A multi-classifier fusion method based on quantum convolutional neural network

Abstract

The application provides a multi-classifier fusion method based on a quantum convolutional neural network, aiming at the problems of large deep learning computing resource demand and poor multi-classifier fusion effect, three quantum convolutional neural networks with different convolutional structures are proposed as base classifiers based on a parameterized quantum circuit by considering entanglement ability and expressibility of the circuit, so that the required quantum bits and training parameters are reduced, and high classification accuracy and certain difference are simultaneously achieved; the output results of the base classifiers are converted into evidence forms, and an improved quantum average combination method is used as a fusion method of the multi-quantum classifier, so that conflicts among the base classifiers are solved, and accurate classification of the multi-classifier fusion system is realized.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of quantum neural networks, and particularly relates to a multi-classifier fusion method based on a quantum convolutional neural network. BACKGROUND

[0002] Multi-classifier fusion has stronger generalization ability than base learners, can reduce the influence of uncertain factors, that is, can turn weak learners that are slightly better than random guessing into strong learners that can accurately predict, so the ensemble learning method has attracted widespread attention. However, in practical applications, the results of multi-classifier fusion are not good using many existing ensemble learning methods, and even worse than the results of a single classifier. On the one hand, the base classifiers are not accurate and different; on the other hand, the multi-classifier fusion method is not effective enough. In order to improve the performance of the base classifier, the network used for training is becoming more and more complex, and the demand for computing resources is also increasing, such as the convolution process in the convolutional neural network is one of the main sources of resource demand in machine learning. Quantum computing has become an important direction to break through the performance bottleneck due to its high-speed parallelism; the existing multi-classifier fusion method of quantum convolutional neural network has the problems of large demand for computing resources caused by complex network structure of base classifiers and low accuracy of multi-classifier fusion method. SUMMARY

[0003] In order to overcome the deficiencies of the prior art and solve the problem of large demand for deep learning computing resources, the application proposes three quantum convolutional neural networks with different convolutional structures as base classifiers based on the entanglement and expressiveness of the parameterized quantum circuit, reduces the required quantum bits and training parameters, and has high classification accuracy and certain diversity; in addition, in order to solve the problem of poor multi-classifier fusion effect, the application converts the output results of each base classifier into evidence form, uses an improved quantum average combination method as the fusion method of multi-quantum classifiers, solves the conflicts between base classifiers, and realizes accurate classification of the multi-classifier fusion system.

[0004] A multi-classifier fusion method based on a quantum convolutional neural network, comprising the following steps:

[0005] Step S100: constructing a base classifier based on a parameterized quantum circuit;

[0006] Step S200: fusing multiple base classifiers based on an improved quantum average method.

[0007] Further, the step of constructing a base classifier based on a parameterized quantum circuit comprises:

[0008] Step S101: constructing a quantum state preparation circuit;

[0009] Step S102: constructing a quantum convolutional neural network;

[0010] The quantum convolutional neural network constructed based on the parameterized quantum circuit is a base classifier based on the parameterized quantum circuit.

[0011] Further, the step of constructing the quantum state preparation circuit is:

[0012] Step S101: Constructing a quantum state preparation circuit;

[0013] The quantum state preparation circuit is a quantum amplitude encoding circuit;

[0014] In the quantum network, the input data χ is converted to a different space by quantum feature mapping, that is, φ: χ→ κ, where φ represents the mapping process, and κ represents a Hilbert space;

[0015] The quantum amplitude encoding circuit is to encode N-dimensional data x = (x1, x2, …, xN) into an n-bit quantum state, and the expression is as follows: N

[0016]

[0017] In the formula, U(x) represents the quantum amplitude encoding circuit, represents an N-dimensional real number space, represents the encoded quantum state, N = 2 n , represents the i-th ground state.

[0018] Further, the step of constructing the quantum convolutional neural network is:

[0019] Step S102-1: Constructing a quantum convolutional filter;

[0020] The quantum convolutional filter includes two qubits, and the qubits include a single-qubit gate with parameters and a double-qubit gate circuit combination;

[0021] The parameterized quantum circuit of the quantum convolutional filter in the same convolutional layer is the same, and the quantum convolutional filter is equivalent to the convolution kernel in the CNN;

[0022] On the basis of the quantum convolutional filter, #1 quantum convolutional filter, #2 quantum convolutional filter and #3 quantum convolutional filter are constructed; the input of the quantum convolutional filter is data converted into a quantum form;

[0023] The structure of the #1 quantum convolutional filter is:

[0024] The data converted into a quantum form is input to two qubits |0> and |1>, and R x (θ x ), R z ​(θ Z ) and the controlled non-gate CNOT acting on |0> and |1>, which constitutes a basic unit u1; four u1s are connected in series to form a 1# quantum convolution filter; R x (θ x ) is an x rotation gate, R z (θ Z ) is a y rotation gate; the initial value of θ x is a random value; the initial value of θ Z is a random value;

[0025] The structure of the 2# quantum convolution filter is:

[0026] The data converted into a quantum form is input to two quantum bits |0> and |1>, and H gates, controlled Z gates and R x (θ x ) are acted on |0> and |1>, which constitutes a basic unit u2; four u2s are connected in series to form a 2# quantum convolution filter; the H gate is a Hadamard gate;

[0027] The structure of the 3# quantum convolution filter is that 3 u1s and 1 u2 are connected in series to form a quantum convolution filter;

[0028] Step S102-2: constructing a quantum pooling structure;

[0029] The quantum pooling structure is a double-qubit gate circuit, which is composed of a CNOT gate and does not contain a free parameter, and the quantum pooling structure is represented by U p ;

[0030] Step S102-3: constructing a quantum convolutional neural network;

[0031] The convolutional neural network based on the parameterized quantum circuit includes a quantum state preparation circuit, a first convolutional layer, a first pooling layer, a second convolutional layer and a second pooling layer, and the quantum pooling circuit of the pooling layer has the same structure and parameters;

[0032] The first convolutional layer contains four identical quantum convolution filters;

[0033] The first pooling layer contains two U p ;

[0034] The second convolutional layer contains a quantum convolution filter;

[0035] The second pooling layer contains a U p ;

[0036] The quantum convolutional neural network based on the 1# quantum convolution filter is BC-QCNN1;

[0037] The quantum convolutional neural network based on a #2 quantum convolution filter is BC-QCNN2;

[0038] The quantum convolutional neural network based on a #3 quantum convolution filter is BC-QCNN3.

[0039] Further, the step of fusing the plurality of base classifiers based on the improved quantum average method is:

[0040] Step S201: constructing the evidence form corresponding to the base classifier;

[0041] For a binary classification task, assuming that the recognition framework is Phi={H1, H2}, the result obtained by the base classifier is p=[p1, p2], that is, p(H1)=p1 and p(H2)=p2, and the basic probability assignment function m(A) is converted through formula (2):

[0042]

[0043] In the formula, alpha is the classification accuracy of the base classifier, which is used as a discount factor here; A is a proposition; three evidences corresponding to the classification results of the three base classifiers are obtained through formula (2), m1 is the evidence form corresponding to the classification result output by BC-QCNN1, m2 is the evidence form corresponding to the classification result output by BC-QCNN2, and m3 is the evidence form corresponding to the classification result output by BC-QCNN3;

[0044] For a binary classification task, the output of the base classifier is a two-dimensional vector in the form of a probability, so it is necessary to convert it into the form of a basic probability assignment function in evidence theory first;

[0045] Step S202: fusing the plurality of base classifiers based on the improved quantum average method;

[0046] An optimal phase parameter is obtained by using the improved quantum average method, and a quantum model of the evidence is established;

[0047] Based on the evidence forms m1, m2 and m3 obtained by the base classifiers, a quantum model |phi1> of m1 is established, a quantum model |phi2> of m2 is established, and a quantum model |phi3> of m3 is established, and |phi1>, |phi2> and |phi3> have different constraint conditions respectively; according to the improved quantum average combination method, |phi1>, |phi2> and |phi3> are fused, and the quantum model of the fused evidence is After quantum measurement operation, the quantum state is collapsed to different categories with corresponding probabilities, that is, and the category to which the sample belongs is determined.

[0048] The beneficial effects of the present application are:

[0049] Compared with the existing quantum convolutional neural network, the BC-QCNN1, BC-QCNN2 and BC-QCNN3 proposed in the application have fewer required parameters while having the same classification accuracy, effectively reducing the demand for computing resources; compared with other methods, the multi-classifier fusion method based on the quantum convolutional neural network proposed in the application obtains the highest classification accuracy on multiple classification tasks. BRIEF DESCRIPTION OF DRAWINGS

[0050] Figure 1 is a general framework diagram of the method of the application;

[0051] Figure 2 is a schematic diagram of the dimension reduction method;

[0052] Figure 3 is a schematic diagram of the #1 quantum convolutional filter structure;

[0053] Figure 4 is a schematic diagram of the #2 quantum convolutional filter structure;

[0054] Figure 5 is a schematic diagram of the #3 quantum convolutional filter structure;

[0055] Figure 6 is a schematic diagram of the quantum pooling structure;

[0056] Figure 7 is the overall structure of the quantum convolutional neural network. DETAILED DESCRIPTION

[0057] The technical solution adopted by the application to solve its technical problems is: a multi-classifier fusion method based on a quantum convolutional neural network, comprising the following steps:

[0058] Step S100: constructing a base classifier based on a parameterized quantum circuit;

[0059] In the noisy intermediate-scale quantum era, research on quantum neural networks mainly focuses on the construction of parameterized quantum circuits; quantum neural networks convert data into quantum data through a quantum state preparation process, and then input the data into the network; unlike the weight matrix of a neural network, a parameterized quantum circuit uses the phase in a quantum gate as a training parameter, and realizes the transformation from a quantum initial state to a desired quantum final state through quantum gate operation, while introducing nonlinearity through quantum measurement operation;

[0060] The step of constructing a base classifier based on a parameterized quantum circuit is:

[0061] Step S101: constructing a quantum state preparation circuit;

[0062] The quantum state preparation circuit is a quantum amplitude encoding circuit;

[0063] The input data χ is converted to a different space in the quantum network by quantum feature mapping, that is, φ: χ→ κ, wherein φ represents a mapping process, and κ represents a Hilbert space;

[0064] The quantum amplitude encoding circuit is used to encode N-dimensional data x=(x1, x2, …, xN) into an n-bit quantum state of a quantum state, and the expression is as follows: N

[0065]

[0066] In the formula, U(x) represents a quantum amplitude encoding circuit, represents an N-dimensional real number space, represents an encoded quantum state, N=2 n , i> represents the i-th ground state;

[0067] Step S102: Constructing a quantum convolutional neural network;

[0068] The input image is processed by using the blank segmentation and the average pooling downsampling method in sequence;

[0069] The quantum convolutional neural network comprises a quantum convolutional layer and a quantum pooling layer.

[0070] The quantum convolutional layer comprises a quantum convolutional filter, the quantum pooling layer comprises a quantum pooling structure, and the quantum convolutional layer comprises a #1 quantum convolutional filter, a #2 quantum convolutional filter and a #3 quantum convolutional filter.

[0071] The quantum convolutional neural network structure construction step is as follows:

[0072] Step S102-1: Constructing a quantum convolutional filter;

[0073] The quantum convolutional filter comprises two qubits, and the qubits comprise a single-qubit gate with parameters and a double-qubit gate circuit combination; this is consistent with the action of the convolution kernel in the traditional convolutional network.

[0074] The quantum convolutional filter is equivalent to the convolution kernel in the CNN, and the design of the quantum convolutional filter retains the feature of convolution kernel weight sharing.

[0075] On the basis of the quantum convolutional filter, the #1 quantum convolutional filter, the #2 quantum convolutional filter and the #3 quantum convolutional filter are constructed; the input of the quantum convolutional filter is data converted into a quantum form.

[0076] The structure of the #1 quantum convolutional filter is as follows:

[0077] ​The data, converted into quantum form, is input into two qubits |0> and |1>, and R... x (θ x ), R z (θ Z The controlled NOT gate CNOT is applied to |0> and |1> to form a basic unit u1; four u1s are cascaded to form a quantum convolution filter #1; R x (θ x ) represents a revolving door, R z (θ Z ) represents a y-shaped revolving door; θ represents a θ-shaped revolving door. x The initial value is a random value; θ Z The initial value is a random value;

[0078] The structure of the #2 quantum convolution filter is as follows:

[0079] The data, converted into quantum form, is input into two qubits |0> and |1>, and the H-gate, controlled Z-gate, and R-gate are used. x (θ x The action is applied to |0> and |1> to form a basic unit u2; four u2s are connected in series to form a quantum convolution filter #2; the H gate is a Hadamard gate;

[0080] The structure of the #3 quantum convolution filter is as follows: three u1s and one u2 are connected in series to form the quantum convolution filter; for example... Figure 5 As shown;

[0081] The #1 quantum convolution filter contains 16 adjustable parameters and has strong expressive power.

[0082] The #2 quantum convolution filter contains eight adjustable parameters and has strong entanglement capabilities;

[0083] #3 The quantum convolution filter integrates the expressive power and entanglement capability of parameterized quantum circuits, and has 14 adjustable parameters;

[0084] Step S102-2: Construct a quantum pooling structure;

[0085] The quantum pooling structure is a two-qubit gate circuit, which consists of a single CNOT gate and contains no free parameters. The quantum pooling structure is represented by U... p Indicate; such as Figure 6 As shown, the two-qubit gate circuit performs a unitary transformation operation on the active qubit, thereby removing redundant information and reducing the complexity of the network.

[0086] The quantum convolutional neural network designed in this invention utilizes quantum pooling circuits to reduce the dimensionality of the obtained quantum state features;

[0087] Step S102-3: constructing a quantum convolutional neural network;

[0088] The convolutional neural network based on the parameterized quantum circuit comprises a quantum state preparation circuit, a first convolutional layer, a first pooling layer, a second convolutional layer and a second pooling layer, and the quantum pooling circuits of the pooling layers have the same structure and parameters;

[0089] The first convolutional layer comprises four identical quantum convolutional filters;

[0090] The first pooling layer comprises two U p ;

[0091] The second convolutional layer comprises one quantum convolutional filter;

[0092] The second pooling layer comprises one U p ;

[0093] As Figure 7 shown;

[0094] The input image data is preprocessed, and the compressed feature vector is input into the quantum convolutional neural network. First, the data is unitarily transformed by the quantum amplitude encoding circuit U(x) of the quantum state preparation circuit, and the feature vector is encoded into a corresponding quantum state. The first convolutional layer and the second convolutional layer and the first pooling layer and the second pooling layer are used to extract features and reduce dimensions of the quantum state data, respectively. The same convolutional layer is composed of the same convolutional filter and has the same parameter θ. The convolutional filters of different layers have the same structure but different parameters θ.

[0095] The quantum convolutional neural network based on the #1 quantum convolutional filter is BC-QCNN1;

[0096] The quantum convolutional neural network based on the #2 quantum convolutional filter is BC-QCNN2;

[0097] The quantum convolutional neural network based on the #3 quantum convolutional filter is BC-QCNN3;

[0098] The constructed BC-QCNN1, BC-QCNN2 and BC-QCNN3 are three base classifiers based on parameterized quantum circuits.

[0099] Step S200: based on the improved quantum average method, the plurality of base classifiers are fused;

[0100] Based on the classification results of the three base classifiers BC-QCNN1, BC-QCNN2 and BC-QCNN3, the step of fusing the plurality of quantum base classifiers is as follows:

[0101] Step S201: constructing an evidence form corresponding to the base classifier;

[0102] For the binary classification task, assuming the recognition framework is Φ = {H1, H2}, the result obtained by the base classifier is p = [p1, p2], that is, p(H1) = p1, p(H2) = p2, which is converted into the basic probability assignment function m(A) by formula (2):

[0103]

[0104] In the formula, α is the classification accuracy of the base classifier, which is used as a discount factor here; A is a proposition; the evidence corresponding to the classification results of the three base classifiers is obtained by formula (2), m1 is the evidence form corresponding to the classification result output by BC-QCNN1, m2 is the evidence form corresponding to the classification result output by BC-QCNN2, and m3 is the evidence form corresponding to the classification result output by BC-QCNN3;

[0105] For the binary classification task, the output of the base classifier is a two-dimensional vector in the form of probability, so it is necessary to convert it into the form of the basic probability assignment function in evidence theory first;

[0106] Step S202: fusing multiple base classifiers based on the improved quantum average method;

[0107] An optimal phase parameter is obtained by using the improved quantum average method, and a quantum model of the evidence is established;

[0108] Based on the evidence forms m1, m2 and m3 obtained by the base classifier, a quantum model |φ1> of m1 is established, a quantum model |φ2> of m2 is established, and a quantum model |φ3> of m3 is established, |φ1>, |φ2> and |φ3> have different constraint conditions respectively; according to the improved quantum average combination method, |φ1>, |φ2> and |φ3> are fused, and the quantum model of the fused evidence is After quantum measurement operation, the quantum state is collapsed to different categories with corresponding probabilities, that is, and the category to which the sample belongs is determined.

[0109] The application will be further described below in combination with the drawings and examples.

[0110] The application method is described by taking the application of the application method on the MNIST data set as an example:

[0111] 1. Base classifier construction based on parameterized quantum circuit

[0112] Select different two digit categories in the MNIST data set as different binary classification tasks, such as {0, 1} classification, {1, 2} classification, {7, 9} classification, etc.

[0113] Three convolution filters with different entanglement ability and expressiveness are constructed according to step 1-1, denoted as convolution filter #1, convolution filter #2 and convolution filter #3.

[0114] The quantum pooling structure is constructed according to step 1-2, denoted as U p .

[0115] Based on step 1-1 and step 1-2, the overall structure of the quantum convolutional neural network is established according to step 1-3, denoted as BC-QCNN1, BC-QCNN2 and BC-QCNN3, with different entanglement ability and expressiveness, respectively as different base classifiers for binary classification tasks. Assuming that the recognition framework corresponding to the binary classification task is Φ = {H1, H2}, the output of BC-QCNN1 is denoted as p a = [p a1 , p a2 ], the output of BC-QCNN2 is denoted as p b = [p b1 , p b2 ], and the output of BC-QCNN3 is denoted as p c = [p c1 , p c2 ].

[0116] 2. Multi-classifier fusion based on improved quantum averaging method;

[0117] Through step 2-1, p a , p b and p c are converted into basic probability assignment functions, denoted as m a , m b and m c , respectively, where α a , α b and α c are the classification accuracies of the base classifiers BC-QCNN1, BC-QCNN2 and BC-QCNN3.

[0118] Through step 2-2, the quantum models corresponding to m a , m b and m c are obtained, denoted as |φ a >, |φ b > and |φ c >, respectively, with constraint conditions C a , C b and C c . Quantum average fusion is performed on |φ a >, |φ b > and |φ c >, and the fused model is denoted as And has constraint condition C. The probabilities p(H1) and p(H2) that the sample in the MNIST data set belongs to different categories are obtained through quantum measurement, and according to the size of p(H1) and p(H2), the category to which the sample belongs is judged.

[0119] The present application carries out comparative experiments on the Fashion-MNIST data set, respectively verifies the classification performance of the base classifier and the effectiveness of the overall multi-classifier fusion method. Select two different commodity categories in the Fashion-MNIST data set as different binary classification tasks, and the evaluation index is the classification accuracy and the number of parameters θ. The comparison experiment results of other base classifiers are shown in Table 1, and the comparison experiment results of the overall multi-classifier fusion method are shown in Table 2. Compared with the existing quantum convolutional neural network, the BC-QCNN1, BC-QCNN2 and BC-QCNN3 proposed in the present application have the same classification accuracy while requiring fewer parameters, which can reduce the demand for computing resources. Compared with other methods, the multi-classifier fusion method based on quantum convolutional neural network proposed in the present application obtains the highest classification accuracy on multiple classification tasks.

[0120] Table 1 Comparison results of each base classifier on different binary classification tasks in the Fashion-MNIST data set

[0121]

[0122] Table 2 Comparison results of the multi-classifier fusion method based on quantum convolutional neural network and other methods

[0123]

[0124]

Claims

1. A multi-classifier fusion method based on a quantum convolutional neural network, characterized in that, Comprising the following steps: Step S100: constructing a base classifier based on a parameterized quantum circuit; The step of constructing a base classifier based on a parameterized quantum circuit is: Step S101: constructing a quantum state preparation circuit; Step S102: constructing a quantum convolutional neural network; For the input image, the blank segmentation and the average pooling downsampling method are used in sequence for processing; The quantum convolutional neural network constructed based on the parameterized quantum circuit is a base classifier based on a parameterized quantum circuit; The step of constructing a quantum convolutional neural network is: Step S102-1: constructing a quantum convolutional filter; The quantum convolutional filter comprises two qubits, and the qubits comprise a single-qubit gate with parameters and a double-qubit gate circuit combination; The parameterized quantum circuit of the quantum convolutional filter in the same convolutional layer is the same, and the quantum convolutional filter is equivalent to a convolution kernel in the CNN; On the basis of the quantum convolutional filter, a #1 quantum convolutional filter, a #2 quantum convolutional filter, and a #3 quantum convolutional filter are constructed; the input of the quantum convolutional filter is data converted into a quantum form; The structure of the #1 quantum convolutional filter is: Data input into two quantum bits in quantum form and above, a basic unit , and a controlled NOT gate CNOT acting on and , constitutes a basic unit ; four in series, to form a 1# quantum convolution filter; is an x rotation gate, is a y rotation gate; The initial value of is a random value; The initial value of is a random value; The structure of the #2 quantum convolutional filter is: Data input into two qubits is converted into quantum form and above, a basic unit is formed by a CNOT gate, a controlled Z gate and acting on and above ; four are connected in series to form a 2# quantum convolution filter The gate is a Hadamard gate The structure of the quantum convolution filter #3 is: 3 and 1 In series in turn to constitute a quantum convolution filter Step S102-2: constructing a quantum pooling structure; The quantum pooling structure is a two-qubit gate circuit, the two-qubit gate circuit is composed of a CNOT gate, does not contain a free parameter, and the quantum pooling structure is represented as ​ Step S102-3: constructing a quantum convolutional neural network; The convolutional neural network based on the parameterized quantum circuit comprises a quantum state preparation circuit, a first convolutional layer, a first pooling layer, a second convolutional layer, and a second pooling layer, and the quantum pooling circuits of the pooling layers have the same structure and parameters; The first convolutional layer comprises four identical quantum convolutional filters; The first pooling layer includes two ; The second convolutional layer comprises one quantum convolutional filter; The second pooling layer includes one ; The quantum convolutional neural network based on the #1 quantum convolutional filter is BC-QCNN1; The quantum convolutional neural network based on the #2 quantum convolutional filter is BC-QCNN2; The quantum convolutional neural network based on the #3 quantum convolutional filter is BC-QCNN3; Step S200: fusing multiple base classifiers based on an improved quantum averaging method; Step S201: constructing an evidence form corresponding to the base classifier; Step S202: fusing multiple base classifiers based on the improved quantum averaging method; An optimal phase parameter is obtained by using the improved quantum averaging method, and a quantum model of the evidence is established; Based on the evidence form obtained by the base classifier , , , the quantum model of is established , the quantum model of is established , the quantum model of is established , , , respectively have different constraint conditions; according to the improved quantum average combination method, the fusion of , , is carried out, and the quantum model of the fused evidence is ; after quantum measurement operation, the quantum state collapses to different categories with corresponding probabilities, i.e. , , and thus the category to which the image belongs is judged.

2. The method of claim 1, wherein the method is based on a quantum convolutional neural network. The step of constructing a quantum state preparation circuit is: Step S101: constructing a quantum state preparation circuit; The quantum state preparation circuit is a quantum amplitude encoding circuit; Mapping input data through quantum feature mapping in a quantum network into a different space, i.e. where represents the mapping process, denotes a Hilbert space; The quantum amplitude encoding circuit is for encoding data into a one-bit quantum state, expressed as follows: ； (1) In the formula, quantum amplitude encoding circuit, denotes dimensional real space, denotes the encoded quantum state, , , denotes the ground state.

3. The method of claim 1, wherein the method is based on a quantum convolutional neural network. The step of constructing an evidence form corresponding to the base classifier is: Step S201: constructing an evidence form corresponding to the base classifier; For binary classification tasks, assume the recognition framework is , and the result obtained by the base classifier is , i.e. , , which is converted into the basic probability assignment function by formula (2) : (2) wherein, is the classification accuracy of the base classifier, which is used as a discount factor here; is a proposition; the evidence corresponding to the classification results of the 3 base classifiers is obtained through formula (2), is the evidence form corresponding to the classification results output by BC-QCNN1, is the evidence form corresponding to the classification results output by BC-QCNN2, is the evidence form corresponding to the classification results output by BC-QCNN3; For a binary classification task, the output of the base classifier is a two-dimensional vector in the form of a probability, so it needs to be converted into the form of a basic probability assignment function in evidence theory first.

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