A strategy generation method for intuitionistic fuzzy Stackelberg game based on weight relationship intervals

Abstract

This invention discloses a strategy generation method for interval intuitionistic fuzzy Stackelberg games based on weighted relationships. The method includes: determining the players in the game, designating the player who takes the first action as the forerunner and the player who takes the second action as the follower; determining the payoffs of the forerunner and follower under various strategy profiles in the interval intuitionistic fuzzy Stackelberg game model through expert decision-making or empirical evaluation, thereby obtaining the interval intuitionistic fuzzy payoff matrix for the forerunner and follower; transforming the solution of the interval intuitionistic fuzzy Stackelberg game model into a multi-round multi-objective programming problem using the concept of a strong Stackelberg equilibrium; and transforming the multi-round multi-objective programming problem into a multi-round single-objective programming problem using weighted relationships, thereby obtaining the mixed-strategy Nash equilibrium solution, i.e., obtaining the strategy optimization results for the forerunner and follower.

Description

Technical Field

[0001] This invention relates to the field of complex network game technology in systems engineering, and in particular to a strategy generation method for intuitionistic fuzzy Stackelberg games based on weight relationship intervals. 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 on this type of problem exists, but existing studies only provide objective evaluation methods based on network topology. For example, in a complete information static or dynamic game framework, these methods use the network connectivity performance index—maximum connected component size—to calculate the payoff matrices for the attacker and defender, and then calculate the corresponding Nash equilibrium strategies. However, in real-world game problems, the understanding of the problem by both parties is uncertain, they have insufficient information, 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.

[0004] In today's networked society, Stackelberg games on complex networks are an important research direction in game theory. Research mainly involves the construction of game models, strategy analysis and solution, and the expansion of application areas. Current research focuses on designing efficient algorithms and tools for analysis and solution, promoting their application in different fields, and further expanding theoretical research to better address the challenges of complex systems in reality. In recent years, this field has made many important advances, providing new ideas and methods for game theory research and application. In the field of fuzzy mathematics, 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 provides inspiration for solving more complex game problems. Currently, there is relatively little research on introducing intuitionistic fuzzy set theory into Stackelberg games, making this research of significant importance. 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 strategy generation method based on weighted interval intuitionistic fuzzy Stackelberg game. The method is based on a strong Stackelberg game, utilizing the payoffs of the forerunner and follower under various strategy profiles to generate an interval intuitionistic fuzzy payoff matrix. The solution of the interval intuitionistic fuzzy Stackelberg game model is transformed into a multi-round multi-objective programming problem, and then further transformed into a multi-round single-objective programming problem using weighted relationships, thereby obtaining a hybrid strategy Nash equilibrium solution.

[0006] The objective of this invention is achieved through the following technical solution: a strategy generation method for intuitionistic fuzzy Stackelberg games based on weighted relation intervals, the method comprising:

[0007] Step 1: Determine the players in the game, designating the player who takes the first action as the forerunner and the player who takes the second action as the follower.

[0008] Step 2: Obtain the topology of the infrastructure network, determine the policy sets of pioneers and followers, and construct an interval intuitionistic fuzzy Stackelberg game model.

[0009] Step 3: Through expert decision-making or empirical evaluation, determine the fuzzy payoffs of the forerunner and follower under each strategy profile in the interval intuition fuzzy Stackelberg game model, thereby obtaining the interval intuition fuzzy payoff matrix of the forerunner and follower.

[0010] Step 4: Using the concept of solution of strong Stackelberg equilibrium, the solution of the interval intuition fuzzy Stackelberg game model is transformed into a multi-round multi-objective programming problem.

[0011] Step 5: Using the weight relationship, the multi-round multi-objective programming problem is transformed into a multi-round single-objective programming problem, thereby obtaining the hybrid policy Nash equilibrium solution, that is, obtaining the policy optimization results of the forerunner and follower.

[0012] 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;

[0013] The interval intuitionistic fuzzy payoff matrix is ​​expressed as follows: in Let m be an interval intuitionistic fuzzy number, where m represents the number of strategies of the forerunner, n represents the number of strategies of the follower, i represents the i-th strategy of the forerunner, and j represents the j-th strategy of the follower. This represents the lower bound of the membership degree of the interval intuitive fuzzy number. This represents the upper bound of the membership degree of the interval intuitive fuzzy number. This represents the lower bound of the non-membership degree of the interval intuitive fuzzy number. It represents the upper bound of the non-membership degree of the interval intuitive fuzzy number.

[0014] Specifically, the forerunner is the party that acts first and has a probability of choosing each of its own strategies. The follower is the party that acts later and knows the probability distribution of the forerunner's commitment to all strategies. Typically, the forerunner has m possible strategies, where i represents the i-th strategy among all strategies, and the follower has n possible strategies, where j represents the j-th strategy among all strategies.

[0015] Specifically, the interval intuitionistic fuzzy payoff matrix is ​​divided into the interval intuitionistic fuzzy payoff matrix for the pioneer and the interval intuitionistic fuzzy payoff matrix for the follower. When the pioneer chooses strategy i and the follower chooses strategy j, the pioneer's gain is the interval intuitionistic fuzzy number. The number of followers winning is an interval intuitionistic fuzzy number. Therefore, the fuzzy payoff matrix for the forerunner under different pure strategy situations is expressed as follows:

[0016]

[0017] Each element in the payoff matrix is ​​an interval intuitionistic fuzzy number. This represents the lower bound of the membership degree of the interval intuitive fuzzy number. The upper bound of the membership degree of the interval intuitive fuzzy number is represented. This represents the lower bound of the non-membership degree of the interval intuitive fuzzy number. The upper bound of the non-membership degree of the interval intuitive fuzzy number is represented;

[0018] The fuzzy payoff matrix for followers under different pure strategy situations is represented as follows:

[0019]

[0020] Each element in the payoff matrix is ​​an interval intuitionistic fuzzy number. This represents the lower bound of the membership degree of the interval intuitive fuzzy number. The upper bound of the membership degree of the interval intuitive fuzzy number is represented. This represents the lower bound of the non-membership degree of the interval intuitive fuzzy number. It represents the upper bound of the non-membership degree of the interval intuitive fuzzy number.

[0021] Furthermore, based on the interval intuitionistic fuzzy payoff matrix for the forerunner and follower described in step 3, for each pure policy t of the follower, we can obtain the forerunner's optimal hybrid policy. By solving the following multi-objective programming problem:

[0022]

[0023] For ease of calculation, based on the weighting relationship, we simplify the above formula into the following multi-objective programming problem:

[0024]

[0025] Wherein, λ represents the decision-maker's preference weight for membership degree and non-membership degree, and the larger the λ is, the more the decision-maker attaches importance to the influence of membership degree; Denotes the probability distribution of any mixed strategies for any first mover; This represents the probability distribution of the mixed strategies for the highest-priority mover; when the mover chooses strategy i and the follower chooses strategy t, Let represent the lower bound of membership degree, the upper bound of membership degree, the lower bound of non-membership degree, and the upper bound of non-membership degree, respectively; when the forer chooses strategy i and the follower chooses strategy j, Let represent the lower bound of membership degree, the upper bound of membership degree, the lower bound of non-membership degree, and the upper bound of non-membership degree, respectively; when the forer chooses strategy i and the follower chooses strategy t, Let represent the lower bound of membership degree, the upper bound of membership degree, the lower bound of non-membership degree, and the upper bound of non-membership degree, respectively; when the forer chooses strategy i and the follower chooses strategy j, Let S represent the lower bound of membership degree, the upper bound of membership degree, the lower bound of non-membership degree, and the upper bound of non-membership degree, respectively, for the follower interval intuitionistic fuzzy number; D Let S represent the set of strategies of the forerunner. A Represents the set of strategies of the followers;

[0026] The forer optimal hybrid strategy is calculated based on the pure strategy t for each follower. Then, we can calculate the optimal objective value of the forerunner under each follower's pure policy t. Take the minimum value

[0027]

[0028] The optimal target value for the pioneer, and The globally optimal hybrid strategy for the pioneer. The best response strategy for followers.

[0029] Furthermore, the multi-round single-objective programming problem described in step 5, i.e., for each pure policy t of the follower, has:

[0030]

[0031] The optimal hybrid strategy for the first player in a single round can be obtained from the above planning problem. Wherein, λ represents the decision-maker's preference weight for membership degree and non-membership degree, and the larger the λ is, the more the decision-maker attaches importance to the influence of membership degree; Denotes the probability distribution of any mixed strategies for any first mover;

[0032] This represents the probability distribution of the highest-priority mixed policy for each pure policy t of the follower; when the forer chooses policy i and the follower chooses policy t, Let represent the lower bound of membership degree, the upper bound of membership degree, the lower bound of non-membership degree, and the upper bound of non-membership degree, respectively; when the forer chooses strategy i and the follower chooses strategy j, Let represent the lower bound of membership degree, the upper bound of membership degree, the lower bound of non-membership degree, and the upper bound of non-membership degree, respectively; when the forer chooses strategy i and the follower chooses strategy t, Let represent the lower bound of membership degree, the upper bound of membership degree, the lower bound of non-membership degree, and the upper bound of non-membership degree, respectively; when the forer chooses strategy i and the follower chooses strategy j, These represent the lower bound of membership degree, the upper bound of membership degree, the lower bound of non-membership degree, and the upper bound of non-membership degree, respectively, for the follower interval intuitive fuzzy number.

[0033] The optimal objective value of the forer under each follower pure policy t.

[0034] To obtain the optimal target value of the pioneer, and This represents the probability distribution of the highest priority mover mixed policy for each pure policy t of the follower; The globally optimal hybrid strategy for the pioneer; The best response strategy for followers;

[0035] From the above multi-round single-objective programming problem, the globally optimal hybrid strategy for the first mover can be obtained. The best response strategy for followers

[0036] Compared with existing methods, the advantages of this invention are as follows: In recent years, Stackelberg dynamic games based on complex networks have attracted widespread attention from scholars both domestically and internationally. However, existing research cannot reflect the fuzziness in decision-makers' understanding of the game problem. This invention, combining fuzzy mathematics theory, proposes a method for generating optimal strategies for strong Stackelberg games based on intuitionistic fuzzy sets. This method yields reasonable strategy choices for both players under fuzzy conditions and analyzes the results. Explaining the uncertainty of strong Stackelberg games based on complex networks using intuitionistic fuzzy theory can greatly broaden the practical application of complex network game research. Attached Figure Description

[0037] Figure 1 A flowchart illustrating an embodiment of the present invention is shown;

[0038] Figure 2 A schematic diagram of the infrastructure network in an embodiment of the present invention is shown. Detailed Implementation

[0039] 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.

[0040] It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0041] This embodiment considers only one forerunner and one follower, 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 railway 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.

[0042] Consider only one forerunner and one follower, both of whom have complete knowledge of the existing network topology. All attacks and defenses target nodes in 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, where the more important the node, the higher the cost of attacking or defending.

[0043] like Figure 1 As shown, a strategy generation method for strong Stackelberg games based on intuitionistic fuzzy sets is described, the method comprising:

[0044] Step 1: Determine the players in the game, designating the player who takes the first action as the forerunner and the player who takes the second action as the follower.

[0045] Step 2: Obtain the topology of the infrastructure network, determine the policy sets of pioneers and followers, and construct an interval intuitionistic fuzzy Stackelberg game model.

[0046] Step 3: Through expert decision-making or empirical evaluation, determine the fuzzy payoffs of the forerunner and follower under each strategy profile in the interval intuition fuzzy Stackelberg game model, thereby obtaining the interval intuition fuzzy payoff matrix of the forerunner and follower.

[0047] Step 4: Using the concept of solution of strong Stackelberg equilibrium, the solution of the interval intuition fuzzy Stackelberg game model is transformed into a multi-round multi-objective programming problem.

[0048] Step 5: Using the weight relationship, the multi-round multi-objective programming problem is transformed into a multi-round single-objective programming problem, thereby obtaining the hybrid policy Nash equilibrium solution, that is, obtaining the policy optimization results of the forerunner and follower.

[0049] 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;

[0050] The interval intuitionistic fuzzy payoff matrix can be expressed as: in Let m be an interval intuitionistic fuzzy number, where m represents the number of strategies of the forerunner, n represents the number of strategies of the follower, i represents the i-th strategy of the forerunner, and j represents the j-th strategy of the follower. This represents the lower bound of the membership degree of the interval intuitive fuzzy number. This represents the upper bound of the membership degree of the interval intuitive fuzzy number. This represents the lower bound of the non-membership degree of the interval intuitive fuzzy number. It represents the upper bound of the non-membership degree of the interval intuitive fuzzy number.

[0051] Specifically, the forerunner is the party that acts first and has a probability of choosing each of its own strategies. The follower is the party that acts later and knows the probability distribution of the forerunner's commitment to all strategies. Typically, the forerunner has m possible strategies, where i represents the i-th strategy among all strategies, and the follower has n possible strategies, where j represents the j-th strategy among all strategies.

[0052] Specifically, the interval intuitionistic fuzzy payoff matrix is ​​divided into the interval intuitionistic fuzzy payoff matrix for the pioneer and the interval intuitionistic fuzzy payoff matrix for the follower. When the pioneer chooses strategy i and the follower chooses strategy j, the pioneer's gain is the interval intuitionistic fuzzy number. The followers' wins are interval intuition fuzzy numbers Therefore, the fuzzy payoff matrix for the forerunner under different pure strategy situations is expressed as follows:

[0053]

[0054] Where m represents the total number of pioneer strategies, n represents the total number of follower strategies, and each element of the payoff matrix is ​​an interval intuitionistic fuzzy number. This represents the lower bound of the membership degree of the interval intuitive fuzzy number. This represents the upper bound of the membership degree of the interval intuitive fuzzy number. This represents the lower bound of the non-membership degree of the interval intuitive fuzzy number. The upper bound of the non-membership degree of the interval intuitive fuzzy number is represented;

[0055] The fuzzy payoff matrix for followers under different pure strategy situations is represented as follows:

[0056]

[0057] Where m represents the total number of pioneer strategies, n represents the total number of follower strategies, and each element of the payoff matrix is ​​an interval intuitionistic fuzzy number. This represents the lower bound of the membership degree of the interval intuitive fuzzy number. This represents the upper bound of the membership degree of the interval intuitive fuzzy number. This represents the lower bound of the non-membership degree of the interval intuitive fuzzy number. It represents the upper bound of the non-membership degree of the interval intuitive fuzzy number.

[0058] Furthermore, based on the interval intuitionistic fuzzy payoff matrix for the forerunner and follower described in step 3, for each pure policy t of the follower, we can obtain the optimal hybrid policy of the forerunner. By solving the following multi-objective programming problem:

[0059]

[0060] For ease of calculation, based on the weighting relationship, we simplify the above formula into the following multi-objective programming problem:

[0061]

[0062] Wherein, λ represents the decision-maker's preference weight for membership degree and non-membership degree, and the larger the λ is, the more the decision-maker attaches importance to the influence of membership degree; Denotes the probability distribution of any mixed strategies for any first mover; This represents the probability distribution of the mixed strategies for the highest-priority mover; when the mover chooses strategy i and the follower chooses strategy t, Let represent the lower bound of membership degree, the upper bound of membership degree, the lower bound of non-membership degree, and the upper bound of non-membership degree, respectively; when the forer chooses strategy i and the follower chooses strategy j, Let represent the lower bound of membership degree, the upper bound of membership degree, the lower bound of non-membership degree, and the upper bound of non-membership degree, respectively; when the forer chooses strategy i and the follower chooses strategy t, Let represent the lower bound of membership degree, the upper bound of membership degree, the lower bound of non-membership degree, and the upper bound of non-membership degree, respectively; when the forer chooses strategy i and the follower chooses strategy j, These represent the lower bound of membership degree, the upper bound of membership degree, the lower bound of non-membership degree, and the upper bound of non-membership degree, respectively, for the follower interval intuitive fuzzy number.

[0063] The forer optimal hybrid strategy is calculated based on the pure strategy t for each follower. Then, we can calculate the optimal objective value of the forerunner under each follower's pure policy t. Take the minimum value

[0064]

[0065] The optimal target value for the pioneer, and The globally optimal hybrid strategy for the pioneer. The best response strategy for followers.

[0066] Furthermore, the multi-round single-objective programming problem described in step 5, i.e., for each pure policy t of the follower, has:

[0067]

[0068] The optimal hybrid strategy for the first player in a single round can be obtained from the above planning problem. Wherein, λ represents the decision-maker's preference weight for membership degree and non-membership degree, and the larger the λ is, the more the decision-maker attaches importance to the influence of membership degree; Denotes the probability distribution of any mixed strategies for any first mover;

[0069] This represents the probability distribution of the highest-priority mixed policy for each pure policy t of the follower; when the forer chooses policy i and the follower chooses policy t, Let represent the lower bound of membership degree, the upper bound of membership degree, the lower bound of non-membership degree, and the upper bound of non-membership degree, respectively; when the forer chooses strategy i and the follower chooses strategy j, Let represent the lower bound of membership degree, the upper bound of membership degree, the lower bound of non-membership degree, and the upper bound of non-membership degree, respectively; when the forer chooses strategy i and the follower chooses strategy t, Let represent the lower bound of membership degree, the upper bound of membership degree, the lower bound of non-membership degree, and the upper bound of non-membership degree, respectively; when the forer chooses strategy i and the follower chooses strategy j, These represent the lower bound of membership degree, the upper bound of membership degree, the lower bound of non-membership degree, and the upper bound of non-membership degree, respectively, for the follower interval intuitive fuzzy number.

[0070] The optimal objective value of the forer under each follower pure policy t. pass

[0071]

[0072] To obtain the optimal target value of the pioneer, and This represents the probability distribution of the highest priority mover mixed policy for each pure policy t of the follower; The globally optimal hybrid strategy for the pioneer; The best response strategy for followers;

[0073] From the above multi-round single-objective programming problem, the globally optimal hybrid strategy for the first mover can be obtained. The best response strategy for followers

[0074] 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 strategy generation method for intuitionistic fuzzy Stackelberg game based on weighted relation intervals, characterized in that, The method includes: Step 1: Determine the players in the game, designating the player who takes the first action as the forerunner and the player who takes the second action as the follower. Step 2: Obtain the topology of the infrastructure network, determine the policy sets of pioneers and followers, and construct an interval intuitionistic fuzzy Stackelberg game model. Step 3: Through expert decision-making or empirical evaluation, determine the fuzzy payoffs of the forerunner and follower under each strategy profile in the interval intuition fuzzy Stackelberg game model, thereby obtaining the interval intuition fuzzy payoff matrix of the forerunner and follower. Step 4: Using the concept of solution of strong Stackelberg equilibrium, the solution of the interval intuition fuzzy Stackelberg game model is transformed into a multi-round multi-objective programming problem. Step 5: Using the weight relationship, the multi-round multi-objective programming problem is transformed into a multi-round single-objective programming problem, thereby obtaining the hybrid policy Nash equilibrium solution, that is, obtaining the policy optimization results of the forerunner and follower. 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; The interval intuitionistic fuzzy payoff matrix is ​​expressed as follows: in Let m be an interval intuitionistic fuzzy number, where m represents the number of strategies of the forerunner, n represents the number of strategies of the follower, i represents the i-th strategy of the forerunner, and j represents the j-th strategy of the follower. This represents the lower bound of the membership degree of the interval intuitive fuzzy number. The upper bound of the membership degree of the interval intuitive fuzzy number is represented. This represents the lower bound of the non-membership degree of the interval intuitive fuzzy number. It represents the upper bound of the non-membership degree of the interval intuitive fuzzy number.

2. The strategy generation method for intuitionistic fuzzy Stackelberg game based on weighted relation intervals according to claim 1, characterized in that, The interval intuitionistic fuzzy payoff matrix is ​​divided into the interval intuitionistic fuzzy payoff matrix for the pioneer and the interval intuitionistic fuzzy payoff matrix for the follower. When the pioneer chooses strategy i and the follower chooses strategy j, the pioneer's win is the interval intuitionistic fuzzy number. The number of followers winning is an interval intuitionistic fuzzy number. Therefore, the fuzzy payoff matrix for the forerunner under different pure strategy situations is expressed as follows: Each element in the payoff matrix is ​​an interval intuitionistic fuzzy number. This represents the lower bound of the membership degree of the interval intuitive fuzzy number. The upper bound of the membership degree of the interval intuitive fuzzy number is represented. This represents the lower bound of the non-membership degree of the interval intuitive fuzzy number. The upper bound of the non-membership degree of the interval intuitive fuzzy number is represented; The fuzzy payoff matrix for followers under different pure strategy situations is represented as follows: Each element in the payoff matrix is ​​an interval intuitionistic fuzzy number. This represents the lower bound of the membership degree of the interval intuitive fuzzy number. The upper bound of the membership degree of the interval intuitive fuzzy number is represented. This represents the lower bound of the non-membership degree of the interval intuitive fuzzy number. It represents the upper bound of the non-membership degree of the interval intuitive fuzzy number.

3. The strategy generation method for intuitionistic fuzzy Stackelberg game based on weighted relation intervals according to claim 2, characterized in that, Based on the interval intuitionistic fuzzy payoff matrices for the forerunner and follower described in step 3, for each pure policy t of the follower, the optimal hybrid policy of the forerunner is obtained by solving the multi-objective programming problem in the next round. : For ease of calculation, based on the weighting relationship, the above formula is simplified into the following multi-objective programming problem: Wherein, λ represents the decision-maker's preference weight for membership degree and non-membership degree, and the larger the λ is, the more the decision-maker attaches importance to the influence of membership degree; Denotes the probability distribution of any mixed strategies for any first mover; This represents the probability distribution of the mixed strategies for the highest-priority mover; when the mover chooses strategy i and the follower chooses strategy t, Let represent the lower bound of membership degree, the upper bound of membership degree, the lower bound of non-membership degree, and the upper bound of non-membership degree, respectively; when the forer chooses strategy i and the follower chooses strategy j, Let represent the lower bound of membership degree, the upper bound of membership degree, the lower bound of non-membership degree, and the upper bound of non-membership degree, respectively; when the forer chooses strategy i and the follower chooses strategy t, Let represent the lower bound of membership degree, the upper bound of membership degree, the lower bound of non-membership degree, and the upper bound of non-membership degree, respectively; when the forer chooses strategy i and the follower chooses strategy j, Let S represent the lower bound of membership degree, the upper bound of membership degree, the lower bound of non-membership degree, and the upper bound of non-membership degree, respectively, for the follower interval intuitionistic fuzzy number; D Let S represent the set of strategies of the forerunner. A Represents the set of strategies of the followers; The forer optimal hybrid strategy is calculated based on the pure strategy t for each follower. Then, calculate the optimal objective value of the forerunner under each follower's pure policy t. Take the minimum value The optimal target value for the pioneer, and The globally optimal hybrid strategy for the pioneer. The best response strategy for followers.

4. The strategy generation method for intuitionistic fuzzy Stackelberg game based on weighted relation intervals according to claim 3, characterized in that, The multi-round single-objective programming problem described in step 5, i.e., for each pure policy t of the follower, has: The above single-objective programming problem yields the probability distribution of the highest priority mixed strategy for each pure strategy t of the follower. Wherein, λ represents the decision-maker's preference weight for membership degree and non-membership degree, and the larger the λ is, the more the decision-maker attaches importance to the influence of membership degree; Denotes the probability distribution of any mixed strategies for any first mover; This represents the probability distribution of the highest-priority mixed policy for each pure policy t of the follower; when the forer chooses policy i and the follower chooses policy t, Let represent the lower bound of membership degree, the upper bound of membership degree, the lower bound of non-membership degree, and the upper bound of non-membership degree, respectively; when the forer chooses strategy i and the follower chooses strategy j, Let represent the lower bound of membership degree, the upper bound of membership degree, the lower bound of non-membership degree, and the upper bound of non-membership degree, respectively; when the forer chooses strategy i and the follower chooses strategy t, Let represent the lower bound of membership degree, the upper bound of membership degree, the lower bound of non-membership degree, and the upper bound of non-membership degree, respectively; when the forer chooses strategy i and the follower chooses strategy j, These represent the lower bound of membership degree, the upper bound of membership degree, the lower bound of non-membership degree, and the upper bound of non-membership degree, respectively, for the follower interval intuitive fuzzy number. The aforementioned multi-round single-objective programming problem asks for the optimal objective value of the forer under each follower's pure policy t. pass To obtain the optimal target value of the pioneer, and This represents the probability distribution of the highest priority mover mixed policy for each pure policy t of the follower; The globally optimal hybrid strategy for the pioneer; The best response strategy for followers; From the above multi-round single-objective programming problem, the globally optimal hybrid strategy for the first mover is obtained. The best response strategy for followers

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