Multistage multi-attribute decision selection method based on subtraction clustering and combined weighting

Abstract

The invention discloses a multi-level multi-attribute decision selection method based on subtraction clustering and combined weighting. The method comprises the following steps: generating a fusion algorithm set; generating a fusion algorithm attribute list and an attribute index matrix; clustering the fusion method by adopting a subtraction clustering algorithm, and outputting to obtain a plurality of subtraction clustering centers; jointly determining the index weight of each type of methods by adopting an analytic hierarchy process and a standard conflict correlation method; and performing multi-level multi-attribute decision selection. According to the method, the uncertainty in the decision making process is reduced, the weight of the method can be updated online when a new method is added or corrected, so that the method set and the whole framework are updated, the effect of decision making selection on the data set can be achieved only by calculating relevant parameters of the to-be-decided algorithm data set in the actual application process, and the decision making efficiency is improved. And the method has relatively high robustness and scene adaptability.

Description

Technical Field

[0001] The present invention relates to the technical field of intelligent decision-making and selection, and in particular to a multi-level multi-attribute decision-making and selection method of subtractive clustering and combined weighting. Background Art

[0002] There are many kinds of fusion methods, and different fusion methods achieve different goals. Domestic and foreign scholars have conducted in-depth research on multimodal information fusion algorithms, and fusion methods can be divided into traditional methods and deep learning methods. Traditional methods include methods based on multiscale transformation, methods based on sparse representation, methods based on subspace, methods based on saliency, hybrid model methods, and methods based on variational models. Fusion methods based on multiscale transformation include multiscale decomposition, multiscale fusion, and multiscale reconstruction, and their decomposition and reconstruction forms include wavelets, pyramids, curvelets, etc. However, the input data, the tasks implemented, and the designed algorithms of these traditional methods are inconsistent, and the fusion effects achieved are also different. In addition, there are problems such as unclear relationship between function and information, and unclear relationship between function estimation and decision selection. Fusion algorithms for different data sources can be divided into image-to-image, image-to-signal, and signal-to-signal fusion algorithms. For example, infrared images have good target detection and recognition capabilities and can avoid the influence of the external environment, but their pixel resolution is low, the contrast is poor, and the background texture is blurred. Visible light images cannot highlight scene targets. Therefore, visible light and infrared can combine the complementary advantages of the two to obtain bright and background-rich fusion images. The fusion between image and signal data also has complementary significance. Both synthetic aperture radar (SAR) and automatic identification system (AIS) have the ability to work around the clock and in all weather conditions, and have complementary advantages in target monitoring. The corresponding information data can be retrieved by image association, and further fusion and complementation can be used to obtain specific information about the target. However, when different types of data sources need to realize fusion tasks according to different scenarios, multi-target and multi-attribute factors such as data type, task requirements, and algorithm performance will affect the fusion method selected for decision-making, and the unknown weights of indicators of different dimensions will have an important impact on the fusion method selected for decision-making. Therefore, in order to solve the problem of multi-method, multi-indicator, and multi-attribute decision-making difficulties, it is necessary to accurately calculate the weights based on factors such as data dimension, task dimension, and algorithm dimension, and make targeted decision-making choices. Summary of the invention

[0003] In view of this, the present invention provides a multi-level multi-attribute decision selection method of subtractive clustering and combined weighting, which can construct a fusion decision framework according to different data and task requirements, establish an information hierarchical relationship between data, tasks and fusion algorithms, analyze different fusion methods and their various characteristics, indicators, efficiency and other evaluation factors, adaptively decide on the fusion method, and finally select one or more fusion algorithms through priority sorting.

[0004] The present invention discloses a multi-level multi-attribute decision-making selection method of subtractive clustering and combined weighting, which comprises:

[0005] Step 1: Generate a fusion algorithm set;

[0006] Step 2: Generate fusion algorithm attribute list and attribute indicator matrix;

[0007] Step 3: Use the subtractive clustering algorithm to cluster the fusion method and output multiple subtractive clustering centers;

[0008] Step 4: Use the analytic hierarchy process and the standard conflict correlation method to jointly determine the indicator weights for each type of method;

[0009] Step 5: Perform multi-level multi-attribute decision-making selection.

[0010] Furthermore, the step 1 comprises:

[0011] For different fusion data sources, each corresponding type of fusion method generates N corresponding fusion algorithms, which constitute a total of M×N fusion algorithm sets. Each fusion method in the generated fusion algorithm set is randomly shuffled and saved as a random fusion algorithm set.

[0012] Furthermore, the step 2 comprises:

[0013] For each fusion method in the random fusion algorithm set, an attribute list and an attribute indicator matrix are generated. The attribute list includes data dimension A, task dimension B, algorithm dimension C and other dimension attributes. Among them, data dimension A includes the following indicators: data size A1, data type A2, data quantity A3, data acquisition difficulty A4 and other indicators, with a total of H dimensions; task dimension B includes the following indicators: task quantity B1, task type B2, task relevance B3 and other indicators, with a total of J dimensions; algorithm dimension C includes the following indicators: recognition accuracy C1, fusion accuracy C2, processing time C3, model complexity C4 and other indicators, with a total of K dimensions; the indicators of each type of attribute list are correlated pairwise to form attribute indicator matrices of H×H, J×J, and K×K, respectively.

[0014] Furthermore, the step 3 comprises:

[0015] Step 31: Obtaining the cluster center and cost function value of the subtractive clustering algorithm according to the first set threshold;

[0016] Step 32: When the cost function value is less than the convergence threshold of the clustering function, the membership of each cluster center to which the fusion method is classified is updated; when the calculated cost function value is greater than the convergence threshold of the clustering function, or the number of iterations for calculating the cluster center is equal to the maximum number of iterations of the cluster function, the cluster center and the membership of each fusion method to which each cluster center is classified are output;

[0017] Step 33: The fusion method output by the clustering algorithm is classified into the membership degree of each cluster center, and the clustering validity function value is calculated;

[0018] Step 34: when the number of subtractive cluster centers is less than the first set threshold, the neighborhood radius is reduced, and the subtractive clustering algorithm is re-adopted to cluster the fusion method until the number of subtractive cluster centers is greater than or equal to the first set threshold; and the cluster center with the largest number of fusion algorithms in the subtractive cluster centers is used as the initial center, and the distribution comprehensive value of the fusion method is clustered using the clustering algorithm to obtain multiple cluster centers; the distance of each fusion method relative to each cluster center is calculated, and all distances are arranged in descending order, and the category with the smallest distance to the cluster center is selected as the membership category of the fusion method;

[0019] Step 35: Calculate the distance between each fusion method and the distribution comprehensive value of each fusion method, take the maximum distribution comprehensive value as the subtraction cluster center, calculate the distribution comprehensive values ​​of the remaining methods, and correct the distribution comprehensive value of each fusion method; when the distribution comprehensive value of the remaining methods is less than the preset value, output all subtraction cluster centers.

[0020] Furthermore, in step 31, the expression of the cluster center of the subtractive clustering algorithm is:

[0021]

[0022] Among them, v i is the subtractive cluster center; n is the total number of fusion methods; μ ij is the fusion method x j Classified into cluster center v i The membership degree is 0≤μ ij ≤1; m is the factor coefficient of the subtractive clustering algorithm, m∈[1,∞);

[0023] The expression of the cost function value of the subtractive clustering algorithm is:

[0024]

[0025] where d ij =||v i -x j || is the subtractive cluster center v i and fusion method xj The distance between them, m is the factor coefficient, set m = 2, λ j , j = 1, ..., n is the Lagrangian factor;

[0026] In step 32, the membership degree of each cluster center classified by the fusion method is updated by the following formula:

[0027]

[0028] Among them, d kj =||v k -x j ||, which is the cluster center v k and fusion method x j The distance between.

[0029] Furthermore, in step 33, the clustering validity function value is calculated by the following formula:

[0030]

[0031] Among them, x j is the jth fusion method in the fusion method set, c is the number of cluster centers, v i is the i-th cluster center, n is the total number of fusion method sets, μ ij is the fusion method x j Classified into cluster center v i The membership degree of ij >u kj When ij =1, otherwise δ ij =0,u kj is the fusion method x j Classified into cluster center x k The membership degree of k≠i, ||x j -v i || is the jth cluster center v j With the i-th fusion method x i The distance between them, ||v i -v j || is the i-th cluster center v i With the jth cluster center v j The distance between

[0032] In step 35, the distribution value of each fusion method is composed of data size A1, data type A2, data quantity A3, data acquisition difficulty A4, other data indicators A o , task quantity B1, task type B2, task relevance B3, other task indicators B p, recognition accuracy C1, fusion accuracy C2, processing time C3, model complexity C4, other model indicators C q A one-dimensional vector composed of o ,B1,...,B2,…,B p ,C1,C2,C3,C4,…,C q ], where the distribution composite value is:

[0033]

[0034] Among them, γ i is the neighborhood radius, D i is the distance between fusion methods, x j and x i is the distribution of the jth and ith fusion methods in the fusion method; N is the total number of fusion methods; |x i -x j | is the distance between the distributions of the i-th fusion method and the j-th fusion method;

[0035] Given x c,1 is the comprehensive distribution value of the last cluster center, D c,1 is the maximum value of the last distribution comprehensive value, then the modified fusion method x is further obtained i The comprehensive distribution value of is:

[0036]

[0037] When the distribution comprehensive value of the remaining methods is less than the preset value, all subtractive cluster centers are output.

[0038] Furthermore, the step 4 comprises:

[0039] Step 41: Use the hierarchical analysis method to determine the weight of each indicator. After summarizing and arranging the fusion algorithm set, three attribute indicator matrix data are obtained: data dimension, task dimension and algorithm dimension. The relative weight of each factor in each matrix is ​​calculated based on the three attribute indicator matrices, and a consistency test is performed.

[0040] Step 42: Integrate the weights between the obtained data dimension, task dimension and algorithm dimension, as well as the relative weights between their respective dimensions, and calculate the total weight of each specific indicator.

[0041] Further, the step 42 includes:

[0042] Step 421: Using the initial sample data, establish a decision matrix for the fusion algorithm:

[0043]

[0044] Among them, x ij is the initial sample data corresponding to the j-th decision plan under the i-th indicator;

[0045] Step 422: Standardize the indicator values ​​in the decision matrix to obtain a standardized decision matrix; where the task dimension indicator is a benefit indicator, the standardized decision matrix element z ij for:

[0046]

[0047] If the data dimension and algorithm dimension indicators are cost-type indicators, then the standardized decision matrix element z i j is

[0048]

[0049] Step 423: According to the Pearson correlation coefficient, the correlation coefficient matrix between indicators is obtained:

[0050]

[0051] Among them, r ij is the correlation coefficient between the i-th indicator and the j-th indicator, and its expression is:

[0052]

[0053] Among them, z ik and z jk are the index standardized values ​​of the kth decision plan under the i-th index and the j-th index respectively; and are the means of indicators i and j respectively;

[0054] Step 424: Calculate the coefficient of variation between indicators:

[0055]

[0056] Among them, ξ i is the coefficient of difference of the i-th indicator, ξ i ∈[0,1], using the coefficient of difference to measure the contrast intensity within the indicator, ξ i =1 means that the contrast intensity of this indicator is the largest, ξ i =0 means the contrast intensity of this indicator is the smallest;

[0057] Step 425: Take the absolute value of the correlation coefficient in the conflict coefficient and calculate the conflict coefficient as:

[0058]

[0059] Calculate the comprehensive information content of the indicator:

[0060] C i =ξ i c i

[0061] Determine the indicator weights:

[0062]

[0063] The larger it is, the more important the role of indicator i in the multi-attribute decision-making process is, and the greater the weight factor of indicator i is;

[0064] μ i is the weight of the ith indicator, w i and v i represent the weights of the criterion level indicators determined by the analytic hierarchy process and the standard conflict correlation method respectively, and the final weight μ i Use w i and v i The linear representation is

[0065] Furthermore, the step 5 comprises:

[0066] Step 51: Construct an evaluation model: Let A = {A1, A2, ..., A m} represents a set of m fusion algorithms, where A i represents the i-th fusion algorithm, the number of A m is the number of fusion methods; C = {C1, C2, …, C n} represents the set of n attributes of each fusion algorithm, where C j represents the jth attribute, and the number of C is the number of attributes of each fusion algorithm; Represents the weight vector of the attribute, where w j For attribute C j The weight satisfies w j ≥0 and The number of weights w is equal to the number of attributes C; ij is the fusion algorithm A i For attribute C j The value of

[0067] Step 52: Standardize the decision-making indicators: Let the task dimension x ij As a benefit indicator, Let the data dimension and algorithm dimension x ij is a cost-based indicator. in,

[0068] Step 53: Order and To standardize the maximum and minimum values ​​of each column in the matrix, we have

[0069] Step 54: Determine the positive ideal solution and the negative ideal solution: define the solution with the maximum value of each indicator attribute as the optimal solution, and the solution with the minimum value as the worst solution. The positive ideal solution and the negative ideal solution are represented by v + and v - If it is expressed, then:

[0070]

[0071] Among them, v ij is the weighted normalized value of candidate node i under selection criterion j, is a positive ideal solution to the nth selection criterion, is the negative ideal solution of the nth selection criterion;

[0072] Step 55: Calculate the group utility value S i and individual regret value R i ;

[0073]

[0074] Step 56: Calculate the compromise decision index value: Calculate the value of the decision index Q based on the group utility value S and the individual regret value R, where v is the decision-making mechanism coefficient. If v is greater than the set value, it means the decision-making mechanism is based on maximizing the group effect; if v is less than the set value, it means the decision-making mechanism is based on minimizing the individual regret value; if v is equal to the set value, it means the decision-making mechanism is based on negotiation to achieve the maximum group effect and the minimum individual regret value with equal importance;

[0075] Step 57: Determine the ranking of alternatives and compromise solutions: Finally, get S i , R i , Q i The value of Q is used to sort the fusion methods in ascending order. i Sort by size, Q i The smaller the value, the better the decision method to be made;

[0076] Step 58: Determine the optimal outcome of individual decisions.

[0077] Further, the step 58 comprises:

[0078] The ratio of the given contrast relationship to the final weights of the two indicators should be the same, that is, w B / w j =a Bj and w j / w W =a jW , a Bj Represents the ratio of the best index to the jth index, a jW Represents the ratio of the jth index to the worst index, and establishes the following planning model:

[0079]

[0080] By solving the above model, we can get the optimal weight vector w=(w1,w2,…,w n ) T and ζ, the consistency ratio CR is expressed as the ratio of the value of ζ to the maximum value of ζ, that is,

[0081] Due to the adoption of the above technical solution, the present invention has the following advantages:

[0082] 1. The present invention can realize the decision selection of fusion algorithm under the influence of multiple attribute factors. The cluster center obtained by subtractive clustering is used to replace the initial cluster center, which can reduce the number of clustering iterations, and the center of subtractive clustering can be corrected again in the online update, so that the obtained cluster center is more reliable. And the specified cluster number update process is combined with the neighborhood radius update process, which can realize accurate clustering of the method.

[0083] 2. In the present invention, the initial neighborhood radius, when the number of subtractive cluster centers is less than the first set threshold, the neighborhood radius is reduced until the number of subtractive cluster centers is greater than or equal to the first set threshold, and different fusion method sets and their corresponding neighborhood radius values ​​can be obtained, and the obtained number of clusters and subtractive cluster centers are more accurate.

[0084] 3. The combined weighting of the present invention can not only subjectively determine the weight coefficient through the opinions of decision-making experts, but also objectively correct the weight coefficient through the standard conflict correlation analysis method, give full play to the advantages of decision-making experts, select high-value information, retain the preferences of decision-making experts, reduce information loss, and maximize the effectiveness of decision-making. Due to the different dimensions and orders of magnitude of indicators, there will be a situation where the correlation coefficient is small but the conflict between different indicators is large. The standard conflict correlation method adopted can measure the comparison intensity within the indicator and the degree of conflict between indicators.

[0085] 4. The present invention aggregates and standardizes decision matrices of different attributes and information types as independent modules, effectively avoiding the information loss caused by converting different forms of indicator information into a unified form, and reducing the uncertainty in the decision-making process. The method can update the method weights online when new methods are added or revised, thereby updating the method set and the entire framework.

[0086] 5. The method of the present invention can process algorithms with different numbers and attributes. In actual application, as long as the relevant parameters of the decision algorithm data set are calculated, the effect of making a decision on the scene data set can be achieved. It has strong robustness and scene adaptability. BRIEF DESCRIPTION OF THE DRAWINGS

[0087] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in the embodiments of the present invention. For ordinary technicians in this field, other drawings can also be obtained based on these drawings.

[0088] Figure 1 A flowchart of a multi-level multi-attribute decision-making selection method for subtractive clustering and combined weighting according to an embodiment of the present invention;

[0089] Figure 2 is the attribute list structure of the fusion algorithm set of the embodiment of the present invention;

[0090] Figure 3 The ranking result of the utility value S of the multi-level multi-attribute decision-making group of the fusion algorithm in the embodiment of the present invention;

[0091] Figure 4 It is the ranking result of individual regret value R of multi-level multi-attribute decision-making by the fusion algorithm of the embodiment of the present invention;

[0092] Figure 5 It is the ranking result of the multi-level multi-attribute decision index value Q of the fusion algorithm of the embodiment of the present invention;

[0093] Figure 6 This is the multi-level multi-attribute decision-making selection result of the fusion algorithm of the embodiment of the invention. DETAILED DESCRIPTION

[0094] The present invention is further described in conjunction with the accompanying drawings and embodiments, and the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by ordinary technicians in this field should fall within the scope of protection of the embodiments of the present invention.

[0095] See also Figure 1 The present invention provides an embodiment of a multi-level multi-attribute decision-making selection method of subtractive clustering and combined weighting, which comprises the following steps:

[0096] Step 1: Generate fusion algorithm set;

[0097] According to different fusion data sources, it can be divided into M types of methods with different sources, such as image and image fusion method, signal and signal fusion method, image and signal fusion method, etc. Each type of fusion method generates N corresponding fusion algorithms, which constitute a total of M×N fusion algorithm sets. Each fusion method in the generated fusion algorithm set is randomly shuffled and saved as a random fusion algorithm set.

[0098] Step 2: Generate fusion algorithm attribute list and attribute indicator matrix;

[0099] For each fusion method in the random fusion algorithm set, an attribute list and an attribute indicator matrix are generated. The attribute list generally includes data dimension A, task dimension B, algorithm dimension C and other dimension attributes. The data dimension A includes the following indicators: data size A1, data type A2, data quantity A3, data acquisition difficulty A4 and other indicators, etc., for a total of H dimensions; the task dimension B includes the following indicators: task quantity B1, task type B2, task relevance B3 and other indicators, etc., for a total of J dimensions; the algorithm dimension C includes the following indicators: recognition accuracy C1, fusion accuracy C2, processing time C3, model complexity C4 and other indicators, etc., for a total of K dimensions. The indicators of each type of attribute list are correlated pairwise to form H×H, J×J, and K×K indicator correlation matrices, respectively.

[0100] Step 3: Fusion algorithm multi-level subtractive clustering;

[0101] The subtractive clustering algorithm is used to cluster the fusion method, and multiple subtractive clustering centers are output. The specific steps are: according to the first set threshold, the clustering center and the cost function value of the subtractive clustering algorithm are obtained, and the first set threshold ε1=3 is set:

[0102]

[0103] Among them, v i is the subtractive cluster center; n is the total number of fusion methods; μ ij is the fusion method x j Classified into cluster center v i The membership degree is 0≤μ ij ≤1; m is the factor coefficient of the subtractive clustering algorithm, m∈[1,∞);

[0104] The cost function value of the subtractive clustering algorithm:

[0105]

[0106] Among them, d ij =||v i -x j || is the subtractive cluster center v iand fusion method x j The distance between them, m is the factor coefficient, set m = 2, λ j , j=1,...,n are Lagrangian factors.

[0107] When the cost function value is less than the convergence threshold of the clustering function, the updated fusion method is classified into the membership of each cluster center:

[0108]

[0109] Among them, d kj =||v k -x j ||, which is the cluster center v k and fusion method x j The distance between.

[0110] When the calculated cost function value is greater than the convergence threshold of the clustering function, or the number of iterations for calculating the cluster centers is equal to the maximum number of iterations of the clustering function, the cluster centers and the membership of each fusion method to each cluster center are output.

[0111] According to the fusion method output by the clustering algorithm, the membership degree of each cluster center is classified and the clustering validity function value is calculated as follows:

[0112]

[0113] Among them, x j is the jth fusion method in the fusion method set, c is the number of cluster centers, v i is the i-th cluster center, n is the total number of fusion method sets, μ ij is the fusion method x j Classified into cluster center v i The membership degree of ij >u kj When ij =1, otherwise δ ij =0,u kj is the fusion method x j Classified into cluster center x k The membership degree of k≠i, ||x j -v i || is the jth cluster center v j With the i-th fusion method x i The distance between them, ||v i -v j || is the i-th cluster center v i With the jth cluster center v j The distance between.

[0114] When the number of subtractive cluster centers is less than the first set threshold, the neighborhood radius is reduced, and the subtractive clustering algorithm is used again to cluster the fusion method until the number of subtractive cluster centers is greater than or equal to the first set threshold. The cluster center with the largest number of fusion algorithms in the subtractive cluster centers is used as the initial center, and the clustering algorithm is used to cluster the distribution comprehensive value of the fusion method, and multiple cluster centers are output. The distance of each fusion method relative to each cluster center is calculated, and all distances are arranged in descending order. The category with the smallest distance to the cluster center is selected as the membership category of the fusion method.

[0115] Then the distance of each fusion method distribution is calculated, where the distribution value of each fusion method is composed of data size A1, data type A2, data quantity A3, data acquisition difficulty A4, other data indicators A o , task quantity B1, task type B2, task relevance B3, other task indicators B p , recognition accuracy C1, fusion accuracy C2, processing time C3, model complexity C4, other model indicators C q A one-dimensional vector is formed, represented as [A1, A2, A3, A4, …, A o ,B1,...,B2,…,B p ,C1,C2,C3,C4,…,C q ], where the distribution composite value is:

[0116]

[0117] Among them, γ i is the neighborhood radius. i is the distance between fusion methods, x j and x i is the distribution of the jth and ith fusion methods in the fusion method; N is the total number of fusion methods; |x i -x j | is the distance between the distributions of the i-th fusion method and the j-th fusion method;

[0118] The maximum distribution comprehensive value is used as the subtractive cluster center to calculate the distribution comprehensive value in the remaining methods. Given x c,1 is the comprehensive distribution value of the last cluster center, D c,1 is the maximum value of the last distribution comprehensive value, then the modified fusion method x is further obtained i The comprehensive distribution value of is:

[0119]

[0120] To avoid the situation where the cluster centers are too close to each other, set γ2=2γ1.

[0121] When the distribution comprehensive value of the remaining methods is less than the preset value, all subtractive cluster centers are output;

[0122] Step 4: Multi-attribute combination weighting;

[0123] After clustering, the analytic hierarchy process and the standard conflict correlation method are used to jointly determine the indicator weights for each type of method. First, the analytic hierarchy process is used to determine the weights of each indicator. After summarizing the fusion algorithm set, three attribute indicator matrix data of data dimension, task dimension and algorithm dimension are obtained. The relative weights of each factor in each matrix are calculated based on the above three attribute indicator matrices, and consistency tests are performed. The calculation formula of consistency index C1 is:

[0124]

[0125] Among them, C1 is the consistency index, λ max is the largest eigenvalue of the attribute indicator matrix, and n is the order of the attribute indicator matrix. R The calculation formula is

[0126]

[0127] If C R <0.05, the consistency of the attribute indicator matrix is ​​considered acceptable; R1 is the random consistency index, and the random consistency index R1 is set to 0.6 in the decision-making process.

[0128] The weights between the obtained data dimension, task dimension and algorithm dimension, as well as the relative weights between their respective dimensions, are integrated to further calculate the total weight of each specific indicator.

[0129] Secondly, the ICRTIC method is used to determine the weights. The main steps are as follows:

[0130] 1) First, use the initial sample data to establish the decision matrix of the fusion algorithm:

[0131]

[0132] x ij is the initial sample data corresponding to the j-th decision plan under the i-th indicator.

[0133] 2) Standardize the indicator values ​​in the decision matrix to obtain a standardized decision matrix. The task dimension indicator is a benefit indicator, so the standardized decision matrix element z ij for

[0134]

[0135] If the data dimension and algorithm dimension indicators are cost-type indicators, then the standardized decision matrix element z ij for

[0136]

[0137] 3) According to the Pearson correlation coefficient, the correlation coefficient matrix between indicators is obtained:

[0138]

[0139] r ij is the correlation coefficient between the i-th indicator and the j-th indicator, and its expression is

[0140]

[0141] z ik and z jk are the index standardized values ​​of the kth decision plan under the i-th index and the j-th index respectively; and are the means of indicators i and j respectively.

[0142] 4) Calculate the coefficient of variation between indicators:

[0143]

[0144] ξ i is the coefficient of difference of the i-th indicator, ξ i ∈[0,1], using the coefficient of difference to measure the contrast intensity within the indicator, ξ i =1 means that the contrast intensity of this indicator is the largest, ξ i =0 means that the contrast intensity of this indicator is the smallest.

[0145] 5) Quantify the degree of conflict between indicators, consider the positive and negative correlation between indicators, take the absolute value of the correlation coefficient in the conflict coefficient, and calculate the conflict coefficient as:

[0146]

[0147] Calculate the comprehensive information content of the indicator:

[0148] C i =ξ i c i

[0149] Determine the indicator weights:

[0150]

[0151] The larger it is, the more important the role of indicator i in the multi-attribute decision-making process is, and the greater the weight factor of indicator i is.

[0152] Finally, the comprehensive weight is determined by the hierarchical analysis method and the standard conflict correlation method. i is the weight of the ith indicator, and v i represent the weights of the criterion level indicators determined by the analytic hierarchy process and the standard conflict correlation method respectively, and the final weight μ i Available and v i The linear representation is

[0153] Step 5: Multi-level multi-attribute decision-making selection;

[0154] After combining weights, multi-level multi-attribute decision making is performed. The specific steps are:

[0155] 1) First, construct the evaluation model: let A = {A1, A2, ..., A m} represents a set of m fusion algorithms, where A i represents the i-th fusion algorithm, and the number m of A is the number of fusion methods. n} represents the set of n attributes of each fusion algorithm, where C j represents the jth attribute, and the number of C is the number of attributes of each fusion algorithm. Represents the weight vector of the attribute, where w j For attribute C j The weight satisfies w j ≥0 and The number of weights w is equal to the number of attributes C; ij is the fusion algorithm A i For attribute C j The value of .

[0156] 2) Standardization of decision-making indicators. Let the task dimension x ij As a benefit indicator, Let the data dimension and algorithm dimension x ij is a cost-based indicator. in,

[0157] 3) Order and To standardize the maximum and minimum values ​​of each column in the matrix, we have

[0158] 4) Determine the positive ideal solution and the negative ideal solution. Define the solution with the maximum value of each indicator attribute as the optimal solution, and the solution with the minimum value as the worst solution. The positive and negative ideal solutions are represented by v + and v -If it is expressed, then:

[0159]

[0160] Among them, v ij is the weighted normalized value of candidate node i under selection criterion j, is a positive ideal solution to the nth selection criterion, is the negative ideal solution of the nth selection criterion.

[0161] 5) Calculate the group utility value S i and individual regret value R i .

[0162] 6) Calculate the compromise decision index value. Calculate the value of the decision index Q based on the group utility value S and the individual regret value R. The smaller the index Q value, the better the solution. v is represented as the decision-making mechanism coefficient. If v>0.5, it means a decision-making mechanism based on maximizing group effect; if v<0.5, it means a decision-making mechanism based on minimizing individual regret value; if v=0.5, it means a decision-making mechanism based on negotiation in which maximum group effect and minimum individual regret value are equally important.

[0163] 7) Determine the ranking of alternatives and compromise solutions. i , R i , Q i Sort the fusion methods in order from small to large, specifically according to Q i Sort by size, Q i The smaller the value, the better the decision method.

[0164] 8) Determine the optimal outcome of individual decisions.

[0165] In order to make a decision and select the optimal result of the fusion algorithm set, the ratio of the comparison relationship given by the expert to the final weight of the two indicators should be the same, that is, w B / w j =a Bj and w j / w W =a jW , a Bj represents the ratio of the best index to the jth index, Represents the ratio of the jth index to the worst index, and establishes the following planning model:

[0166]

[0167] By solving the above model, we can get the optimal weight vector w=(w1,w2,…,w n) T and ζ, the consistency ratio (CR) is expressed as the ratio of the value of ζ to the maximum value of ζ, that is, Among them, maxζ can be calculated according to the formula (a BW -ζ)×(a BW -ζ)=(a BW +ζ). The smaller the value of ζ, the better the consistency ratio. When the consistency ratio CR≤0.25, the evaluation results are consistent and this result is accepted. Otherwise, it is necessary to adjust the comparison relationship between the initial evaluation indicators and recalculate according to the above steps until consistency is achieved.

[0168] Step 6: Online learning updates.

[0169] After successfully deciding to select the fusion method, determine whether the method needs to be updated online, that is, determine whether the distribution comprehensive values ​​of attributes such as data dimension, task dimension and algorithm dimension are all greater than 0.8. If so, make a decision according to the current step; if not, jump to step 2 to re-generate the fusion algorithm attribute list and attribute indicator matrix, perform multi-level subtractive clustering of the fusion algorithm and multi-attribute combination weighting, and re-implement multi-level multi-attribute decision selection.

[0170] For ease of understanding, the present invention provides a more specific embodiment:

[0171] According to different fusion data sources, M types of sources are divided into different methods. Each type of fusion method generates N corresponding fusion algorithms, which constitute a total of M×N fusion algorithm sets. Each fusion method in the generated fusion algorithm set is randomly shuffled and saved as a random fusion algorithm set. Generate an attribute list and attribute indicator matrix for each fusion method in the random fusion algorithm set. The attribute list includes data dimension A, task dimension B, and algorithm dimension C. The data dimension A includes the following indicators: data size A1, data type A2, data quantity A3, data acquisition difficulty A4; the task dimension B includes the following indicators: task quantity B1, task type B2, task relevance B3, and effective processing data volume B4; the algorithm dimension C includes the following indicators: recognition accuracy C1, fusion accuracy C2, processing time C3, and model complexity C4. The indicators of each type of attribute list are correlated with each other to form 4×4, 4×4, and 4×4 indicator correlation matrices, respectively. The attribute list values ​​of the fusion algorithm set are shown in Table 1.

[0172] Table 1 Fusion algorithm set attribute list attribute value

[0173]

[0174]

[0175] For different fusion methods, the initial neighborhood radius value is set, and the fusion algorithm set is clustered by subtractive clustering. When the number of subtractive clustering centers is less than the first set threshold, the neighborhood radius is reduced, and the subtractive clustering algorithm is re-adopted to cluster the fusion method until the number of subtractive clustering centers is greater than or equal to the first set threshold; the first set threshold with a larger comprehensive value of subtractive clustering distribution is used as the initial center of the clustering algorithm, and the initial number of clusters is specified. When the number of subtractive clustering centers is less than the first set threshold, the neighborhood radius is reduced, and subtractive clustering is continued, and finally the fusion method is clustered into 3 categories, such as Figure 2 As shown in the figure, the cluster center obtained by the subtractive clustering method replaces the initial cluster center, which can reduce the number of clustering iterations, and the center of the subtractive clustering method can be corrected again in the online update, so the obtained cluster center is more reliable. The cluster center with the largest number of fusion algorithms in the subtractive cluster center is used as the initial center, and the distribution comprehensive value of the fusion method is clustered using the clustering algorithm to obtain multiple cluster centers; the distance of each fusion method relative to each cluster center is calculated, and all distances are arranged in descending order, and the category with the smallest distance to the cluster center is selected as the category of the fusion method;

[0176] Calculate the distance between each fusion method and the distribution comprehensive value of each fusion method, take the maximum distribution comprehensive value as the subtraction cluster center, calculate the distribution comprehensive value of the remaining methods, and correct the distribution comprehensive value of each fusion method; when the distribution comprehensive value of the remaining methods is less than the preset value, output all subtraction cluster centers. Calculate the distance of each fusion method relative to each cluster center, and arrange all distances in descending order. The one with the smallest distance ranking is the category of the fusion method. After clustering, the hierarchical analysis method and the standard conflict correlation method are used to jointly determine the indicator weights for each type of method. First, the hierarchical analysis method is used to determine the weights of each indicator. After summarizing the fusion algorithm set, the three attribute indicator matrix data of the data dimension, task dimension and algorithm dimension are obtained. The relative weights of each factor in each matrix are calculated according to the above three attribute indicator matrices, and consistency tests are performed.

[0177] The weights between the obtained data dimension, task dimension and algorithm dimension, as well as the relative weights between the respective dimensions, are integrated to further calculate the total weight of each specific indicator. Finally, the comprehensive weight is determined by the hierarchical analysis method and the standard conflict correlation method. After the combined weighting, multi-level multi-attribute decision selection is performed to obtain the fusion algorithm multi-level multi-attribute decision group utility value S ranking results, individual regret value R ranking results, decision index value Q ranking and decision selection results as shown in the figure. Figure 3 , Figure 4 , Figure 5 , Figure 6 As shown, Figures 3 to 6In , a1, a2, a3, and a4 represent fusion algorithm set 1, fusion algorithm set 2, fusion algorithm set 3, and fusion algorithm set 4, respectively.

[0178] After successfully deciding to select the fusion method, determine whether the method needs to be updated online, that is, determine whether the comprehensive distribution values ​​of the data dimension, task dimension, and algorithm dimension are all greater than 0.8. If so, make a decision according to the current step; if not, jump to step 2 to regenerate the attribute list and attribute indicator matrix, multi-level subtractive clustering, and multi-attribute combination weighting, so as to achieve decision selection.

[0179] The method of the present invention can be used in multi-category and multi-attribute algorithm decision selection scenarios. The proposed method can be used in edge computing devices and automated decision-making systems. As an intelligent decision support system, the overall framework involves data acquisition, algorithm generation, algorithm processing, and algorithm decision-making. Combined with the "edge-end-cloud" deployment solution, each designed algorithm can be deployed on devices such as cloud servers or edge servers with GPUs or CPUs.

[0180] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the relevant field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents. Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A multi-level multi-attribute decision-making selection method based on subtractive clustering and combined weighting, characterized in that: include: Step 1: Generate a fusion algorithm set; Step 2: Generate fusion algorithm attribute list and attribute indicator matrix; Step 3: Use the subtractive clustering algorithm to cluster the fusion method and output multiple subtractive clustering centers; Step 4: Use the analytic hierarchy process and the standard conflict correlation method to jointly determine the indicator weights for each type of method; Step 5: Perform multi-level multi-attribute decision-making selection.

2. The method according to claim 1, characterized in that The step 1 comprises: For different fusion data sources, each corresponding type of fusion method generates N corresponding fusion algorithms, which constitute a total of M×N fusion algorithm sets. Each fusion method in the generated fusion algorithm set is randomly shuffled and saved as a random fusion algorithm set.

3. The method according to claim 1, characterized in that The step 2 comprises: For each fusion method in the random fusion algorithm set, an attribute list and an attribute indicator matrix are generated. The attribute list includes data dimension A, task dimension B, algorithm dimension C and other dimension attributes. Among them, data dimension A includes the following indicators: data size A1, data type A2, data quantity A3, data acquisition difficulty A4 and other indicators, with a total of H dimensions; task dimension B includes the following indicators: task quantity B1, task type B2, task relevance B3, effective processing data volume B4 and other indicators, with a total of J dimensions; algorithm dimension C includes the following indicators: recognition accuracy C1, fusion accuracy C2, processing time C3, model complexity C4 and other indicators, with a total of K dimensions; the indicators of each type of attribute list are correlated pairwise to form attribute indicator matrices of H×H, J×J, and K×K, respectively.

4. The method according to claim 1, characterized in that The step 3 comprises: Step 31: Obtaining the cluster center and cost function value of the subtractive clustering algorithm according to the first set threshold; Step 32: When the cost function value is less than the convergence threshold of the clustering function, the membership of each cluster center to which the fusion method is classified is updated; when the calculated cost function value is greater than the convergence threshold of the clustering function, or the number of iterations for calculating the cluster center is equal to the maximum number of iterations of the cluster function, the cluster center and the membership of each fusion method to which each cluster center is classified are output; Step 33: The fusion method output by the clustering algorithm is classified into the membership degree of each cluster center, and the clustering validity function value is calculated; Step 34: when the number of subtractive cluster centers is less than the first set threshold, the neighborhood radius is reduced, and the subtractive clustering algorithm is re-adopted to cluster the fusion method until the number of subtractive cluster centers is greater than or equal to the first set threshold; and the cluster center with the largest number of fusion algorithms in the subtractive cluster centers is used as the initial center, and the distribution comprehensive value of the fusion method is clustered using the clustering algorithm to obtain multiple cluster centers; the distance of each fusion method relative to each cluster center is calculated, and all distances are arranged in descending order, and the category with the smallest distance to the cluster center is selected as the membership category of the fusion method; Step 35: Calculate the distance between each fusion method and the distribution comprehensive value of each fusion method, take the maximum distribution comprehensive value as the subtraction cluster center, calculate the distribution comprehensive values ​​of the remaining methods, and correct the distribution comprehensive value of each fusion method; when the distribution comprehensive value of the remaining methods is less than the preset value, output all subtraction cluster centers.

5. The method according to claim 4, characterized in that In step 31, the expression of the cluster center of the subtractive clustering algorithm is: Among them, v i is the subtractive cluster center; n is the total number of fusion methods; μ ij is the fusion method x j Classified into cluster center v i The membership degree is 0≤μ ij ≤1; m is the factor coefficient of the subtractive clustering algorithm, m∈[1,∞); The expression of the cost function value of the subtractive clustering algorithm is: Among them, d ij =||v i -x j || is the subtractive cluster center v i and fusion method x j The distance between them, m is the factor coefficient, set m = 2, λ j , j = 1, ..., n is the Lagrangian factor; In step 32, the membership degree of each cluster center classified by the fusion method is updated by the following formula: Among them, d kj =||v k -x j ||, which is the cluster center v k and fusion method x j The distance between.

6. The method according to claim 5, characterized in that In step 33, the clustering validity function value is calculated by the following formula: Among them, x j is the jth fusion method in the fusion method set, c is the number of cluster centers, v i is the i-th cluster center, n is the total number of fusion method sets, μ ij is the fusion method x j Classified into cluster center v i The membership degree of ij >u kj When ij =1, otherwise δ ij =0,u kj is the fusion method x j Classified into cluster center x k The membership degree of k≠i, ||x j -v i || is the jth cluster center v j With the i-th fusion method x i The distance between them, ||v i -v j || is the i-th cluster center v i With the jth cluster center v j The distance between In step 35, the distribution value of each fusion method is composed of data size A1, data type A2, data quantity A3, data acquisition difficulty A4, other data indicators A o , task quantity B1, task type B2, task relevance B3, other task indicators B p , recognition accuracy C1, fusion accuracy C2, processing time C3, model complexity C4, other model indicators C q A one-dimensional vector composed of o ,B1,...,B2,…,B p ,C1,C2,C3,C4,…,C q ], where the distribution composite value is: Among them, γ i is the neighborhood radius; D i is the distance between fusion methods, x j and x i is the distribution of the jth and ith fusion methods in the fusion method; N is the total number of fusion methods; |x i -x j | is the distance between the distributions of the i-th fusion method and the j-th fusion method; Given x c,1 is the comprehensive distribution value of the last cluster center, D c,1 is the maximum value of the last distribution comprehensive value, then the modified fusion method x is further obtained i The comprehensive distribution value of is: When the distribution comprehensive value of the remaining methods is less than the preset value, all subtractive cluster centers are output.

7. The method according to claim 1, characterized in that The step 4 comprises: Step 41: Use the hierarchical analysis method to determine the weight of each indicator. After summarizing and arranging the fusion algorithm set, three attribute indicator matrix data are obtained: data dimension, task dimension and algorithm dimension. The relative weight of each factor in each matrix is ​​calculated based on the three attribute indicator matrices, and a consistency test is performed. Step 42: Integrate the weights between the obtained data dimension, task dimension and algorithm dimension, as well as the relative weights between their respective dimensions, and calculate the total weight of each specific indicator.

8. The method according to claim 7, characterized in that The step 42 comprises: Step 421: Using the initial sample data, establish a decision matrix for the fusion algorithm: Among them, x ij is the initial sample data corresponding to the j-th decision plan under the i-th indicator; Step 422: Standardize the indicator values ​​in the decision matrix to obtain a standardized decision matrix; where the task dimension indicator is a benefit indicator, the standardized decision matrix element z i j is: x ij -min(x ij ) If the data dimension and algorithm dimension indicators are cost-type indicators, then the standardized decision matrix element z ij for Step 423: According to the Pearson correlation coefficient, the correlation coefficient matrix between indicators is obtained: Among them, r ij is the correlation coefficient between the i-th indicator and the j-th indicator, and its expression is: Among them, z ik and z jk are the index standardized values ​​of the kth decision plan under the i-th index and the j-th index respectively; and are the means of indicators i and j respectively; Step 424: Calculate the coefficient of variation between indicators: Among them, ξ i is the coefficient of difference of the i-th indicator, ξ i ∈[0,1], using the coefficient of difference to measure the contrast intensity within the indicator, ξ i =1 means that the contrast intensity of this indicator is the largest, ξ i =0 means the contrast intensity of this indicator is the smallest; Step 425: Take the absolute value of the correlation coefficient in the conflict coefficient and calculate the conflict coefficient as: Calculate the comprehensive information content of the indicator: C i =ξ i c i Determine the indicator weights: The larger it is, the more important the role of indicator i in the multi-attribute decision-making process is, and the greater the weight factor of indicator i is; μ i is the weight of the ith indicator, w i and v i represent the weights of the criterion level indicators determined by the analytic hierarchy process and the standard conflict correlation method respectively, and the final weight μ i Use w i and v i The linear representation is 9. The method according to claim 1, characterized in that: The step 5 comprises: Step 51: Construct an evaluation model: Let A = {A1, A2, ..., A m } represents a set of m fusion algorithms, where A i represents the i-th fusion algorithm, the number of A m is the number of fusion methods; C = {C1, C2, …, C n } represents the set of n attributes of each fusion algorithm, where C j represents the jth attribute, and the number of C is the number of attributes of each fusion algorithm; Represents the weight vector of the attribute, where w j For attribute C j The weight satisfies w j ≥0 and The number of weights w is equal to the number of attributes C; ij is the fusion algorithm A i For attribute C j The value of Step 52: Standardize the decision-making indicators: Let the task dimension x ij As a benefit indicator, Let the data dimension and algorithm dimension x ij is a cost-based indicator. in, Step 53: Order and To standardize the maximum and minimum values ​​of each column in the matrix, we have Step 54: Determine the positive ideal solution and the negative ideal solution: define the solution with the maximum value of each indicator attribute as the optimal solution, and the solution with the minimum value as the worst solution. The positive ideal solution and the negative ideal solution are represented by v + and v - If it is expressed, then: Among them, v ij is the weighted normalized value of candidate node i under selection criterion j, is a positive ideal solution to the nth selection criterion, is the negative ideal solution of the nth selection criterion; Step 55: Calculate the group utility value S i and individual regret value R i ; Step 56: Calculate the compromise decision index value: Calculate the value of the decision index Q based on the group utility value S and the individual regret value R, where v is the decision-making mechanism coefficient. If v is greater than the set value, it means the decision-making mechanism is based on maximizing the group effect; if v is less than the set value, it means the decision-making mechanism is based on minimizing the individual regret value; if v is equal to the set value, it means the decision-making mechanism is based on negotiation to achieve the maximum group effect and the minimum individual regret value with equal importance; Step 57: Determine the ranking of alternatives and compromise solutions: Finally, get S i , R i , Q i The value of Q is used to sort the fusion methods in ascending order. i Sort by size, Q i The smaller the value, the better the decision method to be made; Step 58: Determine the optimal outcome of individual decisions.

10. The method according to claim 9, characterized in that The step 58 comprises: The ratio of the given contrast relationship to the final weights of the two indicators should be the same, that is, w B / w j =a Bj and w j / w W =a jW , a Bj Represents the ratio of the best index to the jth index, a jW Represents the ratio of the jth index to the worst index, and establishes the following planning model: By solving the above model, we can get the optimal weight vector w=(w1,w2,…,w n ) T and ζ, the consistency ratio CR is expressed as the ratio of the value of ζ to the maximum value of ζ, that is,

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