Product delivery resource allocation method based on fuzzy community detection

Abstract

The invention discloses a product delivery resource allocation method based on fuzzy community detection, and the method comprises the following steps: modeling a social network as a graph G = (V, E), a node set V representing users in the social network, and an edge set E representing the relation between any two users; the method comprises the following steps: step 1, initializing a membership matrix, determining the line number of the membership matrix based on an interval reduction strategy, and completing initialization of the membership matrix according to an initialization formula; and step 2, updating the membership degree matrix, alternately iterating and alternately executing membership degree smoothing and membership degree enhancement strategies, updating the membership degree matrix obtained in the step 1, and taking the updated membership degree matrix as a final result. According to the invention, the coverage rate and depth of new product information receiving by the whole network are improved, and the income after product delivery is maximized.

Description

Technical Field

[0001] The present invention relates to the field of social networks, and in particular to a product launch resource allocation method based on fuzzy community detection. Background Art

[0002] With the advancement of digitalization and information technology, online social platforms have become increasingly popular, and they have become the main virtual space for social interaction among modern people. From the perspective of graph theory, these social networks can be viewed as graphs consisting of nodes (vertices) and edges, where each user exists as a vertex, and the social connections established between them, such as friend relationships or follow relationships, form the edges in the graph. The structure of the graph facilitates the high-speed dissemination of information on the network, which has aroused the interest of the academic community in the study of its network topology. In terms of practical applications, these network platforms are not only channels for information transmission, but also important carriers for various network services and applications.

[0003] Product placement and promotion in social networks is related to the market penetration and brand influence of enterprises. In order to achieve the best promotion effect, enterprises not only need to target diversified consumer groups, but also need to accurately select nodes that span multiple communities and overlap in position as communication media under limited resources. This strategy can be implemented through fuzzy community detection methods, which focus on finding users with fuzzy positions in social networks and connecting multiple communities. Since these users can pass information to many members belonging to different communities, the value of such users is particularly prominent under limited promotion resources. According to the modeling ideas of the fuzzy community detection problem, the more fuzzy nodes can be defined as users with higher membership in multiple communities. Allocating more resources to these users will undoubtedly improve the coverage and depth of the entire network's reception of new product information.

[0004] For example, suppose an electronic product manufacturer is preparing to promote a new smartwatch. First, they can use fuzzy community detection technology to analyze existing social network data and identify groups with various interests and professional backgrounds, such as health and fitness enthusiasts, technology geeks, fashion trendsetters, etc. In these communities, they will pay special attention to users who are active in multiple groups, such as bloggers who pay attention to both health and technology trends and have a wide range of followers on social platforms. Subsequently, the manufacturer will provide these users with free trial products, exclusive discount codes or preview event invitations to encourage them to share their experience and evaluation. At the same time, according to the affiliation information of these users to various communities, the resources for launching products are allocated with emphasis. These fuzzy nodes will become amplifiers for the dissemination of product information, using their influence in different communities to make information transmitted to each group with a higher probability, thereby maximizing the benefits of promoting products.

[0005] However, existing fuzzy community detection algorithms find it difficult to strike a balance between retaining more fuzzy information and strengthening the relative affiliation between nodes and communities, and are therefore difficult to apply to product launch resource allocation problems in real life. Summary of the invention

[0006] In view of some deficiencies in the prior art, the present invention provides a product launch resource allocation method based on fuzzy community detection, which can not only find sufficiently excellent solutions, but also output solutions within an acceptable time, thus achieving a good balance between effectiveness and efficiency. Specifically, the proposed method initializes the membership matrix based on the interval reduction method, and updates the membership matrix through membership smoothing and membership enhancement strategies. The present invention provides enterprises that launch products with the optimal solution selection to maximize the benefits of resource allocation, thereby meeting the needs of solving practical problems.

[0007] In one aspect of the present invention, the present invention proposes a product launch resource allocation method based on fuzzy community detection. According to an embodiment of the present invention, the following steps are included:

[0008] Model the social network as a graph G = (V, E), where the node set V represents the users in the social network and the edge set E represents the connection between any two users;

[0009] Step 1, initialize the membership matrix, determine the number of rows of the membership matrix based on the interval reduction strategy, and complete the initialization of the membership matrix according to the initialization formula;

[0010] Step 2: Update the membership matrix, alternately iterate and execute the membership smoothing and membership enhancement strategies, update the membership matrix obtained in step 1, and use the updated membership matrix as the final result.

[0011] In addition, the product launch resource allocation method based on fuzzy community detection according to the above embodiment of the present invention may also have the following additional technical features:

[0012] In some embodiments of the present invention, in step 1, initializing the membership matrix specifically includes the following steps:

[0013] Step 1.1, determine the initial community number search interval;

[0014] Step 1.2, calculate the centrality of each node in V:

[0015] Step 1.3, calculate the distance between two nodes;

[0016] Step 1.4: Arrange the nodes from high to low according to the node centrality calculated in step 1.2, and select the central node sets corresponding to the number of communities represented by the left boundary, midpoint and right boundary of the interval respectively; divide the non-central nodes into the community where the central node is located according to the principle of the closest distance, and the distance between the nodes is calculated by step 1.3;

[0017] Step 1.5, calculate the corresponding membership matrix according to the number of communities represented by the left boundary, midpoint and right boundary of the interval;

[0018] Step 1.6, evaluate the membership matrix formed by the left boundary, midpoint and right boundary of the interval respectively, and the evaluation index adopts generalized modularity;

[0019] Step 1.7, select the points of the intervals represented by the two highest generalized modularities among the three to form a new interval;

[0020] Step 1.8, repeat steps 1.5 to 1.7 several times and then stop;

[0021] Step 1.9, select the number of communities with the highest generalized modularity in the left boundary, midpoint and right boundary of the interval obtained last time as the number of rows of the initial membership matrix; initialize the membership matrix according to the membership matrix calculation method described in step 1.5.

[0022] In some embodiments of the present invention, in step 1.2, the centrality calculation formula of each node in V is as follows:

[0023]

[0024] In the formula, Γ(v) represents the neighbor set of node v, Γ(u) represents the neighbor set of node u, and the definition of neighbor node is: i Node and v j There are connections between nodes, that is, in E (v i ,v j )≠0, then node i is the neighbor node of node j; deg(v) represents the degree of node v, deg(u) represents the degree of node u, deg(w) represents the degree of node w; centrality(v) represents the centrality of node v.

[0025] In some embodiments of the present invention, in step 1.3, the distance DK between two nodes is calculated as follows:

[0026] DK=max(K)-K

[0027] Wherein, K represents the diffusion kernel similarity between nodes, and the calculation formula of the diffusion kernel similarity K is as follows:

[0028] K=e-β×L

[0029] Where e is the base of the natural logarithm, a constant, β is a parameter, and L is the Laplace matrix;

[0030] In order to eliminate the influence of the node itself on the similarity between nodes, each element K in the diffusion kernel similarity matrix K ij is further calculated as:

[0031]

[0032] In the formula, K ij Represents the element in the i-th row and j-th column of the diffusion kernel similarity matrix K.

[0033] In some embodiments of the present invention, in step 1.5, the calculation formula of the membership matrix is ​​as follows:

[0034]

[0035] In the formula, u ij represents the element in the i-th row and j-th column of the membership matrix, c represents the number of corresponding communities, k is a natural number that increases from 1 to c during the summation process, d ij represents the distance between node i and node j, d kj Represents the distance between node k and node j. The distance between nodes is calculated by the distance DK between each pair of nodes in step 1.3. m is a parameter.

[0036] In some embodiments of the present invention, in step 1.6, the calculation formula of generalized modularity is as follows:

[0037]

[0038] In the formula, Q g represents the generalized modularity, W represents the weight matrix of the network, and w ij represents the element in the i-th row and j-th column of the weight matrix W, c represents the corresponding number of communities, k is a natural number that increases from 1 to c during the summation process, n represents the number of nodes in the corresponding network, i and j are natural numbers that increase from 1 to n during the summation process, U represents the membership matrix, u ki represents the element in the kth row and ith column of the membership matrix U, u kj represents the element in the kth row and jth column of the membership matrix U, B represents the modularity matrix, m i represents the degree of node i, m j represents the degree of node j, and tr represents the trace of the matrix.

[0039] The calculation formula of the modularity matrix B is as follows:

[0040]

[0041] In the formula, B ij represents the element in the i-th row and j-th column of the modularity matrix B; A represents the adjacency matrix of the network, A ij The element in the i-th row and j-th column of the adjacency matrix A; deg(i) represents the degree of node i, deg(j) represents the degree of node j, and m represents the sum of all edges in the network.

[0042] In some embodiments of the present invention, in step 2, updating the membership matrix specifically includes the following steps:

[0043] Step 2.1, membership smoothing strategy: perform membership smoothing operation on each column of the membership matrix;

[0044] Step 2.2, membership enhancement strategy;

[0045] Step 2.2.1, calculate the k nodes closest to the node represented by each column of the membership matrix to form a set of k nearest neighbor nodes;

[0046] Step 2.2.2, calculate the community set of the nodes represented by each column of the membership matrix;

[0047] Step 2.2.3, perform membership enhancement operation on each element of the membership matrix U;

[0048] Step 2.3, iterate steps 2.1 to 2.2 for multiple times and then stop; the updated membership matrix U obtained is taken as the final result.

[0049] In some embodiments of the present invention, in step 2.1, the smoothing operation formula is as follows:

[0050]

[0051] In the formula, u .i represents the i-th column of the membership matrix, u .j represents the jth column of the membership matrix, t represents the tth generation, t-1 represents the t-1th generation, N co Represents the consensus node set of node i;

[0052] The consensus node set calculation formula is as follows:

[0053] N co ←{j|B nj >0,j∈V}

[0054] In the formula, B represents the modularity matrix, B nj Represents the element in the nth row and jth column of the modularity matrix B; V is the node set of the network.

[0055] In some embodiments of the present invention, in step 2.2.2, the calculation formula of the community set S is as follows:

[0056]

[0057] In the formula, t represents the tth generation, t-1 represents the t-1th generation, C represents the community division obtained by analyzing the membership matrix U, and C p represents the pth community in the community partition C, N kn represents the set of k nearest neighbor nodes of node n, i represents the set N kn The elements in u pi represents the element in the p-th row and i-th column of the membership matrix U, argmax represents the index value when the maximum value is taken, and p is the index value when the maximum value is taken;

[0058] The community partition C={C1,C2,…,C k}, and the following conditions must be met:

[0059]

[0060] In the formula, V is the set of nodes in the network, k is the total number of communities, i is a natural number that increases from 1 to k during the summation process, and C i represents the i-th community, C j represents the jth community.

[0061] In some embodiments of the present invention, in step 2.2.3, the row membership enhancement operation formula is as follows:

[0062]

[0063] In the formula, u ki represents the kth row and ith column of the membership matrix, S is the community set, and k is the element in the community set.

[0064] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0065] 1. The present invention continuously updates the membership matrix by alternately executing the membership smoothing strategy and the membership enhancement strategy, which can not only maintain a clear relative membership relationship between the nodes and each community, but also allow the nodes to retain more fuzzy information.

[0066] 2. The present invention achieves a good balance between efficiency and effectiveness.

[0067] 3. The present invention designs node membership smoothing and membership enhancement strategies, and uses the node membership information obtained by the fuzzy community detection method to effectively identify user sets with high membership in multiple communities in the social network, allocate more resources to these users, improve the coverage and depth of the entire network for new product information reception, and maximize the benefits after product launch. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 It is a flow chart of a product delivery resource allocation method based on fuzzy community detection in an embodiment of the present invention;

[0069] Figure 2 Schematic diagram of membership smoothing strategy in an embodiment of the present invention;

[0070] Figure 3 Schematic diagram of membership enhancement strategy in an embodiment of the present invention. DETAILED DESCRIPTION

[0071] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0072] like Figure 1 As shown in FIG. 1 , a product launch resource allocation method based on fuzzy community detection is performed in the following steps:

[0073] Model the social network as a graph G = (V, E), where the node set V represents the users in the social network and the edge set E represents the connection between any two users;

[0074] Step 1, initialize the membership matrix, determine the number of rows of the membership matrix based on the interval reduction strategy, and complete the initialization of the membership matrix according to the initialization formula;

[0075] Step 1.1, determine the initial community number search interval;

[0076] Step 1.2, calculate the centrality of each node in V:

[0077]

[0078] In the formula, Γ(v) represents the neighbor set of node v, Γ(u) represents the neighbor set of node u, and the definition of neighbor node is: i Node and v j There are connections between nodes, that is, in E (v i ,v j)≠0, then node i is the neighbor node of node j; deg(v) represents the degree of node v, deg(u) represents the degree of node u, deg(w) represents the degree of node w; centrality(v) represents the centrality of node v.

[0079] Step 1.3: Calculate the distance between two nodes. The distance calculation formula is as follows:

[0080] DK=max(K)-K (2)

[0081] Wherein, K represents the diffusion kernel similarity between nodes, and the calculation formula of the diffusion kernel similarity K is as follows:

[0082] K=e -β×L (3)

[0083] Where e is the base of the natural logarithm, a constant, β is a parameter, and L is the Laplace matrix;

[0084] In order to eliminate the influence of the node itself on the similarity between nodes, each element K in the diffusion kernel similarity matrix K ij is further calculated as:

[0085]

[0086] Step 1.4: Arrange the nodes from high to low according to the node centrality calculated in step 1.2, and select the central node sets corresponding to the number of communities represented by the left boundary, midpoint and right boundary of the interval respectively; divide the non-central nodes into the community where the central node is located according to the principle of the closest distance, and the distance between the nodes is calculated by step 1.3:

[0087] Step 1.5: Calculate the corresponding membership matrix U according to the number of communities represented by the left boundary, the middle point and the right boundary of the interval. The calculation formula of the membership matrix is ​​as follows:

[0088]

[0089] In the formula, u ij represents the element in the i-th row and j-th column of the membership matrix, c represents the number of corresponding communities, k is a natural number that increases from 1 to c during the summation process, d ij represents the distance between node i and node j, d kj Represents the distance between node k and node j. The distances between nodes are calculated in step 1.3. m is a parameter.

[0090] Step 1.6: Evaluate the membership matrix formed by the left boundary, midpoint and right boundary of the interval respectively. The evaluation index adopts generalized modularity. The calculation formula of the generalized modularity is as follows:

[0091]

[0092] In the formula, Q g represents the generalized modularity, W represents the weight matrix of the network, and w ij represents the element in the i-th row and j-th column of the weight matrix W, c represents the corresponding number of communities, k is a natural number that increases from 1 to c during the summation process, n represents the number of nodes in the corresponding network, i and j are natural numbers that increase from 1 to n during the summation process, U represents the membership matrix, u ki represents the element in the kth row and ith column of the membership matrix U, u kj represents the element in the kth row and jth column of the membership matrix U, B represents the modularity matrix, m i represents the degree of node i, m j represents the degree of node j, and tr represents the trace of the matrix.

[0093] The calculation formula of the modularity matrix B is as follows:

[0094]

[0095] In the formula, B ij represents the element in the i-th row and j-th column of the modularity matrix B; A represents the adjacency matrix of the network, A ij The element in the i-th row and j-th column of the adjacency matrix A; deg(i) represents the degree of node i, deg(j) represents the degree of node j, and m represents the sum of all edges in the network.

[0096] Step 1.7, select the points of the intervals represented by the two highest generalized modularities among the three to form a new interval;

[0097] Step 1.8: Repeat steps 1.5 to 1.7 5 times and then stop;

[0098] Step 1.9, select the number of communities with the highest generalized modularity in the left boundary, midpoint and right boundary of the interval obtained last time as the number of rows of the initial membership matrix; initialize the membership matrix according to the membership matrix calculation formula (5) described in step 1.5;

[0099] Step 2: Update the membership matrix. Based on the alternating strategy, iteratively perform the membership smoothing and membership enhancement strategies, update the membership matrix obtained in step 1, and use the updated membership matrix as the final result.

[0100] Step 2.1, membership smoothing strategy: Perform membership smoothing operation on each column of the membership matrix U, and the smoothing operation formula is as follows:

[0101]

[0102] In the formula, u .i represents the i-th column of the membership matrix, u .j represents the jth column of the membership matrix, t represents the tth generation, t-1 represents the t-1th generation, N co Represents the consensus node set of node i;

[0103] The consensus node set calculation formula is as follows:

[0104] N co ←{j|B nj >0,j∈V} (9)

[0105] In the formula, B represents the modularity matrix, B nj Represents the element in the nth row and jth column of the modularity matrix B; V is the node set of the network.

[0106] like Figure 2 As shown, node 1 is the node to be updated. Before node 1 is smoothed, its membership is [0.8, 0.2, 0]'. Nodes 2 and 3 constitute the consensus node set of node 1. The membership of node 1 is updated according to formula (8) in step 2.1. After the update, the membership of node 1 becomes [0.54, 0.33, 0.13]'.

[0107] Step 2.2: Membership enhancement strategy

[0108] Step 2.2.1, calculate the k nodes closest to the node represented by each column of the membership matrix U, and form a set of k nearest neighbor nodes. The distance between the nodes is calculated by formula (2) in step 1.3:

[0109] Step 2.2.2, calculate the community set S of the nodes represented by each column of the membership matrix U. The calculation formula of the set S is as follows:

[0110]

[0111] In the formula, t represents the tth generation, t-1 represents the t-1th generation, C represents the community division obtained by analyzing the membership matrix U, and C p represents the pth community in the community partition C, N kn represents the set of k nearest neighbor nodes of node n, i represents the set N kn The elements in u pi represents the element in the p-th row and i-th column of the membership matrix U, argmax represents the index value when the maximum value is taken, and p is the index value when the maximum value is taken;

[0112] The community partition C={C1,C2,…,C k}, and the following conditions must be met:

[0113]

[0114] In the formula, V is the set of nodes in the network, k is the total number of communities, i is a natural number that increases from 1 to k during the summation process, and C i represents the i-th community, C j represents the jth community.

[0115] Step 2.2.3: Perform a membership enhancement operation on each element of the membership matrix U. The enhancement operation formula is as follows:

[0116]

[0117] In the formula, u ki represents the kth row and ith column of the membership matrix, S is the community set, and k is the element in the community set.

[0118] like Figure 3 As shown, node 1 and node 2 are nodes to be updated. Before node 1 is enhanced, its membership is [0.4, 0.3, 0.1, 0.2]'. Node 1, node 3 and node 4 constitute the set of 3 nearest neighbor nodes of node 1. The maximum membership values ​​of node 1, node 3 and node 4 fall in communities 1, 2 and 4 respectively. Therefore, the community set S formed by node 1 is S = {C1, C2, C4}. According to formula (12) in step 2.2.3, node 1 is updated. After the update, the membership of node 1 is [0.45, 0.33, 0, 0.22]'; similarly, the membership of node 2 is updated from [0.1, 0.5, 0.2, 0.2]' to [0, 0.71, 0.29, 0]'.

[0119] Step 2.3, iterate step 2.1 to step 2.2 100 times and then stop; the updated membership matrix U is taken as the final result.

[0120] The above contents are merely examples and explanations of the structure of the present invention. The technicians in this technical field may make various modifications or additions to the specific embodiments described or replace them in a similar manner. As long as they do not deviate from the structure of the present invention or exceed the scope defined by the claims, they should all fall within the protection scope of the present invention.

Claims

1. A product launch resource allocation method based on fuzzy community detection, characterized in that: The following steps are involved: Model the social network as a graph G = (V, E), where the node set V represents the users in the social network and the edge set E represents the connection between any two users; Step 1, initialize the membership matrix, determine the number of rows of the membership matrix based on the interval reduction strategy, and complete the initialization of the membership matrix according to the initialization formula; Step 2: Update the membership matrix, alternately iterate and execute the membership smoothing and membership enhancement strategies, update the membership matrix obtained in step 1, and use the updated membership matrix as the final result.

2. According to the method of product release resource allocation based on fuzzy community detection in claim 1, it is characterized in that: In step 1, initializing the membership matrix specifically includes the following steps: Step 1.1, determine the initial community number search interval; Step 1.2, calculate the centrality of each node in V: Step 1.3, calculate the distance between two nodes; Step 1.4: Arrange the nodes from high to low according to the node centrality calculated in step 1.2, and select the central node sets corresponding to the number of communities represented by the left boundary, midpoint and right boundary of the interval respectively; divide the non-central nodes into the community where the central node is located according to the principle of the closest distance, and the distance between the nodes is calculated by step 1.3; Step 1.5, calculate the corresponding membership matrix according to the number of communities represented by the left boundary, midpoint and right boundary of the interval; Step 1.6, evaluate the membership matrix formed by the left boundary, midpoint and right boundary of the interval respectively, and the evaluation index adopts generalized modularity; Step 1.7, select the points of the intervals represented by the two highest generalized modularities among the three to form a new interval; Step 1.8, repeat steps 1.5 to 1.7 several times and then stop; Step 1.9, select the number of communities with the highest generalized modularity in the left boundary, midpoint and right boundary of the interval obtained last time as the number of rows of the initial membership matrix; initialize the membership matrix according to the membership matrix calculation method described in step 1.

5.

3. The method for allocating product resources based on fuzzy community detection according to claim 2, characterized in that: In step 1.2, the centrality calculation formula of each node in V is as follows: In the formula, Γ(v) represents the neighbor set of node v, Γ(u) represents the neighbor set of node u, and the definition of neighbor node is: i Node and v j There are connections between nodes, that is, in E (v i , v j )≠0, then node i is the neighbor node of node j; deg(v) represents the degree of node v, deg(u) represents the degree of node u, deg(w) represents the degree of node w; centrality(v) represents the centrality of node v.

4. The method for allocating product launch resources based on fuzzy community detection according to claim 3, characterized in that: In step 1.3, the distance DK between two nodes is calculated as follows: DK=max(K)-K Wherein, K represents the diffusion kernel similarity between nodes, and the calculation formula of the diffusion kernel similarity K is as follows: K=e -β ×L Where e is the base of the natural logarithm, a constant, β is a parameter, and L is the Laplace matrix; In order to eliminate the influence of the node itself on the similarity between nodes, each element K in the diffusion kernel similarity matrix K ij is further calculated as: In the formula, K ij Represents the element in the i-th row and j-th column of the diffusion kernel similarity matrix K.

5. The method for allocating product resources based on fuzzy community detection according to claim 4 is characterized in that: In step 1.5, the calculation formula of the membership matrix is ​​as follows: In the formula, u ij represents the element in the i-th row and j-th column of the membership matrix, c represents the number of corresponding communities, k is a natural number that increases from 1 to c during the summation process, d ij represents the distance between node i and node j, d kj Represents the distance between node k and node j. The distance between nodes is calculated by the distance DK between each pair of nodes in step 1.

3. m is a parameter.

6. The method for allocating product resources based on fuzzy community detection according to claim 5, characterized in that: In step 1.6, the calculation formula of generalized modularity is as follows: In the formula, Q g represents the generalized modularity, W represents the weight matrix of the network, and w ij represents the element in the i-th row and j-th column of the weight matrix W, c represents the corresponding number of communities, k is a natural number that increases from 1 to c during the summation process, n represents the number of nodes in the corresponding network, i and j are natural numbers that increase from 1 to n during the summation process, U represents the membership matrix, u ki represents the element in the kth row and ith column of the membership matrix U, u kj represents the element in the kth row and jth column of the membership matrix U, B represents the modularity matrix, m i represents the degree of node i, m j represents the degree of node j, tr represents the trace of the matrix; The calculation formula of the modularity matrix B is as follows: In the formula, B ij represents the element in the i-th row and j-th column of the modularity matrix B; A represents the adjacency matrix of the network, A ij The element in the i-th row and j-th column of the adjacency matrix A; deg(i) represents the degree of node i, deg(j) represents the degree of node j, and m represents the sum of all edges in the network.

7. The method for allocating product resources based on fuzzy community detection according to claim 1, characterized in that: In step 2, updating the membership matrix specifically includes the following steps: Step 2.1, membership smoothing strategy: perform membership smoothing operation on each column of the membership matrix; Step 2.2, membership enhancement strategy; Step 2.2.1, calculate the k nodes closest to the node represented by each column of the membership matrix to form a set of k nearest neighbor nodes; Step 2.2.2, calculate the community set of the nodes represented by each column of the membership matrix; Step 2.2.3, perform membership enhancement operation on each element of the membership matrix U; Step 2.3, iterate steps 2.1 to 2.2 for multiple times and then stop; the updated membership matrix U obtained is taken as the final result.

8. The method for allocating product resources based on fuzzy community detection according to claim 7, characterized in that: In step 2.1, the smoothing operation formula is as follows: In the formula, u. i represents the i-th column of the membership matrix, u. j represents the jth column of the membership matrix, t represents the tth generation, t-1 represents the t-1th generation, N co represents the consensus node set of node i; The consensus node set calculation formula is as follows: N co ←{j|B nj >0,j∈V} In the formula, B represents the modularity matrix, B nj Represents the element in the nth row and jth column of the modularity matrix B; V is the node set of the network.

9. The method for allocating product launch resources based on fuzzy community detection according to claim 7, characterized in that: In step 2.2.2, the calculation formula of the community set S is as follows: In the formula, t represents the tth generation, t-1 represents the t-1th generation, C represents the community division obtained by analyzing the membership matrix U, and C p represents the pth community in the community partition C, N kn represents the set of k nearest neighbor nodes of node n, i represents the set N kn The elements in u pi represents the element in the p-th row and i-th column of the membership matrix U, argmax represents the index value when the maximum value is taken, and p is the index value when the maximum value is taken; The community partition C={C1,C2,…,C k }, and the following conditions must be met: In the formula, V is the set of nodes in the network, k is the total number of communities, i is a natural number that increases from 1 to k during the summation process, and C i represents the i-th community, C j represents the jth community.

10. The method for allocating product launch resources based on fuzzy community detection according to claim 9, characterized in that: In step 2.2.3, the row membership enhancement operation formula is as follows: In the formula, u ki represents the element in the kth row and ith column of the membership matrix, S is the community set, and k is the element in the community set.

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