Multi-index fusion attack-defense game strategy solving method based on fuzzy language

Abstract

The application discloses a multi-index fusion attack and defense game strategy solving method based on fuzzy language, and the method comprises the following steps: constructing an infrastructure network game model; determining EI evaluation indexes representing network performance; for each index, respectively calculating the payoff matrix of player 1 and player 2 in the infrastructure network game under various strategy profiles, and obtaining the payoff matrix corresponding to the EI indexes; dividing the threat degree of the strategy under each evaluation index into T grades by using fuzzy language; dividing the values in the payoff matrix into threat grades; when the value of the payoff matrix falls within a certain interval, converting the value of the payoff matrix into an intuitionistic fuzzy number according to the threat grade corresponding to the interval, and obtaining EI intuitionistic fuzzy set payoff matrices; and combining the intuitionistic fuzzy set theory to convert the solving of the infrastructure network game model into the solving of a nonlinear programming problem, and obtaining the mixed strategy Nash equilibrium solution of player 1 and player 2.

Description

Technical Field

[0001] This invention relates to the field of complex network game technology in systems engineering, and in particular to a method for solving attack and defense game strategies based on fuzzy language and multi-index fusion. Background Technology

[0002] In the current field of game theory research, there is a special type of network game where the network is not a real-world computer system, but rather a network topology that abstracts critical infrastructure, such as train stations and airports, into nodes, and the connections between different sites into edges, creating a complex infrastructure network. In the security field, critical nodes in infrastructure are vulnerable to attacks, which can impact public order and normal social life. Security departments need to protect these nodes. Complex network game theory can be used to study the attack and protection of critical nodes in infrastructure networks, helping to formulate optimal protection strategies and explore the importance of these nodes.

[0003] Current research addresses this type of problem, but existing studies only provide objective evaluation methods based on network topology. For example, in a fully informed static or dynamic game framework, they use the network connectivity performance metric—maximum connected component size—to calculate the payoff matrices for attackers and defenders, and then calculate the corresponding Nash equilibrium strategies. However, in real-world game problems, the understanding of the problem by both sides is uncertain, information is insufficient, and the decision-making environment is unpredictable. Existing methods cannot effectively incorporate the subjective judgments of decision-makers and cannot express the ambiguity and uncertainty of real-world game problems. Currently, some related studies only use the maximum connected component size as an indicator when evaluating network performance, which is only a limited...

[0004] Professor Zadeh proposed fuzzy set theory, providing a reasonable approach to solving such problems. Addressing the limitations of fuzzy set theory and the practical need to express hesitation, Atanassov proposed intuitionistic fuzzy set theory, which uses two scales (membership and non-membership) to represent support, opposition, and hesitation in fuzzy phenomena. This theory offers insights into solving more complex game theory problems. Currently, there is limited research on applying intuitionistic fuzzy set theory to complex network games in infrastructure, making this area of ​​research significant. Summary of the Invention

[0005] This invention aims to at least solve one of the technical problems existing in the prior art. To this end, this invention discloses a method for solving attack-defense game strategies based on fuzzy language and multi-index fusion. The method utilizes the two-person zero-sum matrix game of intuitionistic fuzzy sets, proposing a method to generate an intuitionistic fuzzy payoff matrix based on a correspondence table of data intervals, fuzzy language, and intuitionistic fuzzy numbers. Under intuitionistic fuzzy conditions, an efficient algorithm is used to solve for the Nash equilibrium solution, ultimately obtaining an optimized method and result for the attacker's strategy.

[0006] The objective of this invention is achieved through the following technical solution: a multi-index fusion attack-defense game strategy solution based on fuzzy language, the method comprising:

[0007] Step 1: Obtain the topology of the infrastructure network, with the attacker and defender being Player 1 and Player 2, respectively. Determine the strategy sets of Player 1 and Player 2, and construct the infrastructure network game model.

[0008] Step 2: Determine EI evaluation metrics representing network performance. For each metric, calculate the payoff matrix for player 1 and player 2 in the infrastructure network game under various strategy profiles, obtaining the payoff matrices P1, P2, ..., P1 corresponding to the EI metrics. EI ;

[0009] Step 3: Use fuzzy language to divide the threat level of the strategy under each evaluation indicator into T levels, with each level corresponding to an intuitionistic fuzzy number;

[0010] Step 4, for the payment matrix P1, P2, ..., P mentioned in Step 2 EI The values ​​in the payoff matrix are used to classify threat levels. When the values ​​in the payoff matrix fall within a certain interval, the values ​​in the payoff matrix are converted into intuitionistic fuzzy numbers according to the threat level corresponding to the interval, resulting in EI intuitionistic fuzzy set payoff matrices.

[0011] Step 5: Give the weights w1, w2, ..., w of the EI evaluation indicators. EI EI intuitionistic fuzzy set payment matrix By using intuitionistic fuzzy weighted set sub-weighted fusion, a comprehensive intuitionistic fuzzy set payment matrix is ​​obtained.

[0012] Step 6: Combining intuitionistic fuzzy set theory, the solution of the infrastructure network game model is transformed into the solution of a nonlinear programming problem, and the mixed strategy Nash equilibrium solution of player 1 and player 2 is obtained.

[0013] The infrastructure network is represented as a simple undirected graph G(V,E), where V={v1,v2,...,v...}N} represents the set of all nodes in the infrastructure network, where N = |V| represents the number of nodes in the infrastructure network. It is the set of all edges in the infrastructure network.

[0014] Specifically, the attacker's attack strategy set is S. A For an attack strategy vector s A =[x1,x2,...,x N ]∈S A x i Indicate whether the i-th infrastructure has been attacked, denoted by . Let i be the set of attacking nodes, and let v be the i-th node. i Being attacked, i.e., v i ∈V A x i =1, otherwise x i =0; the set of defense strategies of the defending side is S. D A defense strategy vector s of the defending side D =[y1,y2,...,y N ]∈S D y i Indicates whether the i-th infrastructure is defended, denoted by . Let i be the set of defense nodes, and let v be the i-th node. i Being defended, i.e., v i ∈V D y i =1, otherwise y i =0, for the attacked node v i If x exists simultaneously i =1 and y i =0, meaning that although attacked, node v is not protected. i It will be removed;

[0015] For the i-th node v i ,remember and Let these be the attack cost for the attacker and the defense cost for the defender, respectively. When the cost is even, Let the resources available to the attacker be n. A The defending side has n available resources. D This refers to the number of nodes attacking or defending; the set of all defending nodes is denoted as . So The infrastructure network after the defense node is removed is denoted as:

[0016] Furthermore, the payment matrix includes the attacker's payment matrix and the defender's payment matrix. Let i be the attacker's payoff function under network performance metric i, then This represents the attacker's gain when choosing attack strategy X and the defender's gain when choosing defense strategy Y under network performance metric i. Let represent the benefit to the defender when the attacker chooses attack strategy X and the defender chooses defense strategy Y under network performance metric i. The benefits to the attacker and the defender are as follows:

[0017]

[0018] Wherein, Γ1,Γ2,......,Γ EI Let Γ1(G), Γ2(G), ..., Γ2(G) be the calculation functions for different evaluation metrics under the same strategy profile, representing the different return values ​​calculated by different evaluation metrics. EI (G) represents the function value of the initial network under various evaluation metrics, and the set of all removed nodes is denoted as . The network formed after the nodes are removed is It is the set of all edges in the infrastructure network formed after nodes are removed. Let represent the function values ​​of the network under various evaluation metrics after one round of attack and defense game, and satisfy:

[0019] Specifically, a correspondence table between fuzzy language and intuitionistic fuzzy numbers is designed:

[0020]

[0021]

[0022] For the payment matrix P1, P2, ..., P corresponding to the EI evaluation indicators EI The threat levels are determined by the numerical values ​​in the table, and the corresponding relationships are as follows:

[0023]

[0024] in, This indicates the right boundary of threat level 1 under assessment indicator 1. This indicates the right boundary of threat level 8 under the assessment indicator EI. Other symbols in the table represent the boundaries of the corresponding intervals.

[0025] When the values ​​of the payoff matrix fall within a certain interval, the values ​​are converted into intuitionistic fuzzy numbers based on the threat level corresponding to that interval, thus obtaining EI intuitionistic fuzzy set payoff matrices. If the attacker chooses strategy s i =[x1,x2,...,xN ]∈S A The defending side chooses strategy s j =[y1,y2,...,y N ]∈S D Transformed into intuitive fuzzy numbers a according to the correspondence relationship ij =(μ ij ,ν ij In the evaluation indicator c i Below, the defender's intuitive fuzzy matrix is ​​represented as:

[0026]

[0027] in, These respectively represent the evaluation indicators c g The intuitionistic fuzzy number is obtained by converting the payoff values ​​of different strategy profiles, where m represents the number of attack strategies of the attacker and n represents the number of defense strategies of the defender.

[0028] Let a j =<μ j ,ν j >(j=1,2,…,k) is a set of intuitionistic fuzzy sets. The intuitionistic fuzzy weighted set sub-calculation is defined as:

[0029]

[0030] In the formula, ω=(ω1,ω2,…,ω k ) is a j The weight vector (j = 1, 2, ..., k) satisfies the condition 0 ≤ ω j ≤1, Using Intuitive Fuzzy Weighted Set Calculation Subsidiary IFWA ω The EI intuitionistic fuzzy set payoff matrices are weighted and aggregated into a comprehensive intuitionistic fuzzy set payoff matrix. Right now

[0031]

[0032] Among them, a ij =(μ ij ,v ij ), Indicator c g Membership function; Indicator c g The non-membership function is ω; i represents the attack strategy of the attacker; j represents the defense strategy of the defender; ω g This indicates the weight value of the corresponding evaluation indicator.

[0033] Furthermore, for the comprehensive intuitionistic fuzzy set payoff matrix, the nonlinear programming problem is:

[0034] min{(1-μ) λ ν 1-λ}

[0035]

[0036] and

[0037] min{(1-σ) λ ρ 1-λ}

[0038]

[0039] Where i represents the attacking side's i-th attack strategy, with a total of m attack strategies; j represents the defending side's j-th defense strategy, with a total of n defense strategies; μ ij This represents the membership function value in the attacker's intuitionistic fuzzy set payoff matrix when the attacker chooses the i-th attack strategy and the defender chooses the j-th defense strategy. ij Let represent the non-membership function value in the attacker's intuitionistic fuzzy set payoff matrix when the attacker chooses the i-th attack strategy and the defender chooses the j-th defense strategy; λ represents the relative weights of the membership / non-membership function constraints. Once λ is determined, the resulting Nash equilibrium solution is: (p,q,<μ,ν>,<σ,ρ>); p=(p1,p2,...,p m ) T Let q = (q1, q2, ..., q...) represent the probability vector of the attacker's mixed strategy. m ) T Let represent the probability vector of the defender's mixed strategy; <μ,ν> represent the attacker's payoff in the game problem; and <σ,ρ> represent the defender's payoff in the game problem. Both are intuitionistic fuzzy sets.

[0040] Compared with existing methods, the advantages of this invention are as follows: Network attack-defense game theory has been a research hotspot in recent years; however, existing research cannot reflect the ambiguity of decision-makers' understanding of the game problem. This invention proposes a multi-index fusion strategy solution method for attack-defense games based on fuzzy language, provides a method for generating and solving the intuitionistic fuzzy payoff matrix under uncertain conditions, and finally obtains the reasonable strategy choices that both attackers and defenders should make under fuzzy conditions, and analyzes the results. Using intuitionistic fuzzy theory to explain the uncertainty of network attack-defense games can greatly broaden the practical application of network attack-defense game research. Attached Figure Description

[0041] Figure 1 A flowchart illustrating an embodiment of the present invention is shown;

[0042] Figure 2 A schematic diagram of the infrastructure network in an embodiment of the present invention is shown. Detailed Implementation

[0043] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are merely some embodiments of this invention, and not all embodiments. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0044] It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0045] This embodiment considers only one attacker and one defender, both of whom have complete knowledge of the existing network topology. A critical infrastructure, such as a railway network, can be abstracted as a simple undirected graph G(V,E), where V={v1,v2,...,v...} N} represents the set of all nodes in the network, i.e., the stations in the railway network, where N = |V| represents the number of nodes in the network. It is the set of all edges in a network, i.e., the railway lines in a railway network.

[0046] Consider only one attacker and one defender, both with complete knowledge of the existing network topology. All attacks and defenses target nodes within the network. A node is considered successfully compromised when it is attacked by the attacker and not protected by the defender. This is a two-player zero-sum game; the more important the node, the higher the cost of attacking or defending.

[0047] like Figure 1 As shown, a multi-index fusion attack-defense game strategy solution method based on fuzzy language is presented, the method comprising:

[0048] Step 1: Obtain the topology of the infrastructure network, with the attacker and defender being Player 1 and Player 2, respectively. Determine the strategy sets of Player 1 and Player 2, and construct the infrastructure network game model.

[0049] Step 2: Determine EI evaluation metrics representing network performance. For each metric, calculate the payoff matrix for player 1 and player 2 in the infrastructure network game under various strategy profiles, obtaining the payoff matrices P1, P2, ..., P1 corresponding to the EI metrics. EI ;

[0050] Step 3: Use fuzzy language to divide the threat level of the strategy under each evaluation indicator into T levels, with each level corresponding to an intuitionistic fuzzy number;

[0051] Step 4, for the payment matrix P1, P2, ..., P mentioned in Step 2 EI The values ​​in the payoff matrix are used to classify threat levels. When the values ​​in the payoff matrix fall within a certain interval, the values ​​in the payoff matrix are converted into intuitionistic fuzzy numbers according to the threat level corresponding to the interval, resulting in EI intuitionistic fuzzy set payoff matrices.

[0052] Step 5: Give the weights w1, w2, ..., w of the EI evaluation indicators. EI EI intuitionistic fuzzy set payment matrix By using intuitionistic fuzzy weighted set sub-weighted fusion, a comprehensive intuitionistic fuzzy set payment matrix is ​​obtained.

[0053] Step 6: Combining intuitionistic fuzzy set theory, the solution of the infrastructure network game model is transformed into the solution of a nonlinear programming problem, and the mixed strategy Nash equilibrium solution of player 1 and player 2 is obtained.

[0054] The infrastructure network is represented as a simple undirected graph G(V,E), where V={v1,v2,...,v...} N} represents the set of all nodes in the infrastructure network, where N = |V| represents the number of nodes in the infrastructure network. It is the set of all edges in the infrastructure network.

[0055] Specifically, the attacker's attack strategy set is S. A For an attack strategy vector s A =[x1,x2,...,x N ]∈S A x i Indicate whether the i-th infrastructure has been attacked, denoted by . Let i be the set of attacking nodes, and let v be the i-th node. i Being attacked, i.e., v i ∈V A x i =1, otherwise x i =0; the set of defense strategies of the defending side is S. D A defense strategy vector s of the defending side D =[y1,y2,...,y N ]∈S D y i Indicates whether the i-th infrastructure is defended, denoted by . Let i be the set of defense nodes, and let v be the i-th node. i Being defended, i.e., v i ∈V Dy i =1, otherwise y i =0, for the attacked node v i If x exists simultaneously i =1 and y i =0, meaning that although attacked, node v is not protected. i It will be removed;

[0056] For the i-th node v i ,remember and Let these be the attack cost for the attacker and the defense cost for the defender, respectively. When the cost is even, Let the resources available to the attacker be n. A The defending side has n available resources. D This refers to the number of nodes attacking or defending; the set of all defending nodes is denoted as . So The infrastructure network after the defense node is removed is denoted as:

[0057] Furthermore, the payment matrix includes the attacker's payment matrix and the defender's payment matrix. |S A |×|S D Let | be the attacker's profit function under network performance metric i, then This represents the attacker's gain when choosing attack strategy X and the defender's gain when choosing defense strategy Y under network performance metric i. Let represent the benefit to the defender when the attacker chooses attack strategy X and the defender chooses defense strategy Y under network performance metric i. The benefits to the attacker and the defender are as follows:

[0058]

[0059]

[0060] Wherein, Γ1,Γ2,……,Γ EI Let EI be the calculation function for three different evaluation metrics, representing the different return values ​​calculated for different evaluation metrics under the same strategy profile, Γ1(G), Γ2(G), ..., Γ EI (G) represents the function value of the initial network under various evaluation metrics, and the set of all removed nodes is denoted as . The network formed after the nodes are removed is It is the set of all edges in the infrastructure network formed after nodes are removed. Let represent the function values ​​of the network under various evaluation metrics after one round of attack and defense game, and satisfy:

[0061] Specifically, a correspondence table between fuzzy language and intuitionistic fuzzy numbers is designed:

[0062]

[0063] For the payment matrix P1, P2, ..., P corresponding to the EI evaluation indicators EI The threat levels are determined by the numerical values ​​in the table, and the corresponding relationships are as follows:

[0064]

[0065]

[0066] in, This indicates the right boundary of threat level 1 under assessment indicator 1. This indicates the right boundary of threat level 8 under the assessment indicator EI. Other symbols in the table represent the boundaries of the corresponding intervals.

[0067] When the values ​​of the payoff matrix fall within a certain interval, the values ​​are converted into intuitionistic fuzzy numbers based on the threat level corresponding to that interval, thus obtaining EI intuitionistic fuzzy set payoff matrices. If the attacker chooses strategy s i =[x1,x2,...,x N ]∈S A The defending side chooses strategy s j =[y1,y2,...,y N ]∈S D Transformed into intuitive fuzzy numbers a according to the correspondence relationship ij =(μ ij ,ν ij In the evaluation indicator c i Below, the defender's intuitive fuzzy matrix is ​​represented as:

[0068]

[0069] in, These respectively represent the evaluation indicators c g The intuitionistic fuzzy number is obtained by converting the payoff values ​​of different strategy profiles, where m represents the number of attack strategies of the attacker and n represents the number of defense strategies of the defender.

[0070] Let a j =<μ j ,ν j Let (j=1,2,λ,k) be a set of intuitionistic fuzzy sets. The intuitionistic fuzzy weighted set sub-calculation is defined as:

[0071]

[0072] In the formula, ω=(ω1,ω2,λ,ω k ) is a j The weight vector (j = 1, 2, ..., k) satisfies the condition 0 ≤ ω j ≤1, Using Intuitive Fuzzy Weighted Set Calculation Subsidiary IFWA ω The EI intuitionistic fuzzy set payoff matrices are weighted and aggregated into a comprehensive intuitionistic fuzzy set payoff matrix. Right now

[0073]

[0074] Among them, a ij =(μ ij ,v ij ), Indicator c g Membership function; Indicator c g The non-membership function is ω; i represents the attack strategy of the attacker; j represents the defense strategy of the defender; ω g This indicates the weight value of the corresponding evaluation indicator.

[0075] Furthermore, for the comprehensive intuitionistic fuzzy set payoff matrix, the nonlinear programming problem is:

[0076] min{(1-μ) λ ν 1-λ}

[0077]

[0078] and

[0079] min{(1-σ) λ ρ 1-λ}

[0080]

[0081] Where i represents the attacking side's i-th attack strategy, with a total of m attack strategies; j represents the defending side's j-th defense strategy, with a total of n defense strategies; μ ij This represents the membership function value in the attacker's intuitionistic fuzzy set payoff matrix when the attacker chooses the i-th attack strategy and the defender chooses the j-th defense strategy. ijLet represent the non-membership function value in the attacker's intuitionistic fuzzy set payoff matrix when the attacker chooses the i-th attack strategy and the defender chooses the j-th defense strategy; λ represents the relative weights of the membership / non-membership function constraints. Once λ is determined, the resulting Nash equilibrium solution is: (p,q,<μ,ν>,<σ,ρ>); p=(p1,p2,...,p m ) T Let q = (q1, q2, ..., q...) represent the probability vector of the attacker's mixed strategy. m ) T Let <μ,ν> represent the probability vector of the defender's mixed strategy; let <σ,ρ> represent the attacker's payoff in the game problem; and let <σ,ρ> represent the defender's payoff in the game problem. Both are intuitionistic fuzzy sets.

[0082] In real life, infrastructure network structures vary widely. This experiment uses a 16-node scale-free network structure as an example. Figure 2 As shown.

[0083] In a specific embodiment, three indicators are used: maximum connected component size, number of connected nodes, and network efficiency. Fuzzy logic is used to divide each indicator into eight levels, with weights of 0.33, 0.33, and 0.33 for each indicator. The resulting payoff matrix under different evaluation indicators is shown below:

[0084]

[0085]

[0086] Based on the transformation table between threat levels and intuitionistic fuzzy sets, the above precise payoff matrix is ​​converted into an intuitionistic fuzzy set matrix, as shown below:

[0087]

[0088]

[0089]

[0090] Based on the intuitionistic fuzzy weighted ensemble operator, and given the weights of the three evaluation indicators as ω1 = 0.33, ω2 = 0.33, and ω3 = 0.33, the intuitionistic fuzzy set payoff matrix is ​​obtained as follows:

[0091]

[0092] After obtaining the intuitionistic fuzzy set payoff matrix, the model solution process can yield the Nash equilibrium mixed strategy solution.

[0093] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

Claims

1. A method for solving attack-defense game strategies based on multi-index fusion using fuzzy language, characterized in that, The method includes: Step 1: Obtain the topology of the infrastructure network, with the attacker and defender being Player 1 and Player 2, respectively. Determine the strategy sets of Player 1 and Player 2, and construct the infrastructure network game model. Step 2: Determine EI evaluation metrics representing network performance. For each metric, calculate the payoff matrix for player 1 and player 2 in the infrastructure network game under various strategy profiles, obtaining the payoff matrices P1, P2, ..., P1 corresponding to the EI metrics. EI ; Step 3: Use fuzzy language to divide the threat level of the strategy under each evaluation indicator into T levels, with each level corresponding to an intuitionistic fuzzy number; Step 4, for the payment matrix P1, P2, ..., P mentioned in Step 2 EI The values ​​in the payoff matrix are used to classify threat levels. When the values ​​in the payoff matrix fall within a certain interval, the values ​​in the payoff matrix are converted into intuitionistic fuzzy numbers according to the threat level corresponding to the interval, resulting in EI intuitionistic fuzzy set payoff matrices. , ,......, ; Step 5: Give the weights w1, w2, ..., w of the EI evaluation indicators. EI EI intuitionistic fuzzy set payment matrix , ,......, By using intuitionistic fuzzy weighted set sub-weighted fusion, a comprehensive intuitionistic fuzzy set payment matrix is ​​obtained. ; Step 6: Combining intuitionistic fuzzy set theory, the solution of the infrastructure network game model is transformed into the solution of a nonlinear programming problem, and the mixed strategy Nash equilibrium solution of player 1 and player 2 is obtained. The infrastructure network is represented as a simple undirected graph. ,in Represents the set of all nodes in the infrastructure network, where, This indicates the number of nodes in the infrastructure network. It is the set of all edges in the infrastructure network; Specifically, when the value of the payoff matrix falls within a certain interval, the value of the payoff matrix is ​​converted into an intuitionistic fuzzy number based on the threat level corresponding to the interval, thereby obtaining EI intuitionistic fuzzy set payoff matrices. , ,......, If the attacker chooses an attack strategy The defender chooses a defense strategy. Transformed into intuitive fuzzy numbers according to the correspondence relationship In the evaluation indicators Below, the defender's intuitive fuzzy matrix is ​​represented as: in, , ,......, These respectively represent the evaluation indicators The intuitionistic fuzzy numbers obtained by converting the payoff values ​​of different strategy profiles. This indicates the number of attack strategies employed by the attacker. Indicates the number of defensive strategies employed by the defending side; set up Given a set of intuitionistic fuzzy sets, the intuitionistic fuzzy weighted set sub-calculator is defined as: In the formula, for The weight vector satisfies the condition , , Using intuitionistic fuzzy weighted set to calculate the quant The EI intuitionistic fuzzy set payoff matrices are weighted and aggregated into a comprehensive intuitionistic fuzzy set payoff matrix. ,Right now in, , , , Indicators Membership function; Indicators The non-membership function; Indicates the attacker's... One attack strategy; The first one represents the defending side One defense strategy; This indicates the weight value of the corresponding evaluation indicator.

2. The method for solving attack and defense game strategies based on fuzzy language according to claim 1, characterized in that, The attack strategy set of the attacker is as follows: For an attack strategy vector , Indicates the first Whether the infrastructure has been attacked, record Let be the set of attacking nodes, if the first... Nodes Being attacked, i.e. , ,otherwise The set of defense strategies of the defending side is as follows: A defense strategy vector of the defending side , Indicates the first Whether the infrastructure is defended, record Let be the set of defense nodes, if the first... Nodes Being defended, i.e. , ,otherwise For the attacked node If both exist and That is, if a node is attacked but not protected, then... It will be removed; For the Nodes ,remember and Let these be the attack cost for the attacker and the defense cost for the defender, respectively. When the cost is uniform... , Assume the resources available to the attacker are... The resources available to the defender are This refers to the number of nodes attacking or defending; the set of all defending nodes is denoted as . ,So The infrastructure network after the defense node is removed is denoted as: .

3. The method for solving multi-index fusion attack-defense game strategies based on fuzzy language according to claim 1 or 2, characterized in that, The payment matrix includes the attacker's payment matrix and the defender's payment matrix, and the defender's set of defense strategies is as follows: The attacker's attack strategy set is as follows: , Let i be the attacker's payoff function under network performance metric i, then This represents the attacker's gain when choosing attack strategy X and the defender's gain when choosing defense strategy Y under network performance metric i. Let represent the benefit to the defender when the attacker chooses attack strategy X and the defender chooses defense strategy Y under network performance metric i. The benefits to the attacker and the defender are as follows: in, Let EI be the calculation function for different evaluation metrics, indicating that under the same strategy profile, different evaluation metrics yield different return values. Let represent the function values ​​of the initial network under various evaluation metrics, and denote the set of all removed nodes as . The network formed after the nodes are removed is , It is the set of all edges in the infrastructure network formed after nodes are removed. Let represent the function values ​​of the network under various evaluation metrics after one round of attack and defense game, and satisfy: , .

4. The method for solving attack-defense game strategies based on fuzzy language according to claim 3, characterized in that, Design a table showing the correspondence between fuzzy language and intuitionistic fuzzy numbers: For the payment matrix P1, P2, ..., P corresponding to the EI evaluation indicators EI The threat levels are determined by the numerical values ​​in the table, and the corresponding relationships are as follows: in, This indicates the right boundary of threat level 1 under assessment indicator 1. This indicates the right boundary of threat level 8 under the assessment indicator EI. Other symbols in the table represent the boundaries of the corresponding intervals.

5. The method for solving attack-defense game strategies based on fuzzy language according to claim 4, characterized in that, For a comprehensive intuitionistic fuzzy set payoff matrix, the nonlinear programming problem is: and in, Indicates the attacker's... There are 10 attack strategies, totaling 1 One attack strategy; The first one represents the defending side One defense strategy, total One defense strategy; This represents the membership function value in the attacker's intuitionistic fuzzy set payoff matrix when the attacker chooses the i-th attack strategy and the defender chooses the j-th defense strategy. Let λ represent the non-membership function value in the attacker's intuitionistic fuzzy set payoff matrix when the attacker chooses the i-th attack strategy and the defender chooses the j-th defense strategy; λ represents the relative weights of the membership / non-membership function constraints. Once λ is determined, the resulting Nash equilibrium solution is: ; This represents the probability vector of the attacker's mixed strategy. This represents the probability vector of the defender's hybrid strategy; This represents the payoff value for the attacker in a game theory problem. The values ​​represent the payoffs of the defender in a game problem, and are all in the form of intuitionistic fuzzy sets.

Images