Image identification and classification method of interval type-2 fuzzy restricted Boltzmann machine

Abstract

The invention discloses an image recognition and classification method for an interval type-2 fuzzy restricted Boltzmann machine, and the method comprises the steps: carrying out the preprocessing of collected image data, and forming a training set and a test set; constructing a fuzzy free energy function by adopting a symmetric triangular fuzzy number, an asymmetric triangular fuzzy number or a Gaussian fuzzy number, and obtaining a deblurred free energy function through defuzzification processing of a clear probability mean value; performing parameter updating by adopting a contrast divergence algorithm; and testing the model by using a test set, evaluating the robustness of the model on salt-containing and pepper noise, Gaussian noise and Poisson noise data by taking a reconstruction error as an index, and evaluating the image classification performance of the model through classification accuracy, mean value and standard deviation. According to the invention, the method achieves the recognition and classification of the displayed complex image, and also has good robustness when facing a variety of noise data.

Description

Technical Field

[0001] The present invention relates to the technical field of image recognition and classification, and in particular to an image recognition and classification method of an interval type-2 fuzzy restricted Boltzmann machine. Background Art

[0002] With the rapid development of information technology and the advent of the big data era, the importance of complex system modeling and uncertainty reasoning has become increasingly prominent in fields such as industrial control, intelligent decision-making, and pattern recognition. Traditional modeling methods often struggle to balance model accuracy and robustness when faced with high-noise, nonlinear, and strongly coupled dynamic systems. Their generalization capabilities are particularly limited when data is ambiguous, incomplete, or dynamically evolving. Therefore, building intelligent computing models that can effectively handle uncertainty has become a key issue in the field of artificial intelligence that urgently needs to be addressed.

[0003] Fuzzy systems are widely used in uncertainty modeling due to their ability to simulate human semantic reasoning. However, traditional Type-1 fuzzy systems (IT2FLS) have inherent limitations when dealing with complex uncertainty problems: their membership functions are exact values, making them difficult to dynamically adapt to environmental changes or data noise, resulting in insufficient model generalization. To address this issue, Interval-Type-2 Fuzzy Logic Systems (IT2FLS) have emerged. By introducing three-dimensional membership functions and the Footprint of Uncertainty (FOU), these systems can more flexibly represent the uncertainty relationship between input and output, significantly improving the model's robustness to noise.

[0004] On the other hand, the Restricted Boltzmann Machine (RBM), as a probabilistic generative model, possesses powerful feature extraction and data reconstruction capabilities and has been widely used in deep learning. Its bidirectional connection structure between visible and hidden layers effectively exploits nonlinear features in high-dimensional data. However, traditional RBMs have shortcomings in generating fuzzy rules and quantifying uncertainty, making them difficult to directly apply to modeling complex systems with ambiguous semantics.

[0005] In recent years, the fusion of fuzzy theory and deep learning model has become an important research direction to improve the performance of intelligent systems. Although scholars have tried to combine type-1 fuzzy system with RBM (such as Fuzzy RBM), it is still difficult to fully describe high-order uncertainty in complex environments. Interval type-2 fuzzy sets (IT2FS) provide a new theoretical path for the fuzzy extension of RBM due to its advantage in expressing uncertainty. By constructing an interval type-2 fuzzy restricted Boltzmann machine (IT2FRBM), fuzzy semantic reasoning and deep feature learning mechanisms can be deeply integrated, while retaining the powerful representation ability of RBM and giving the model the ability to adapt to dynamic uncertainty.

[0006] Traditional modeling methods often have difficulty in balancing model accuracy and robustness when facing high-noise, nonlinear, and strongly coupled dynamic systems, especially when data has fuzziness, incompleteness, or dynamic evolution characteristics, and its generalization ability is significantly limited. Therefore, an interval type-2 fuzzy restricted Boltzmann machine image recognition and classification method is needed. SUMMARY

[0007] The purpose of the present application is to provide an interval type-2 fuzzy restricted Boltzmann machine image recognition and classification method that can be used for complex image recognition and noise data processing to solve the problems existing in the prior art.

[0008] To achieve the above purpose, the present application is implemented according to the following technical solutions:

[0009] On the one hand, the present application includes the following steps:

[0010] Pretreat the collected image data to form a training set and a test set;

[0011] Use symmetric triangular fuzzy numbers, asymmetric triangular fuzzy numbers, or Gaussian fuzzy numbers to construct a fuzzy free energy function, and de-fuzzify the free energy function by clear probability mean value to obtain a de-fuzzified free energy function;

[0012] Use the contrast divergence algorithm for parameter updating;

[0013] Test it using the test set, and the test index is the reconstruction error, which is as follows:

[0014]

[0015] The reconstruction error is used as an indicator to evaluate the robustness of the model on data containing salt and pepper noise, Gaussian noise, and Poisson noise. The classification accuracy, mean, and standard deviation are used to evaluate the image classification performance of the model.

[0016] Furthermore, the preprocessing includes dividing the collected image data containing handwritten numbers 0-9 and 10 categories of fashion items into a training set and a training set according to a ratio of 6:1, converting the sample pixel values ​​of the training set and the training set into double-precision floating point numbers and performing normalization processing.

[0017] Furthermore, when updating the parameters, the learning rate is set to 0.01, the number of visible layer neurons is 784, the number of hidden layer neurons is 100, the number of training rounds is 30, the training set batch size is 128, the weights, visible layer bias and hidden layer bias are initialized, the hidden layer activation probability is calculated by forward propagation and the hidden layer state is sampled, and then the visible layer activation probability is calculated by reconstruction and the visible layer state is sampled. After repeating the forward propagation, the update amount of the weight and bias is calculated according to the hidden layer state to complete the parameter update.

[0018] Furthermore, when symmetric triangular fuzzy numbers are used, the weight update formula of the interval-valued type-2 fuzzy restricted Boltzmann machine is:

[0019]

[0020] Δw=x (0) h (0) -x (1) h (1)

[0021] Δb=x (0) -x (1)

[0022] Δc=h (0) -h (1)

[0023] Furthermore, when asymmetric triangular fuzzy numbers are used, the weight update formula of the interval-valued type-2 fuzzy restricted Boltzmann machine is specifically:

[0024]

[0025] Δw M =8(x (0) h (0) -x (1) h (1) )

[0026] Δb M =8(x (0) -x (1) )

[0027] ΔcM =8(h (0) -h (1) )

[0028] Furthermore, when Gaussian triangular fuzzy numbers are used, the weight update formula of the interval-valued type-2 fuzzy restricted Boltzmann machine is specifically:

[0029]

[0030] Δw U =σ U (x (0) h (0) -x (1) h (1) )

[0031] Δw L =σ L (x (0) h (0) -x (1) h (1) )

[0032] Δb U =σ U (x (0) -x (1) )

[0033] Δb L =σ L (x (0) -x (1) )

[0034] Δc U =σ U (h (0) -h (1) )

[0035] Δc L =σ L (h (0) -h (1) )

[0036] Furthermore, for interval type-2 triangular fuzzy numbers, the formula of the free energy function after defuzzification is:

[0037]

[0038] Furthermore, for interval type-2 asymmetric triangular fuzzy numbers, the formula for the approximate defuzzified free energy function is:

[0039]

[0040] Furthermore, for interval type-II Gaussian fuzzy numbers, the free energy function after approximate defuzzification can be obtained through theoretical analysis:

[0041]

[0042] The beneficial effects of the present invention are:

[0043] The present invention is an image recognition and classification method using an interval type-2 fuzzy restricted Boltzmann machine. Compared with the prior art, the present invention has the following technical effects:

[0044] The present invention uses the clear probability mean defuzzification method and interval type-II fuzzy theory to establish an interval type-II fuzzy restricted Boltzmann machine. This model deeply integrates fuzzy system theory with the probability generation model, focusing on solving core problems such as uncertainty modeling in complex data, noise robustness enhancement and unsupervised feature learning, and realizes the recognition and classification of complex images. It can also have good robustness when facing various noise data.

[0045] This paper explicitly and quantitatively models the uncertainty surrounding membership through interval-type II fuzzy theory. This capability directly leads to greater robustness and more natural language modeling, addressing uncertainties that traditional type I fuzzy sets cannot effectively handle, and exhibits potential performance advantages in many practical applications involving high levels of uncertainty. Furthermore, its relatively simple interval structure achieves a good balance between computational feasibility and practicality.

[0046] Based on fuzzy system theory and probabilistic generative models, this paper develops an interval-type II fuzzy restricted Boltzmann machine (RBM) to recognize and classify complex images. This method demonstrates robustness even in the presence of multiple types of noisy data. By explicitly and quantitatively modeling the uncertainty inherent in the membership degree through interval-type II fuzzy theory, it achieves enhanced robustness and more natural language modeling. This approach addresses the uncertainty that traditional Type I fuzzy sets cannot effectively handle, demonstrating potential performance advantages in many practical applications involving high levels of uncertainty. Furthermore, its relatively simple interval structure ensures a good balance between computational feasibility and practicality. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 is a basic restricted Boltzmann machine structure diagram of the present invention;

[0048] Figure 2 This is a schematic diagram of interval type-2 symmetric triangular fuzzy numbers of the present invention;

[0049] Figure 3 This is a schematic diagram of interval type-2 asymmetric triangular fuzzy numbers of the present invention;

[0050] Figure 4 Schematic diagram of interval type-2 Gaussian fuzzy numbers of the present invention;

[0051] Figure 5 This is a schematic diagram of the test error of the present invention on the MNIST data set;

[0052] Figure 6 This is a schematic diagram of the test error of the Fashion-MNIST dataset of the present invention; DETAILED DESCRIPTION

[0053] The present invention will be further described below through specific examples. The illustrative examples and descriptions of the present invention are used to explain the present invention but are not intended to limit the present invention.

[0054] like Figure 1 As shown, an image recognition and classification method using interval type-2 fuzzy restricted Boltzmann machine includes the following steps:

[0055] 1. Data Preprocessing

[0056] We collected images of fashion items representing the real-world written numerals 0 to 9 and 10, each with corresponding labels for classification. We collected 60,000 samples as a training set and 10,000 samples as a test set. We converted the pixel values ​​into double-precision floating-point numbers, normalized them, and fed them into the model for analysis.

[0057] The pixel values ​​of the two datasets were converted to double-precision floating-point numbers and then normalized and input into the model for analysis. 60,000 samples were used as the training set and 10,000 samples were used as the test set. Mini-batch calculations were used in both the training and testing processes. The parameter settings are shown in the following table:

[0058] parameter Numerical Number of neurons in the visible layer 784 Number of hidden layer neurons 100 Learning rate 0.01 Number of training rounds 30 Training set batch size 128 Test set evaluation interval number of rounds 5 Test set batch size 256

[0059] 2. Basic Restricted Boltzmann Machine (RBM) Design

[0060] 2.1 Basic Structure

[0061] RBM is an undirected graph model with a bipartite graph structure. Figure 1 As shown. RBM has n visible units x=(x1,x2,...,x n ) and m hidden units h=(h1,h2,...,h m ), the visible layers typically represent the input data, and the hidden layers represent the learned features or latent representations of the data. "Restricted" means there are no connections within the layers: there are no connections between visible layer units, and there are no connections between hidden layer units. Full connections exist only between visible layer units and hidden layer units. This restriction greatly simplifies learning and inference.

[0062] 2.2 Energy Function

[0063] RBM is an energy-based model. The model defines a scalar energy E(x,h) for each possible state (x,h) of the system. The lower the energy, the "better" the state (x,h) is, and the model believes it is more likely to occur.

[0064]

[0065] Where W=(w ij ) m×n is the weight matrix, w ij represents the weight of the i-th hidden unit and the j-th visible unit. b=(b j ) 1×n and c=(c i ) 1×m are the bias terms associated with visible units and hidden units respectively. j and c i Tend to x j and h i Activation, weight w ij Represents x j and h i The strength of the association of simultaneous activation or simultaneous inhibition. A positive value indicates that they tend to be activated at the same time, and a negative value indicates that they tend not to be activated at the same time.

[0066] 2.3 Probability Distribution

[0067] The model defines the joint probability distribution P(x,h) of the system state (x,h) as the Boltzmann distribution:

[0068]

[0069] Here, Z is called the partition function, which sums all possible (x, h) states and normalizes them to ensure that the sum of probabilities is 1. Computing Z is typically extremely difficult because it requires enumerating all possible state combinations, which takes exponential time. This is a key challenge in RBM training and inference.

[0070] 2.4 Conditional Independence

[0071] Because of the "restricted" structure of RBM layers without connections, the units in one layer are conditionally independent given another layer. This is the basis for efficient learning and inference of RBMs. Given the visible layer x, the hidden units are conditionally independent of each other:

[0072]

[0073] Given a hidden layer h, the visible units are conditionally independent of each other:

[0074]

[0075] When both visible units and hidden units are binary, that is, (x,h)∈{0,1} n+m When , the conditional probability of each visible unit and hidden unit is:

[0076]

[0077] Where σ is the Logistic function, that is It maps real-valued inputs to the interval (0,1), representing the probability of the unit being activated.

[0078] 2.5 Training Objective (Maximum Likelihood Estimation)

[0079] RBM finds the optimal parameters θ = (W, b, c) by maximizing the likelihood function. Given a set of training samples S, its negative log-likelihood function is:

[0080]

[0081] The contrastive divergence (CD-k) algorithm is used to update the parameters.

[0082] 3. Fuzzy Restricted Boltzmann Machine (FRBM) Design

[0083] 3.1 Free energy function

[0084] To simplify the calculation, h is marginalized to obtain the free energy function F(x,θ):

[0085]

[0086] When (x,h)∈{0,1} n+m , the free energy function can be written as:

[0087]

[0088] in

[0089] Maximizing the likelihood is equivalent to minimizing lnL(θ,S). Usually, stochastic gradient descent is used to find the optimal parameter θ, and the gradient is:

[0090]

[0091] 3.2 Fuzzy free energy function

[0092] Fuzzy RBM is based on RBM and uses fuzzy numbers to describe weights and biases. For a binary FRBM, the fuzzy free energy function F(x) can be written as:

[0093]

[0094] in and In previous studies, the commonly used fuzzy numbers are symmetric triangular fuzzy numbers, asymmetric triangular fuzzy numbers and Gaussian fuzzy numbers.

[0095] 3.3 Clear Probability Mean Defuzzification

[0096] The deblurring method used in the present invention is clear mean probability deblurring, which is defined as:

[0097]

[0098] Among them A L (α) and A R (α) respectively represent the interval [A L (α),A R (α)] are called fuzzy numbers. α-cut.

[0099] Taking the symmetric triangular fuzzy number as an example, the free energy function F after defuzzification p (x) is defined as:

[0100]

[0101] Among them F L (α) and F R (α) is the corresponding upper and lower bound fuzzy free energy function.

[0102] This paper designs three types of IT2FRBMs corresponding to fuzzy numbers: Symmetric Triangular Fuzzy Numbers (STFNs), Asymmetric Triangular Fuzzy Numbers (ATFNs), and Gaussian Fuzzy Numbers. They can be selected according to different practical needs.

[0103] 4. Parameter Update

[0104] 4.1IT2RBM_STFN

[0105] Given a small batch of training samples, set the learning rate to 0.01 and initialize the weights and visible layer bias and the hidden layer bias First, forward propagation is performed, which consists of input data and calculation as well as Then sample the hidden layer states from them respectively as well as After reconstruction, for each visible unit and the hidden layer state obtained by sampling, and Also sample the visible layer state from it as well as Forward propagation is performed again, and the visible layer state obtained by each hidden layer unit and sampling is calculated and Sample hidden layer states from as well as Calculate the weight update formula:

[0106]

[0107] Δw=x (0) h (0) -x (1) h (1)

[0108] Δb=x (0) -x (1)

[0109] Δc=h (0) -h (1)

[0110] Finally, update the weights:

[0111]

[0112] Visible layer bias update:

[0113] Hidden layer bias update:

[0114] Where ε is the rate of change.

[0115] 4.2IT2FRBM_ATFN

[0116] ATFNs and STFNs are similar in forward propagation and reconstruction. and The weight update part is different:

[0117]

[0118] Δw M =8(x (0) h (0) -x (1) h (1) )

[0119] Δb M =8(x (0) -x (1) )

[0120] Δc M =8(h (0) -h (1) )

[0121] Weight update:

[0122] w M =w M +εΔw M

[0123] Visible layer bias update:

[0124]

[0125] Hidden layer bias update:

[0126] c M =c M +εΔc M

[0127] 4.3 IT2FRBM_GFN

[0128] The difference between GFNs and STFNs is the introduction of sub-membership, so the change is mainly reflected in the weight update:

[0129]

[0130] Δw U =σ U (x (0) h (0) -x (1) h (1) )

[0131] Δw L =σ L (x (0) h (0) -x (1) h (1) )

[0132] Δb U =σ U (x (0) -x (1) )

[0133] Δb L =σ L (x (0) -x (1) )

[0134] Δc U =σ U (h (0) -h (1) )

[0135] Δc L =σ L (h (0) -h (1) )

[0136] The parameter update is consistent with STFNs.

[0137] 5. Training and testing IT2FRBMs

[0138] The representation capabilities of the proposed IT2FRBMs will be tested on two datasets: the MNIST handwritten digit recognition dataset and the Fashion-MNIST dataset, which is more complex and more realistic. Classification experiments are designed on both datasets to compare the classification capabilities of the models. Furthermore, to compare the robustness of the models, different noise levels are introduced to analyze the reconstruction errors of each model on both datasets. Finally, the trained models are used for image reconstruction to compare their reconstruction accuracy under complex data distributions.

[0139] 5.1IT2FRBM_STFN

[0140] Each interval-type-2 fuzzy number is characterized by an upper bound membership function (UMF) and a lower bound membership function (LMF). To define these functions mathematically, the following notations are introduced to specify their bounds:

[0141] The left endpoint of the α-cut of the upper bound membership function.

[0142] The right endpoint of the α-cut of the upper bound membership function.

[0143] The left endpoint of the α-cut of the lower bound membership function.

[0144] The right endpoint of the α-cut of the lower bound membership function.

[0145] For interval-type-2 triangular fuzzy numbers, the clear mean probability defuzzification can be expanded to:

[0146]

[0147] For interval type-2 symmetric triangular fuzzy numbers, such as Figure 2 As shown, substituting the fuzzy free energy function F(x) into the defuzzified fuzzy free energy function can be obtained:

[0148]

[0149] Expanding this gives the linear part of the free energy function:

[0150]

[0151] According to the properties of symmetric triangular fuzzy numbers Where Δ j The half-width of the triangle.

[0152] The above formula can be written as

[0153]

[0154] About the free energy function F p The nonlinear part of (x) can be approximated as follows according to the corresponding theoretical derivation:

[0155]

[0156] in

[0157]

[0158]

[0159] For interval-type-2 triangular fuzzy numbers, the following approximate defuzzified free energy function is obtained:

[0160]

[0161] Now it is possible to define the probability distribution of IT2FRBM for:

[0162]

[0163] in The negative log-likelihood function is:

[0164]

[0165] So we can get the gradient:

[0166]

[0167] in

[0168]

[0169] Calculate the derivatives of each parameter to For example, other parameters are similar.

[0170]

[0171] in Given the hidden layer, the conditional probability of the visible layer is expressed as

[0172] 5.2IT2FRBM_ATFN

[0173] Extend the above IT2FRBM to ATFNs, such as Figure 3 , unlike STFNs, the center (W M ,b M ,c M ) is determined by the average of the left and right bounds, and they should be considered as additional parameters that must be trained in the learning process. According to the properties of asymmetric triangular fuzzy numbers, we can obtain:

[0174]

[0175] The parameter a is the endpoint of the fuzzy number.

[0176] Substituting the clear mean probability for deblurring, we get

[0177]

[0178] From the above formula, for interval type-2 asymmetric triangular fuzzy numbers, the free energy function after approximate defuzzification can be obtained through theoretical analysis:

[0179]

[0180] Compared to STFNs, there is one more gradient:

[0181]

[0182] where θ M =(W M ,b M ,c M ).

[0183] Calculate the derivatives of each parameter to and θ M For example, other parameters are similar.

[0184]

[0185] in

[0186]

[0187] 5.3IT2FRBM_GFN

[0188] For interval type-II GFNs, the variance σ is fuzzy with upper and lower bounds, such as Figure 4 As shown, the learning algorithm is similar to STFN:

[0189]

[0190] Substituting the above formula into the clear mean probability defuzzification, we can obtain that for the interval type-II Gaussian fuzzy number, the approximate defuzzified free energy function can be obtained through theoretical analysis:

[0191]

[0192] The gradient and derivative calculation parts are similar to STFNs.

[0193] Test the trained network using the test set

[0194] After training IT2FRBMs using the contrastive divergence algorithm, they are tested using the test set. The test metric is the reconstruction error, which is defined as follows:

[0195]

[0196] The smaller the reconstruction error, the better. Figure 5 This is a graph of test error changes on the MNIST dataset. Figure 6 This is a graph showing the test error variation on the Fashion-MNIST dataset. To systematically evaluate the robustness of each model under different noise environments, this paper adds three typical noises to the original MNIST images and Fashion-MNIST images: Salt & Pepper Noise, Gaussian Noise, and Poisson Noise. The results are shown in the table below.

[0197]

[0198] The classification experiments were mainly conducted on the test sets of the two datasets. The test set contains 10,000 samples with 10 categories of labels. The classification accuracy (%) is calculated based on the number of correctly classified samples in 10,000. The mean and standard deviation of the accuracy of the 10 categories of samples are also calculated. The results are shown in the table below:

[0199]

[0200]

[0201] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. An image recognition and classification method based on interval type-2 fuzzy restricted Boltzmann machine, characterized in that: The following steps are involved: Preprocess the collected image data to form training sets and test sets; The fuzzy free energy function is constructed using symmetric triangular fuzzy numbers, asymmetric triangular fuzzy numbers or Gaussian fuzzy numbers, and the defuzzified free energy function is obtained by defuzzification using the clear probability mean. The contrast divergence algorithm is used to update parameters; The test set is used to test it, and the test indicator is the reconstruction error. The formula is as follows: Where B is the batch size, D is the visible layer dimension, and y ij is the jth pixel value of the i-th sample in the original input data, is the jth pixel value of the i-th sample in the reconstructed data; The reconstruction error is used as an indicator to evaluate the robustness of the model on data containing salt and pepper noise, Gaussian noise, and Poisson noise. The classification accuracy, mean, and standard deviation are used to evaluate the image classification performance of the model.

2. The image recognition and classification method of interval type-2 fuzzy restricted Boltzmann machine according to claim 1, characterized in that: The preprocessing includes collecting image data containing handwritten numbers 0-9 and 10 categories of fashion items, dividing the image data into a training set and a training set according to a 6:1 ratio, converting the sample pixel values ​​of the training set and the training set into double-precision floating point numbers and performing normalization processing.

3. The image recognition and classification method of interval type-2 fuzzy restricted Boltzmann machine according to claim 1, characterized in that: When updating parameters, the learning rate is set to 0.01, the number of neurons in the visible layer is 784, the number of neurons in the hidden layer is 100, the number of training rounds is 30, the batch size of the training set is 128, the weights, visible layer bias and hidden layer bias are initialized, the hidden layer activation probability is calculated by forward propagation and the hidden layer state is sampled, and then the visible layer activation probability is calculated by reconstruction and the visible layer state is sampled. After repeating the forward propagation, the update amount of the weight and bias is calculated according to the hidden layer state to complete the parameter update.

4. The image recognition and classification method of interval type-2 fuzzy restricted Boltzmann machine according to claim 1, characterized in that: When symmetric triangular fuzzy numbers are used, the weight update formula of interval-valued type-2 fuzzy restricted Boltzmann machine is: Δw=x (0) h (0) -x (1) h (1) Δb=x (0) -x (1) Δc=h (0) -h (1) Among them, x (0) 、x (1) 、 as well as is the relevant value of the visible layer state, h (0) 、h (1) 、 as well as is the hidden layer state related value, Δw, Δb and Δc are the changes in weight and bias respectively, where U and L represent the upper and lower bounds, and L and R represent the left and right bounds.

5. The image recognition and classification method of interval type-2 fuzzy restricted Boltzmann machine according to claim 1, characterized in that: When asymmetric triangular fuzzy numbers are used, the weight update formula of the interval-valued type-2 fuzzy restricted Boltzmann machine is as follows: Δw M =8(x (0) h (0) -x (1) h (1) ) Δb M =8(x (0) -x (1) ) Δc M =8(h (0) -h (1) ) where x M(1) is the relevant value of the visible layer state, h M(0) and h M(1) is the hidden layer state related value, Δw M , Δb M and Δc M is the corresponding weight and bias change, and M represents the middle bound.

6. The image recognition and classification method of interval type-2 fuzzy restricted Boltzmann machine according to claim 1, characterized in that: When Gaussian triangular fuzzy numbers are used, the weight update formula of the interval-valued type-2 fuzzy restricted Boltzmann machine is as follows: Δw U =σ U (x) (0) h (0) -x (1) h (1) ) Δw L =σ L (x) (0) h (0) -x (1) h (1) ) Δb U =s U (x (0) -x (1) ) Δb L =s L (x (0) -x (1) ) Δc U =σ U (h (0) -h (1) ) Δc L =σ L (h (0) -h (1) ) Among them, σ U and σ L are the variances of the upper and lower bound membership functions, Δw U , Δw L , Δb U , Δb L , Δc U and Δc L are the weights of the upper and lower bound membership functions and the bias changes respectively.

7. The image recognition and classification method of interval type-2 fuzzy restricted Boltzmann machine according to claim 1, characterized in that: For interval type-2 triangular fuzzy numbers, the free energy function F after defuzzification p The formula for (x) is: in as well as are the weights and biases between neurons in the interval type-2 fuzzy restricted Boltzmann machine, respectively.

8. The image recognition and classification method of interval type-2 fuzzy restricted Boltzmann machine according to claim 1, characterized in that: For interval type-2 asymmetric triangular fuzzy numbers, the formula for the approximate defuzzified free energy function is: in θ M =(W M ,b M ,c M ) are the weights and biases between neurons in the interval type-II fuzzy restricted Boltzmann machine.

9. The image recognition and classification method of interval type-2 fuzzy restricted Boltzmann machine according to claim 1, characterized in that: For interval type-II Gaussian fuzzy numbers, the free energy function after approximate defuzzification can be obtained through theoretical analysis:

Images