Convolution neural network (convolutional neural network, CNN) because of its unique structure, at the same time of image feature extraction, will also be able to extract more details of image information. This not only solves the problem of many parameters and slow training in most traditional neural networks, but also prevents the occurrence of over fitting. Since AlphaGo defeated world go champion lee sedol in 2016, convolutional neural network has been pushed into a wave again, especially in the field of computer vision. Convolutional neural networks have two important characteristics: 1) Shared weights. In the traditional neural network, the weight w of each layer is only used once, and different weight w will be generated when it is used again. However, in the convolutional network, the convolution kernel is convolved with each pixel value (input vector) in the image, so only a set of weights is required. When the input vector is finished with the set of weights, it indicates that the convolution operation is completed. The design of Shared weights does not reduce the time consumption in the forward propagation stage, but to some extent, the number of weight parameters required by the whole model is greatly reduced, which greatly improves the computing performance of the computer. In the operation of convolution, the convolution kernel slides from left to right, from top to bottom on the input image in accordance with the given step size s until the end of the operation. Compared with the traditional neural network, the number of parameters of convolutional neural network is not only reduced, but also its operation speed is improved to a certain extent. 2) sparse connection. In order to mine the information of local association in image space, convolutional neural network adopts the mode of local connection by strengthening the nodes between adjacent layers in the neural network, and abandons the mode of full connection, that is, it adopts the mode of less than the input kernel to complete. For example, if there is a m a n input output, the traditional neural network to each output with each input matrix multiplication, the time complexity, and extraction only meaningful k convolutional neural network input, its time complexity is, because in actual application, general is far less than m, k is more practical significance, and this reduces the time complexity, on the one hand and improve the efficiency of storage.

The CNN algorithm is a decision behavior that uses fuzzy reasoning to imitate human being in the uncertain environment [6]. The

fuzzy rules are constantly adjusted to imitate the system output from the self-training function of the neural network from the initial given fuzzy rules [7, 8, 9]. In the fuzzy algorithm, two main methods are used to express the fuzzy set: one is expressed output set of the fuzzy rules, such as NB, PB, and so on. The other is the formula expression of the fuzzy rule after the input language variable, and the typical case is the linear combination of the input variables. Because the model is first proposed by Takagi and Sugeno, As a result, the T-S algorithm is usually called a fuzzy system.

The convolutional layer is the core structure of the network. Each neuron in this layer is locally connected with the previous layer, and the weight matrix connected is called convolution kernel or filter. The convolution kernel extracts the features of different positions of the input image in the way of “sliding window” with step size s, and outputs a feature graph. A feature graph corresponds to a convolution kernel, that is, the weights of each neuron in the feature graph are Shared. But the features extracted from different feature maps are different. The convolution kernel is the receptive field in the analog visual system, and the size of the convolution kernel

Corresponding to the magnitude of the sensory field, the direction of the convolution kernel corresponds to the direction of the sensory field axon. Different directions of the convolution kernel are used to extract features in different directions, and the first convolution layer is used to extract simple features such as edges or lines. Since the size of the output feature graph decreases with the depth of the convolutional neural network

In the transmission process, the image feature information is not missing, and the number of output feature graph should be increased layer by layer, so that the information in the transmission (the size of output feature graph multiplied by the number) is non-decreasing. Although only simple features are extracted in the low level of the network, with the increase of the network level, each neuron in the high level will feel an increasing number of low-level regions, that is, those simple features extracted in the low level will constantly converge to form complex features in the high level, and finally

obtain the global feature information

Each component *xi* of the input vector *X* is a fuzzy set. The set of linguistic variable values is $T\left({x}_{i}\right)=\left\{{A}_{i}^{1},{A}_{i}^{2}\cdots {A}^{{m}_{i}}\right\},\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}i=1,2,\cdots n$,where ${A}_{i}^{{s}_{i}}\left({s}_{i}=1,2\cdots {m}_{i}\right)$is *si* th language variable value of *xi* . Membership function:

$${u}_{{A}_{i}}^{{s}_{i}}\left({x}_{i}\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(i=1,2\cdots n;{s}_{i}=1,2\cdots {m}_{i}\right)$$If the output vector is Y, the fuzzy rules of the proposed methods is in the form of (1) ${R}_{j}:\text{F}\text{\hspace{0.17em}}{x}_{1}\text{\hspace{0.17em}}\text{is}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{A}_{1}^{{s}_{1j}},{x}_{2}\text{\hspace{0.17em}}\text{is}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{A}_{2}^{{s}_{2j}},\cdots ,{x}_{n}\text{\hspace{0.17em}}\text{is}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{A}_{n}^{{s}_{ji}}$

$${\text{THEN\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}y}}_{\text{i}}={w}_{j0}+{w}_{j1}\times {x}_{1}+{w}_{j2}\times {x}_{2}+\cdots {w}_{ji}\times {x}_{n}$$(1)where $j=1,2,\cdots m;m\le {\displaystyle \prod _{i=1}{m}_{i}}.$If the input quantity is fuzzed by the single point fuzzy set, the applicability of each rule can be ${a}_{j}={u}_{{A}_{1}}^{{s}_{1j}}\left({x}_{1}\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}\wedge {u}_{{A}_{2}}^{{s}_{2j}}\left({x}_{2}\right)\wedge \cdots \wedge {u}_{{A}_{n}}^{{s}_{ji}}\left({x}_{n}\right)$the output of the fuzzy system can be written as

$$Y={\displaystyle \sum _{j=1}^{m}{a}_{j}{y}_{j}}/{\displaystyle \sum _{j=1}^{m}{a}_{j}}={\displaystyle \sum _{j=1}^{m}{\overline{a}}_{j}{y}_{j}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{\overline{a}}_{j}={a}_{j}/{\displaystyle \sum _{j=1}^{m}{a}_{j}}$$(2)According to the fuzzy model given above, system diagram of the proposed algorithm is shown in Figure 2. The network is composed of two parts of the forward part network and the post part network. The forward part network is satisfied with the fuzzy rules, and the post part is related to produce the post of the fuzzy rules.

Figure 2 The system diagram of the new proposed algorithm

We will analyze each layer of the network, and give the node functions of each layer:

Input layer: Each node is directly connected to each node *xi* , and it plays the role of sending the input information to the next level.

$${f}_{i}^{\left(1\right)}={x}^{\left(0\right)}={x}_{i},\text{\hspace{0.17em}}\text{\hspace{0.17em}}{x}^{\left(1\right)}={g}_{i}^{\left(1\right)}={f}_{i}^{\left(1\right)}$$(3)The input value of the zero nodes in the input layer is

$${x}_{0}=1\text{\hspace{0.17em}},\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{W}_{j0},j=1,2,\cdots m\text{\hspace{0.17em}}{\text{\hspace{0.17em}}}_{\xb7}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{node\hspace{0.17em}:}\text{\hspace{0.17em}}{N}_{1}=n+1$$(4)The middle 1-layer of forward part network: Each node represents the value of one language variables. Its effect is to compute membership functions of all input components in fuzzy sets of linguistic variables.

${u}_{i}^{{s}_{i}}\left({x}_{i}\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{where}{u}_{i}^{{s}_{i}}\left(i=1,2\cdots n;{s}_{i}=1,2\cdots {m}_{i}\right)$. *m* is the input’ dimensions. *mi* is the fuzzy division number of *si* .

$${N}_{2}={\displaystyle \sum _{i=1}^{n}{m}_{i}}$$(5)(3) The middle 2-layer of forward part network: Its main task is to compute the fitness of each rule.

$${N}_{3}=m$$(6)(4) The middle 3-layer of the forward part

network: The implementation of this level is the normalization calculation.

$$\begin{array}{l}{f}_{j}^{\left(4\right)}={x}_{j}^{\left(3\right)}/{\displaystyle \sum _{i=1}^{m}{a}_{i},{x}_{j}^{\left(3\right)}={\overline{a}}_{j}={g}_{j}^{4}={f}_{j}^{\left(4\right)},}\\ {\overline{a}}_{j}={a}_{j}/{\displaystyle \sum _{i=1}^{m}{a}_{j}}\text{\hspace{0.17em}},\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{N}_{4}=m\end{array}$$(7)(5) The middle layer of the post part network: Each node represents a rule whose action is to express the consequent of formulating rule.

(6) Output layer computing system:

$$Y={\displaystyle \sum _{j=1}^{m}{a}_{j}{y}_{j}}/{\displaystyle \sum _{j=1}^{m}{a}_{j}}={\displaystyle \sum _{j=1}^{m}{\overline{a}}_{j}{y}_{j}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{\overline{a}}_{j}={a}_{j}/{\displaystyle \sum _{j=1}^{m}{a}_{j}}$$(8)It can be seen that *Y* is the cumulating of each rule post, and the weighting coefficient is the normalized applicability. Assuming that the number of fuzzy partitions of each input component is predetermined, the parameter *Wji* to learn is mainly the connection power of the post network. And the central values *Ci*,*s*_{i} and widths *ei*,*s*_{i} of the membership functions in the middle-layer of the front part are 1. Assuming the error cost function is $E=\frac{1}{2}\left[\overline{Y}-Y\right],\text{\hspace{0.17em}}\text{\hspace{0.17em}}\overline{Y},Y$means the expected output and real output.

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