**1.1 Neural net**

72 Recurrent Neural Networks and Soft Computing

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left and the right sides of fuzzy number, Computers and Mathematics with

An artificial neural net is a computational model which imitates natural biological system actions, through neurons that adapt their gains as occurs in the brain, and these are interconnected constructing a neural net system (Nikola, 1996) (Medel, García y Sánchez, 2008), shown in figure 1.

Fig. 1. Neural Network Interconnections (Source: Benedict Campbell 2008).

The Biological neuron is described illustratively in figure 2, taking into account a biological description.

In traditional concepts a neuron operates receiving signals from other neurons through bioelectrical connections, called *synapses*. The combination of these signals, in excess of a certain *threshold* or *activation* level, will result in the neuron *firing* that is sending a signal on to other interconnected neurons. Some signals act as *excitations* and others as *inhibitions* to a neuron firing.

These acts applied in a hundred billion interconnected neurons generate "thinking actions".

Each neuron has a body, called the *soma*. The soma is much like the body of any other cell, containing the cell nucleus, various bio-chemical factors and other components that support

Neuro-Fuzzy Digital Filter 75

The computational Neural Network structures are based on biological neural configurations. The basic neural network is a model neuron, shown in figure 2, consisting of Multiple Inputs and a Single Output (MISO structure). Each input is modified by a *weight*, which multiplies the input value. The neuron combines these dendrite weight inputs and if the soma biological actions exceed a threshold value, then the nucleus in biological sense and activation function in computational actions, determines its output answer. In an electronic computational device as shown in Figure 3, a behavioral additional condition has

Meanwhile understanding how an individual neuron operates many researches generate the way neurons organize themselves and the mechanisms used by arrays of neurons to adapt their behavior to external bounded stimuli. There are a huge number of experimental neural network computational structures, and actually laboratories and researchers continue

The common computational neural net used, is called *back-propagation network* and is characterized with a mathematical structure model, which knows its behavioral stability

Intuitively it is built taking a number of neurons and arrays them forming a *layer*. A layer is formed having all inputs and nodes interconnected with others nodes, but not both within the same node. A layer finishes with a node set connected with a succeeding layer or outputs giving the answer. The multiple layers are arrayed as an input layer, multiple intermediate layers and an output layer as shown in Figure 4; where the intermediate layers

Back-propagation neural networks are usually *fully connected*. This means that each neuron

conditions (bounded inputs and bounded output, BIBO conditions).

is connected to every output from the preceding layer.

do not have inputs or outputs to the external world and are called *hidden layers*.

**1.2 Neural network structure** 

the answer close to the real neuron actions.

Fig. 3. Neuron device computational model

building new neural net configurations.

ongoing activity, and surround the soma *dendrites*. The dendrites have the receptor functions with respect to signals generated by other neurons. These signals combined may determine whether or not that neuron will fire.

Fig. 2. Basic Biological Neuron with its elements.

If a neuron fires, an electrical impulse noise is generated. This impulse starts at the base, called the *hillock*, of a long cellular extension, called the *axon*, and proceeds down the axon to its ends. The end of the axon is split into multiple ends, called the *buttons*. The buttons are connected to the dendrites of other neurons and the resulting interconnections are the previously discussed synapses. (In figure 2, the buttons do not touch other dendrites having a small gap generating an electrical potential difference between them; i.e., if a neuron has fired, the electrical impulse noise that has been generated stimulates the buttons and results in electro-chemical activity which transmits the signal across the synapses dendrites actions).

Commonly, the neuron maintains an electrical interval potential 35, 65 milli-volts; but when a neuron fires an electrical impulse noise it increases its chemical electric energy releasing an electrical potential 90, 110 milli-volts. This impulse noise is transmitted with an interval velocity 0.5, 100 in meters per second and is distributed on average in a 1 milli-second. The fast rate repetition on average corresponds to 10 milli-seconds per firing.

Considering an electronic computer whose signals travel on average at <sup>9</sup> sec 2.0 10 *<sup>m</sup> <sup>X</sup>* (speed of electrical energy in a wire is 0.7 of that in air), whose impulse noises last for ten nanoseconds and may repeat such an impulse noise in each succeeding 10 nano-seconds. Therefore, an electronic computer has at least a two thousand times advantage in signal transmission speed considering the biological basic neuron, and a thousand times advantage in signal fire repetition. This difference in velocity manifests itself in at least one important way; the human brain is not as fast as an arithmetic electronic computer, which is many times faster and hugely more capable of patterns recognition and perception relationships. The main advantage of the brain in respect to other electronic devices is it is capable of "selfprogramming" with changing external stimuli, known as "adaptability". In other words, it can learn dynamically and in all conditions.

Naturally, the brain has developed the neuron ways changing their response to new stimulus so that similar events may affect future neighborhood responses. The adaptability of a brain corresponds to survival actions.

ongoing activity, and surround the soma *dendrites*. The dendrites have the receptor functions with respect to signals generated by other neurons. These signals combined may

If a neuron fires, an electrical impulse noise is generated. This impulse starts at the base, called the *hillock*, of a long cellular extension, called the *axon*, and proceeds down the axon to its ends. The end of the axon is split into multiple ends, called the *buttons*. The buttons are connected to the dendrites of other neurons and the resulting interconnections are the previously discussed synapses. (In figure 2, the buttons do not touch other dendrites having a small gap generating an electrical potential difference between them; i.e., if a neuron has fired, the electrical impulse noise that has been generated stimulates the buttons and results in electro-chemical activity

Commonly, the neuron maintains an electrical interval potential 35, 65 milli-volts; but when a neuron fires an electrical impulse noise it increases its chemical electric energy releasing an electrical potential 90, 110 milli-volts. This impulse noise is transmitted with an interval velocity 0.5, 100 in meters per second and is distributed on average in a 1 milli-second. The fast rate repetition on average corresponds to 10 milli-seconds per firing.

of electrical energy in a wire is 0.7 of that in air), whose impulse noises last for ten nanoseconds and may repeat such an impulse noise in each succeeding 10 nano-seconds. Therefore, an electronic computer has at least a two thousand times advantage in signal transmission speed considering the biological basic neuron, and a thousand times advantage in signal fire repetition. This difference in velocity manifests itself in at least one important way; the human brain is not as fast as an arithmetic electronic computer, which is many times faster and hugely more capable of patterns recognition and perception relationships. The main advantage of the brain in respect to other electronic devices is it is capable of "selfprogramming" with changing external stimuli, known as "adaptability". In other words, it

Naturally, the brain has developed the neuron ways changing their response to new stimulus so that similar events may affect future neighborhood responses. The adaptability

sec 2.0 10 *<sup>m</sup> <sup>X</sup>* (speed

Considering an electronic computer whose signals travel on average at <sup>9</sup>

determine whether or not that neuron will fire.

Fig. 2. Basic Biological Neuron with its elements.

can learn dynamically and in all conditions.

of a brain corresponds to survival actions.

which transmits the signal across the synapses dendrites actions).
