are the I-order and III-order,
also called
correlation model, in which the object has one control value and one output signal. is
directly included in the next part of the second-order fuzzy model, which is the inverse
version of models with.
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It should be noted that only two of these three types of models considered were
developed under the assumption that a four-input
model is being considered, which is
ambiguous.
Figure 3. Structure of a modified neuro-fuzzy model
Bodyansky E.V. and et. proposed the neuro-fuzzy neuron. In fact, it refers to a radial
basis neural network with a zero-order Takagi-Sugeno inference mechanism. In addition, a
modified neuro-fuzzy model is implemented in a multivariate version using the structure
shown in [8].
The results of our research show that when using E.V.Bodyansky's modified neuro-fuzzy
model, it is necessary to minimize two instantaneous errors
and update two weight
coefficients accordingly, but it is not necessary to study the effect of fuzzy set parameters.
