Fuzzy neural network fitting method and device, equipment and storage medium

Abstract

The invention provides a fuzzy neural network fitting method and device, equipment and a storage medium, and the method comprises the steps: initializing a network structure and parameters of an input layer, a fuzzy layer, a hidden layer and an output layer; a forward propagation process is executed, the training data of the input layer is fuzzified through the fuzzy layer and then transmitted to the hidden layer, a forward propagation result is calculated through the output layer, and a loss function is calculated; a back propagation process is executed based on the loss function, a gradient of parameter updating is obtained through layer-by-layer transmission, parameters are updated by using an LM nonlinear least square optimization algorithm, and a fuzzy neural network after fitting is completed is obtained after iteration is finished; and evaluating the performance of the fuzzy neural network. According to the method, the expression ability of uncertainty and fuzziness of the input data is enhanced by utilizing fuzzification processing; the LM algorithm is introduced to optimize the weight and bias, and the training speed can be remarkably increased while the convergence stability is kept.

Description

Technical Field

[0001] This invention relates to the field of neural network fitting technology, and in particular to a method, apparatus, device, and storage medium for fitting fuzzy neural networks. Background Technology

[0002] With the rapid development of artificial intelligence technology, deep learning neural networks have been widely used in fields such as data modeling, pattern recognition, and nonlinear function approximation. In related technologies, traditional neural network fitting methods typically rely on optimization algorithms such as gradient descent when dealing with complex nonlinear problems. Traditional neural networks cannot effectively handle cognitive uncertainty. Fuzzy neural networks are networks that combine fuzzy systems and neural networks. By combining neural networks with fuzzy systems, they are multi-layer neural networks built on the foundation of traditional neural networks, i.e., a special kind of deep neural network. They provide a rigorous uncertainty modeling framework through fuzzy set theory, and fuzzy logic can effectively express uncertainty and fuzziness, improving the fitting ability of neural networks in complex environments. However, fuzzy neural networks suffer from slow training and are prone to getting trapped in local optima. The nonlinear least squares optimization algorithm (Levenberg-Marquardt, LM) has the characteristics of fast convergence speed and high accuracy, making it suitable for weight optimization of neural networks.

[0003] Based on the above analysis of the development status of this technology field, there is a lack of existing technologies that combine the LM algorithm with fuzzy deep learning neural networks and use the LM algorithm to update parameters. Summary of the Invention

[0004] The purpose of this invention is to provide a method, apparatus, device, and storage medium for fitting fuzzy neural networks, aiming to solve the aforementioned problems in the prior art.

[0005] According to a first aspect of the present invention, a method for fitting a fuzzy neural network is provided, comprising: Initialization includes the network structure and parameters of the input layer, blur layer, hidden layer, and output layer; The forward propagation process is performed by blurring the training data of the input layer through a blurring layer before transmitting it to the hidden layer. The forward propagation result is calculated through the output layer, and the loss function is also calculated. The backpropagation process is performed based on the loss function, and the gradient for parameter update is obtained by passing it layer by layer. The parameters are then updated using the LM nonlinear least squares optimization algorithm. After the iteration is completed, a fuzzy neural network with a complete fit is obtained. Evaluate the performance of the fuzzy neural network.

[0006] According to a second aspect of the present invention, a fitting apparatus for a fuzzy neural network is provided, comprising: The initialization module is used to initialize the network structure and parameters, including the input layer, fuzzy layer, hidden layer, and output layer. The forward propagation module is used to perform the forward propagation process. It fuzzes the training data of the input layer through the fuzzing layer before transmitting it to the hidden layer. The output layer calculates the forward propagation result and the loss function. The backpropagation module is used to perform the backpropagation process based on the loss function, pass the gradient of parameter update layer by layer, and use the LM nonlinear least squares optimization algorithm to update the parameters. After the iteration, the fitted fuzzy neural network is obtained. The evaluation module is used to evaluate the performance of the fuzzy neural network.

[0007] According to a third aspect of the present invention, an electronic device is provided, comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the computer program, when executed by the processor, implements the steps of the fitting method for a fuzzy neural network as provided in the first aspect of the present disclosure.

[0008] According to a fourth aspect of the present invention, a computer-readable storage medium is provided, on which an information transmission implementation program is stored, which, when executed by a processor, implements the steps of the fuzzy neural network fitting method provided in the first aspect of the present disclosure.

[0009] The technical solution provided by the embodiments of the present invention has the following beneficial effects: the fuzzification process enhances the ability to express the uncertainty and fuzziness of input data, enabling the network to exhibit higher fitting accuracy in complex nonlinear function modeling; the introduction of the LM algorithm to optimize weights and biases is equivalent to combining the advantages of the steepest descent method and the Gauss-Newton method, which can significantly accelerate the training speed while maintaining convergence stability.

[0010] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and are not intended to limit this disclosure. Attached Figure Description

[0011] To more clearly illustrate the technical solutions in one or more embodiments of this specification or in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this specification. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0012] Figure 1 This is a flowchart of a fuzzy neural network fitting method according to an embodiment of the present invention; Figure 2This is a schematic diagram of the network structure according to an embodiment of the present invention; Figure 3 This is a schematic diagram illustrating how the training variance changes with the number of training iterations in an embodiment of the present invention; Figure 4 This is a schematic diagram of the fitting results after training according to an embodiment of the present invention; Figure 5 This is a schematic diagram of the post-training test results of an embodiment of the present invention; Figure 6 This is a schematic diagram of a fitting device for a fuzzy neural network according to an embodiment of the present invention; Figure 7 This is a schematic diagram of an electronic device according to an embodiment of the present invention. Detailed Implementation

[0013] To enable those skilled in the art to better understand the technical solutions in one or more embodiments of this specification, the technical solutions in one or more embodiments of this specification will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this specification, and not all of the embodiments. Based on one or more embodiments of this specification, all other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of this document.

[0014] Method Implementation Examples According to an embodiment of the present invention, a fitting method for a fuzzy neural network is provided. Figure 1 This is a flowchart of the fitting method for a fuzzy neural network according to an embodiment of the present invention, as shown below. Figure 1 As shown, the fitting method of the fuzzy neural network according to an embodiment of the present invention specifically includes: In step S110, the network structure and parameters, including the input layer, fuzzy layer, hidden layer, and output layer, are initialized, specifically including: The number of neurons in the input layer of the neural network is determined by the feature dimension of the input data, and it can directly receive preprocessed data. The fuzzy layer is not a hierarchical neuron structure as understood in traditional neural networks, but rather uses Gaussian membership functions to fuzzify the data, thereby improving its ability to express uncertain data. The number of hidden layers and the number of neurons in each layer are user-defined, and appropriate activation functions can be selected according to task requirements. The output layer is set to a single neuron that does not use an activation function, directly outputting the numerical value of the fitted result; the number of neurons is determined by the task.

[0015] Figure 2 This is a schematic diagram of the network structure according to an embodiment of the present invention, such as... Figure 2As shown, the basic network structure of a fuzzy neural network is illustrated. From bottom to top, it consists of an input layer, a fuzzy layer, a hidden layer, and an output layer. The hidden layer and the fuzzy layer are fully connected. In this embodiment of the invention, the fuzzy neural network is a BP fuzzy neural network.

[0016] In step S120, the forward propagation process is performed. The training data of the input layer is blurred through a blurring layer before being transmitted to the hidden layer. The forward propagation result is calculated through the output layer, and the loss function is calculated. Specifically, this includes: During the forward propagation phase, the training data is divided into input neurons of the input layer according to the feature dimension; The training data is fuzzified by using the Gaussian membership function in the fuzzy layer to enhance the ability to express uncertain information, obtain the membership values ​​of each neuron in the input layer, and pass the membership values ​​to the hidden layer. Gaussian membership functions are commonly used in fuzzification. A Gaussian membership function consists of two indices. and Confirmed, the Gaussian membership function can be represented using Formula 5: Formula 5; in, Width is usually positive. This indicates the location of the curve; The center defines the core position of the fuzzy concept, and the width defines the fuzzy range of the fuzzy concept. For example, by substituting the value of the feature temperature into the Gaussian function, three fuzzy sets are defined: temperature, comfort, and high temperature. Each fuzzy set has a corresponding (b,c) value. Similarly, a similar operation is performed on the corresponding features of other input layers. The number of fuzzy sets defined corresponds to the number of edges for each neuron in the input layer. The network performance can be adjusted by changing the number and width of Gaussian functions. Increasing the number of Gaussian functions increases the network complexity. Experiments have shown that increasing the number of Gaussian functions in this network structure results in less overfitting and avoids severe overfitting.

[0017] The membership values ​​of each neuron in the hidden layer are weighted and summed, and then nonlinearly transformed using a selected activation function. This result is then used as the input to the next layer, and the nonlinear transformation result of the last hidden layer is passed to the output layer. The input to the hidden layer neurons is the sum of all weighted sums. Output use Function activation Right now ,but ; The forward propagation result is obtained by weighted summation of all nonlinear transformation results at the output layer. In this embodiment of the invention, the output layer does not use an activation function, thereby completing one forward propagation calculation.

[0018] Preferably, if the fuzzy neural network model has multiple outputs, the network's... The error between each output and the corresponding expected output is , No. The error performance index function for each sample is approximately: ,in, This indicates the number of neurons in the network's output layer.

[0019] After completing the forward propagation, the forward propagation result is obtained as the output value of the current iteration. Based on the output value and the expected true output value, the loss function is calculated using the mean squared error function, and the mean squared error is calculated using Formula 6: Formula 6; in, Represents the loss function. Indicates the number of samples. Indicates the first The expected true value of the output for each sample. Indicates the first The output value of the current iteration for each sample, i.e., the predicted output.

[0020] Preferably, if the fuzzy neural network model has multiple outputs, then the first... In the sample data of the th , the ... The loss function for each output is expressed as: The training error is Similarly, the error in subsequent tests is... ; The mean squared error function not only reflects the overall fitting accuracy, but also serves as the basis for updating weights and biases during backpropagation. By gradually minimizing the error, the network is ensured to continuously approach the optimal solution during training, thereby achieving a high-precision fitting effect.

[0021] In step S130, a backpropagation process is performed based on the loss function, passing the gradient for parameter updates layer by layer, and the parameters are updated using the LM nonlinear least squares optimization algorithm. After the iteration is completed, a fitted fuzzy neural network is obtained, specifically including: The gradient of the loss function with respect to the output layer neurons is used as the initial error signal, which is then propagated layer by layer to each hidden layer. The error signal is calculated using Equation 1, and the gradients for weight and bias updates are calculated using Equation 2. ⊙ Formula 1; Formula 2; in, Indicates the first l Layer error signal, Indicates the first l The weight matrix of the layer, This represents the activation function, and ⊙ represents element-wise multiplication. This represents the result of a weighted sum of the membership values ​​in the hidden layer. Indicates the first l+ The nonlinear transformation result of the first layer output, Represents the loss function. Indicates the first l Layer bias, Indicates the first l Layer weights update gradient, Indicates the first l The gradient is updated based on the layer's bias.

[0022] The gradient information mentioned above serves as the basis for parameter updates and is dynamically adjusted in conjunction with the LM algorithm, thereby improving local convergence speed while ensuring global convergence. The improved gradient descent algorithm, also known as the LM algorithm, is a least-squares estimation method for regression parameters in nonlinear regression. It combines the steepest descent method and the Taylor series linearization method. The connection weights of the output layer and hidden layers... The learning algorithm is , Represents the network weight vector; The weights and biases are updated using the LM nonlinear least squares optimization algorithm. Equation 3 represents the change in parameters, and Equation 4 represents the update process. Formula 3; Formula 4; in, Indicates the weight or bias parameter. Indicates the amount of change in the parameter. This represents the Jacobian matrix of the loss function with respect to the parameters. The values ​​in the Jacobian matrix are the parameter gradients of the samples. This represents the output error vector. Indicates the damping factor. Represents the identity matrix. Indicates the iteration round; During each iteration, the damping factor is reduced as the error decreases. To accelerate convergence; increase when the error does not decrease. This ensures convergence stability. Consequently, network weights and biases can maintain stable convergence globally while achieving rapid optimization in local regions, thereby improving fitting accuracy and generalization ability.

[0023] Based on the network structure with updated parameters in the current iteration, the forward and backward propagation processes of the next iteration are executed, and the iteration ends after the parameters converge. In each iteration, the weights of each sample are trained and updated sequentially until all samples have been trained, and then the next iteration is performed, until the requirements are met.

[0024] In step S140, the performance of the fuzzy neural network is evaluated, specifically including: Performance was evaluated using mean squared error on both the validation and test sets.

[0025] After the neural network training is complete, to evaluate the model's generalization ability, a validation set, independent of the training set, is input into the network for forward propagation to obtain the predicted output value; by analyzing the predicted output... Compared with the actual output of the validation set For comparison, the mean squared error (MSE) is calculated using Formula 7 as a performance metric: Formula 7; in, To measure the number of validation set samples, this metric can be used to quantify the model's fitting accuracy on unseen data, thereby judging the network's generalization performance. If the error is too large, the network structure or training parameters can be further adjusted to improve the model's performance.

[0026] After the model training is complete and it has been optimized on the validation set, an independent test set is input into the neural network for forward propagation to obtain the predicted output. To evaluate the model's fitting ability and generalization performance in practical applications, the mean squared error of the test set is calculated using Equation 8: Formula 8; in, The number of test set samples is used as a metric to intuitively measure the network's prediction accuracy on unseen data and to provide a basis for further optimization of the network structure or training parameters. By adjusting the learning rate, the number of layers, and the number of nodes, network performance can be adjusted, avoiding severe overfitting.

[0027] Preferably, in this embodiment of the invention, if overfitting occurs, the fuzzy neural network structure can be optimized by reducing the number of fuzzy sets, and learnable importance weights can be added to the original Gaussian membership function. Fuzzy set pruning can be performed by using an importance threshold.

[0028] The method further includes: In step S150, the dataset is divided into a training set, a validation set, and a test set before initialization.

[0029] In this embodiment of the invention, the dataset is divided as follows: 70% of the data is the training set; 15% of the data is the validation set, used to verify whether the network is generalizing and to stop training before overfitting; and 15% of the data is the test set, used to independently test the network's generalization.

[0030] In this embodiment of the invention, K sets of data are set, each set of data has m inputs and n outputs. The inputs and outputs of each set of data have a certain non-linear mapping relationship. Therefore, fuzzy deep learning neural network training can be performed on the inputs and outputs of this dataset to achieve input-output fitting. In the dataset, columns 1 to m of each set of data are input variables, and columns (m+1) to (m+n) are output variables. That is, the input layer contains m neurons and the output layer contains n neurons. The model is trained using K sets of sample data and tested using N sets of new experimental data to verify the fitting effect of the neural network.

[0031] The above technical solutions of the embodiments of the present invention will be illustrated with reference to the following accompanying drawings.

[0032] Figure 3 This is a schematic diagram illustrating the change in training variance with the number of training iterations in an embodiment of the present invention, as shown below. Figure 3 As shown, this illustrates the process of training gradually converging. Figure 4 This is a schematic diagram of the training and fitting results of an embodiment of the present invention, as shown below. Figure 4 As shown, the fitting effect on the original training set is demonstrated; Figure 5 This is a schematic diagram of the post-training test results of an embodiment of the present invention, as shown below. Figure 5 As shown, the results are presented on the new samples in the test set, with circles representing predicted outputs and straight lines representing true values.

[0033] In summary, to address the existing problems, this invention proposes a fitting method for fuzzy neural networks. By utilizing fuzzification processing, it enhances the ability to express the uncertainty and fuzziness of input data, enabling the network to exhibit higher fitting accuracy in modeling complex nonlinear functions. The introduction of the LM algorithm to optimize weights and biases is equivalent to combining the advantages of the steepest descent method and the Gauss-Newton method, which can significantly accelerate the training speed while maintaining convergence stability.

[0034] Device Examples According to embodiments of the present invention, a fitting device for a fuzzy neural network is provided. Figure 6 This is a schematic diagram of a fitting device for a fuzzy neural network according to an embodiment of the present invention, as shown below. Figure 6 As shown, the fitting device for the fuzzy neural network according to an embodiment of the present invention specifically includes: Initialization module 60 is used to initialize the network structure and parameters, including the input layer, fuzzy layer, hidden layer and output layer; Forward propagation module 62 is used to perform the forward propagation process. It blurs the training data of the input layer through a blurring layer before transmitting it to the hidden layer. The output layer calculates the forward propagation result and the loss function. Specifically, it is used for: The training data is divided into input neurons of the input layer according to the feature dimension; The training data is fuzzified by using the Gaussian membership function in the fuzzy layer to obtain the membership values ​​of each neuron in the input layer, and the membership values ​​are then passed to the hidden layer. The membership values ​​of each neuron in the hidden layer are weighted and summed, and a nonlinear transformation is performed. The result of the nonlinear transformation is then transmitted to the output layer of a single neuron. The forward propagation result is obtained by weighted summation of all nonlinear transformation results in the output layer.

[0035] The forward propagation result is obtained as the output value of the current iteration. Based on the output value and the expected true value of the output, the loss function is calculated using the mean squared error function.

[0036] Backpropagation module 64 is used to perform the backpropagation process based on the loss function, passing the gradients for parameter updates layer by layer, and updating the parameters using the LM nonlinear least squares optimization algorithm. After iteration, a fitted fuzzy neural network is obtained. Specifically, it is used for: The gradient of the loss function with respect to the output layer neurons is used as the initial error signal, which is then propagated layer by layer to each hidden layer. The error signal is calculated using Equation 1, and the gradients for weight and bias updates are calculated using Equation 2. ⊙ Formula 1; Formula 2; in, Indicates the first l Layer error signal, Indicates the first l The weight matrix of the layer, This represents the activation function, and ⊙ represents element-wise multiplication. This represents the result of a weighted sum of the membership values ​​in the hidden layer. Indicates the first l+ The nonlinear transformation result of the first layer output, Represents the loss function. Indicates the first l Layer bias, Indicates the first l Layer weights update gradient, Indicates the first l Layer bias update gradient; The weights and biases are updated using the LM nonlinear least squares optimization algorithm. Equation 3 represents the change in parameters, and Equation 4 represents the update process. Formula 3; Formula 4; in, Indicates the weight or bias parameter. Indicates the amount of change in the parameter. This represents the Jacobian matrix of the loss function with respect to the parameters. This represents the output error vector. Indicates the damping factor. Represents the identity matrix. Indicates the iteration round.

[0037] Based on the network structure with updated parameters in the current iteration round, the forward and backward propagation processes for the next iteration round are executed. The iteration ends after the parameters converge.

[0038] Evaluation module 66 is used to evaluate the performance of the fuzzy neural network, specifically for: Performance was evaluated using mean squared error on both the validation and test sets.

[0039] The device further includes: The data partitioning module 68 is used to partition the dataset into training, validation and test sets before initialization.

[0040] In summary, to address the existing problems, this invention provides a fitting device for fuzzy neural networks. By utilizing fuzzification processing, it enhances the ability to express the uncertainty and fuzziness of input data, enabling the network to exhibit higher fitting accuracy in modeling complex nonlinear functions. The introduction of the LM algorithm to optimize weights and biases is equivalent to combining the advantages of the steepest descent method and the Gauss-Newton method, which can significantly accelerate the training speed while maintaining convergence stability.

[0041] Electronic device examples Figure 7 This is a schematic diagram of an electronic device according to an embodiment of the present invention. The electronic device 700 may include at least one processor 710 and a memory 720. The processor 710 can execute instructions stored in the memory 720. The processor 710 is communicatively connected to the memory 720 via a data bus. In addition to the memory 720, the processor 710 can also be communicatively connected to an input device 730, an output device 740, and a communication device 750 via the data bus.

[0042] The processor 710 can be any conventional processor, such as a commercially available CPU. The processor may also include graphics processing units (GPUs), field-programmable gate arrays (FPGAs), systems on chips (SoCs), application-specific integrated circuits (ASICs), or combinations thereof.

[0043] The memory 720 can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic storage, flash memory, magnetic disk or optical disk.

[0044] In this embodiment of the present disclosure, the memory 720 stores executable instructions, and the processor 710 can read the executable instructions from the memory 720 and execute the instructions to implement all or part of the steps of the fitting method of any of the above exemplary embodiments of the fuzzy neural network.

[0045] Computer-readable storage medium embodiments In addition to the methods and apparatus described above, exemplary embodiments of this disclosure may also be a computer program product or a computer-readable storage medium storing the computer program product, the computer product including computer program instructions that can be executed by a processor to implement all or part of the steps described in any of the fuzzy neural network fitting methods in the exemplary embodiments described above.

[0046] Computer program products can be written in any combination of one or more programming languages ​​to perform the operations of the embodiments of this application. Programming languages ​​include object-oriented programming languages ​​such as Java and C++, as well as conventional procedural programming languages ​​such as C or similar languages, and scripting languages ​​(e.g., Python). The program code can be executed entirely on the user's computing device, partially on the user's device, as a standalone software package, partially on the user's computing device and partially on a remote computing device, or entirely on a remote computing device or server.

[0047] Computer-readable storage media may be any combination of one or more readable media. A readable medium may be a readable signal medium or a readable storage medium. A readable storage medium may be, for example,, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of readable storage media include: static random access memory (SRAM) having one or more electrically connected wires; electrically erasable programmable read-only memory (EEPROM); erasable programmable read-only memory (EPROM); programmable read-only memory (PROM); read-only memory (ROM); magnetic storage; flash memory; magnetic disk or optical disk; or any suitable combination thereof.

[0048] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A fitting method for a fuzzy neural network, characterized in that, include: Initialization includes the network structure and parameters of the input layer, blur layer, hidden layer, and output layer; The forward propagation process is performed by blurring the training data of the input layer through the blurring layer before transmitting it to the hidden layer. The forward propagation result is calculated through the output layer, and the loss function is calculated. The backpropagation process is performed based on the loss function, and the gradient for parameter update is obtained by passing it layer by layer. The parameters are then updated using the LM nonlinear least squares optimization algorithm. After the iteration is completed, a fuzzy neural network with a complete fit is obtained. Evaluate the performance of the fuzzy neural network.

2. The method according to claim 1, characterized in that, The method further includes: Before initialization, the dataset is divided into training, validation, and test sets.

3. The method according to claim 1, characterized in that, The forward propagation process, which involves blurring the training data of the input layer through the blurring layer before transmitting it to the hidden layer, and calculating the forward propagation result through the output layer, specifically includes: The training data is divided into input neurons of the input layer according to the feature dimension; The training data is fuzzified using the Gaussian membership function through a fuzzy layer to obtain the membership values ​​of each neuron in the input layer, and the membership values ​​are then passed to the hidden layer. The hidden layer performs a weighted summation of all membership values ​​by each neuron and then performs a nonlinear transformation, which is then passed to the output layer. The forward propagation result is obtained by weighted summation of all nonlinear transformation results at the output layer.

4. The method according to claim 1, characterized in that, The loss function specifically includes: The forward propagation result is obtained as the output value of the current iteration. Based on the output value and the expected true value of the output, the loss function is calculated using the mean squared error function.

5. The method according to claim 1, characterized in that, The process of performing backpropagation based on the loss function, obtaining the gradient for parameter updates layer by layer, and updating the parameters using the LM nonlinear least squares optimization algorithm specifically includes: The gradient of the loss function with respect to the output layer neurons is used as the initial error signal, and it is passed layer by layer to each hidden layer. The error signal is calculated using Equation 1, and the gradient of the weight and bias update is calculated using Equation 2. ⊙ Official 1; Official 2; in, Indicates the first l Layer error signal, Indicates the first l The weight matrix of the layer, This represents the activation function, and ⊙ represents element-wise multiplication. This represents the result of a weighted sum of the membership values ​​in the hidden layer. Indicates the first l+ The nonlinear transformation result of the first layer output, Represents the loss function. Indicates the first l Layer bias, Indicates the first l Layer weights update gradient, Indicates the first l Layer bias update gradient; The weights and biases are updated using the LM nonlinear least squares optimization algorithm. Equation 3 represents the change in parameters, and Equation 4 represents the update process. Official 3; Official 4; in, Indicates the weight or bias parameter. Indicates the amount of change in the parameter. This represents the Jacobian matrix of the loss function with respect to the parameters. This represents the output error vector. Indicates the damping factor. Represents the identity matrix. Indicates the iteration round.

6. The method according to claim 1, characterized in that, The process of obtaining a fully fitted fuzzy neural network after the iteration specifically includes: based on the network structure updated with parameters in the current iteration round, executing the forward propagation process and backward propagation process for the next iteration round, and ending the iteration after the parameters converge.

7. The method according to claim 1, characterized in that, The evaluation of the performance of the fuzzy neural network specifically includes: evaluating the performance using mean squared error on both the validation set and the test set.

8. A fitting device for a fuzzy neural network, characterized in that, include: The initialization module is used to initialize the network structure and parameters, including the input layer, fuzzy layer, hidden layer, and output layer. The forward propagation module is used to perform the forward propagation process. It fuzzes the training data of the input layer through the fuzzing layer before transmitting it to the hidden layer. It calculates the forward propagation result through the output layer and calculates the loss function. The backpropagation module is used to perform the backpropagation process based on the loss function, pass the gradient of parameter update layer by layer, and update the parameters using the LM nonlinear least squares optimization algorithm. After the iteration is completed, the fitted fuzzy neural network is obtained. An evaluation module is used to evaluate the performance of the fuzzy neural network.

9. An electronic device, characterized in that, include: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the computer program, when executed by the processor, implements the steps of the fitting method for the fuzzy neural network as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores an implementation program for information transmission, which, when executed by a processor, implements the steps of the fitting method for the fuzzy neural network as described in any one of claims 1 to 7.

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