A method for revenue distribution of hesitant fuzzy cooperative game based on participation weight
By constructing a hesitant fuzzy cooperative game model based on participation weights, the problems of dynamics and loss of fine-grained information in existing fuzzy cooperative game models are solved, and fair and scientific distribution of benefits and risk assessment are achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- LIAONING NORMAL UNIVERSITY
- Filing Date
- 2026-04-03
- Publication Date
- 2026-06-12
AI Technical Summary
Existing fuzzy cooperative game models neglect the dynamic nature of alliance formation when dealing with complex profit distribution, leading to distorted Shapley value allocation. Furthermore, existing methods forcibly compress the discrete 'hesitation' of decision-makers into a continuous range, resulting in the loss of fine-grained preference information required for accurate calculation of feature functions.
By constructing a hesitant fuzzy cooperative game model based on participation weights, including data cleaning, multi-value interval processing, dynamic weight vector generation, interval lower limit priority comparison rule, and hesitant fuzzy Shapley value allocation model, the participation of attributes is dynamically captured, and the interval revenue and marginal contribution of the alliance are calculated.
It achieves dynamic weight allocation while preserving the original hesitation information of decision-makers, thereby enhancing the fairness and anti-interference ability of the distribution of benefits, satisfying the efficiency, monotonicity and symmetry axioms of game theory, and is suitable for complex group decision-making scenarios.
Smart Images
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Abstract
Description
Technical Field
[0001] This invention belongs to the field of artificial intelligence decision analysis and game theory technology, and in particular relates to a method for distributing the payoffs of hesitant fuzzy cooperative games based on participation weights. Background Technology
[0002] In traditional fuzzy set theory, the membership degree of an element to a set is usually a definite numerical value. However, in actual business cooperation, supply chain restructuring, or technology alliances, decision-makers often face high levels of hesitation and uncertainty when assessing resources and allocating profits. Hesitant fuzzy sets, by extending the membership degree to a set of possible numerical values, can more realistically express the psychological state and complex preferences of decision-makers.
[0003] In recent years, fuzzy cooperative game theory, which combines fuzzy concepts with cooperative game theory, has received widespread attention. However, existing fuzzy cooperative game models still have significant limitations when dealing with complex profit allocation: First, existing models typically rely on static weighting schemes, neglecting the dynamic nature of alliance formation. In real-world environments, there are significant differences in "participation" levels or data density across different attributes. Ignoring this dynamic participation leads to distorted Shapley value allocation, failing to accurately reflect the true contribution of attributes with lower uncertainty. Second, the widespread use of simple interval values in existing methods often forces decision-makers' discrete "hesitation" into a continuous range, resulting in the loss of fine-grained preference information needed for accurate calculation of feature functions.
[0004] Therefore, how to overcome the rigidity of static weights and construct a game model that can both retain the original hesitation information of decision-makers and dynamically allocate weights according to the participation of attributes is a technical problem that urgently needs to be solved in this field. Summary of the Invention
[0005] The purpose of this invention is to provide a method for allocating payoffs in hesitant fuzzy cooperative games based on participation weights, aiming to solve the problems mentioned in the background art.
[0006] The present invention is implemented as follows: a method for allocating payoffs in a hesitant fuzzy cooperative game based on participation weights, comprising the following steps: Step 1: Obtain the evaluation data of cooperative game participants under multi-dimensional attributes, construct the hesitant fuzzy evaluation matrix of participants and attributes, and perform data cleaning and multi-value interval processing on the hesitant fuzzy evaluation matrix based on the preset outlier removal criteria. Step 2: For the cleaned attribute range data, traverse all possible alliance combinations, calculate the local participation degree of each attribute in different alliance combinations, and aggregate the total participation degree of each attribute accordingly, and then construct a dynamic weight vector based on participation degree. Step 3: Based on the dynamic weight vector and the participants' interval performance on each attribute, the feature function under different degrees of fuzzy alliance cooperation is calculated using the interval lower limit priority comparison rule to determine the interval revenue of each alliance; Step 4: Based on the interval returns of each alliance, construct a hesitant fuzzy Shapley value allocation model, and use the interval subtraction rule to calculate the weighted marginal contribution of each participant to the alliance, so as to obtain the final return allocation result or risk assessment index.
[0007] A further technical solution, in step 1, specifically includes the outlier removal criteria and multi-value interval processing: For any set of attribute values in the hesitant fuzzy evaluation matrix, calculate its mean. and standard deviation ; Compare the attribute values in the collection If it exists Then determine the attribute value. These are outliers and should be removed. Convert the hesitant fuzzy set after removing outliers into interval value form. ,in and These represent the minimum and maximum values in the filtered set, respectively.
[0008] A further technical solution, in step 2, specifically includes the following method for constructing the dynamic weight vector: For any alliance and attributes The alliance All members in the attribute The values are merged to form a set, and the local participation degree is defined. The difference between the maximum and minimum values of the set: (1); in, For the maximum value operator of a set, For the minimum value operator of a set, For the union operator, For participants In attributes The set of evaluation values on; Computed properties Total participation It represents the local participation of all non-air alliances. sum; Total participation The attributes are calculated by performing normalization processing. Dynamic weights : (2); in, For the first Total participation of each attribute This represents the total number of dimensions / number of attributes.
[0009] A further technical solution, in step 3, specifically involves the calculation method of the characteristic function and the alliance interval return as follows: Define the characteristic function of hesitant fuzzy cooperative games. for: (3); in, For interval weighted summation operators, To select the alliance The operator representing the maximum interval representation of a member on a specific attribute; The max operation follows the rule of prioritizing the lower limit of the interval: if the lower limits of the participants' intervals are different, the interval with the larger lower limit is selected; if the lower limits are the same, the interval with the larger upper limit is selected.
[0010] A further technical solution, in step 4, is that the hesitant fuzzy Shapley value assignment model is specifically as follows: Calculate participants Fuzzy Shapley values : (4); in, The total number of participants. For those who do not include participants any of the sub-alliances, The set consisting of all participants.
[0011] In a further technical solution, in step 4, the interval subtraction operation rule is defined as follows: for any two fuzzy numbers and ,in For fuzzy numbers The lower limit of the interval, For fuzzy numbers The upper limit of the interval, For fuzzy numbers The lower limit of the interval, For fuzzy numbers The upper limit of the interval; its marginal contribution of subtraction is .
[0012] The present invention provides a method for allocating payoffs in a hesitant fuzzy cooperative game based on participation weights, the beneficial effects of which are as follows: (1) Breaking through the limitations of static weights and dynamically capturing true contributions: This invention innovatively introduces the attribute "participation" index, and dynamically generates weights by calculating the characteristic span of attributes in different alliances. The model can automatically identify and assign higher weights to attributes with the greatest volatility and the highest distinguishability, avoiding the distribution distortion caused by static weighting, and significantly enhancing the fairness and anti-interference ability of income distribution.
[0013] (2) Complete retention of hesitation information and improved decision fidelity: Compared with intuitionistic fuzzy game, this invention adopts the form of discrete preference set to directly integrate expert opinions. Through scientific outlier cleaning and multi-value intervalization, the granularity of decision information is maintained without forced data smoothing, which is closer to the actual uncertainty assessment environment.
[0014] (3) Highly scalable axiomatic allocation architecture: The hesitant fuzzy Shapley value allocation mechanism proposed in this invention strictly satisfies the axioms of efficiency, monotonicity and symmetry in game theory. This model not only has a solid mathematical foundation, but also has excellent cross-domain transferability, and can be widely applied to complex group decision-making scenarios such as global supply chain collaboration, technology alliance building and joint carbon quota emission reduction. Detailed Implementation
[0015] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.
[0016] The specific implementation of the present invention will be described in detail below with reference to specific embodiments.
[0017] An embodiment of the present invention provides a method for allocating payoffs in a hesitant fuzzy cooperative game based on participation weights, comprising the following steps: Step 1: Obtain the evaluation data of cooperative game participants under multi-dimensional attributes, construct the hesitant fuzzy evaluation matrix of participants and attributes, and perform data cleaning and multi-value interval processing on the hesitant fuzzy evaluation matrix based on the preset outlier removal criteria. Step 2: For the cleaned attribute range data, traverse all possible alliance combinations, calculate the local participation degree of each attribute in different alliance combinations, and aggregate the total participation degree of each attribute accordingly, and then construct a dynamic weight vector based on participation degree. Step 3: Based on the dynamic weight vector and the participants' interval performance on each attribute, the feature function under different degrees of fuzzy alliance cooperation is calculated using the interval lower limit priority comparison rule to determine the interval revenue of each alliance; Step 4: Based on the interval returns of each alliance, construct a hesitant fuzzy Shapley value allocation model, and use the interval subtraction rule to calculate the weighted marginal contribution of each participant to the alliance, so as to obtain the final return allocation result or risk assessment index.
[0018] In a preferred embodiment of the present invention, step 1 specifically includes the outlier removal criteria and multi-value interval processing: For any set of attribute values in the hesitant fuzzy evaluation matrix, calculate its mean. and standard deviation ; Compare the attribute values in the collection If it exists Then determine the attribute value. These are outliers and should be removed. Convert the hesitant fuzzy set after removing outliers into interval value form. ,in and These represent the minimum and maximum values in the filtered set, respectively.
[0019] In a preferred embodiment of the present invention, step 2, the method for constructing the dynamic weight vector specifically includes: For any alliance and attributes The alliance All members in the attribute The values are merged to form a set, and the local participation degree is defined. The difference between the maximum and minimum values of the set: (1); in, For the maximum value operator of a set, For the minimum value operator of a set, It is a union operator (representing the merging of the attribute values of each member). For participants In attributes The set of evaluation values on; Computed properties Total participation It represents the local participation of all non-air alliances. sum; Total participation The attributes are calculated by performing normalization processing. Dynamic weights : (2); in, For the first Total participation of each attribute This represents the total number of dimensions / number of attributes.
[0020] In a preferred embodiment of the present invention, the method for calculating the characteristic function and the alliance interval return in step 3 is as follows: Define the characteristic function of hesitant fuzzy cooperative games. for: (3); in, For interval weighted summation operators, To select the alliance The operator representing the maximum interval representation of a member on a specific attribute; The max operation follows the rule of prioritizing the lower limit of the interval: if the lower limits of the participants' intervals are different, the interval with the larger lower limit is selected; if the lower limits are the same, the interval with the larger upper limit is selected.
[0021] In a preferred embodiment of the present invention, the hesitant fuzzy Shapley value assignment model in step 4 is specifically as follows: Calculate participants Fuzzy Shapley values : (4); in, The total number of participants. For those who do not include participants any of the sub-alliances, The set consisting of all participants; the interval subtraction operation rule is defined as: for any two fuzzy numbers and ,in For fuzzy numbers The lower limit of the interval, For fuzzy numbers The upper limit of the interval, For fuzzy numbers The lower limit of the interval, For fuzzy numbers The upper limit of the interval; its marginal contribution of subtraction is .
[0022] To verify the effectiveness of the fusion model of hesitant fuzzy concept lattice and fuzzy cooperative game, a supply chain management case is selected for analysis. In this case, there are three main participants: supplier X, manufacturer Y, and retailer Z. Due to the uncertainty of the market environment, the parties hesitate and are ambiguous about the cooperation method and the distribution of benefits. Let the participant set P = {X, Y, Z}, and the attribute set C = {c1, c2, c3}, representing: supply chain stability (c1), willingness to cooperate (c2), and risk tolerance (c3), respectively.
[0023] Step 1: Data Construction and Preprocessing; The attribute data of each node is extracted and transformed into a hesitant fuzzy set. A hesitant fuzzy background matrix is then established, as shown in Table 1 below. Table 1. Background of Hesitation and Ambiguity in the Characteristics of Supply Chain Participants
[0024] First, outlier filtering is performed. Taking supplier X's willingness to cooperate {0.1, 0.8, 0.9} as an example, the calculated mean is 0.6, and the standard deviation is approximately 0.33. Based on the judgment criteria, the severely outlier 0.1 is removed. Then, interval processing is performed to convert the hesitant fuzzy sets into interval value form: Supplier X: c1=[0.6, 0.7], c2=[0.8, 0.9], c3=[0.3, 0.5]; Manufacturer Y: c1=[0.7, 0.9], c2=[0.7, 0.7], c3=[0.6, 0.7]; Retailer Z: c1=[0.5, 0.6], c2=[0.5, 0.7], c3=[0.7, 0.8]; Step 2: Dynamic attribute weight measurement; Iterate through all possible alliance types (single member, two members, grand alliance), calculate the range of each attribute, and sum them up.
[0025] c1 (Supply Chain Stability) Total Participation: 0.1(X)+0.2(Y)+0.1(Z)+0.3(XY)+0.2(XZ)+0.4(YZ)+0.4(XYZ)=1.7; c2 (willingness to cooperate) total participation: 0.1(X)+0(Y)+0.2(Z)+0.2(XY)+0.4(XZ)+0.2(YZ)+0.4(XYZ)=1.5; c3 (Risk Tolerance) Total Participation: 0.2(X)+0.1(Y)+0.1(Z)+0.4(XY)+0.5(XZ)+0.2(YZ)+0.5(XYZ)=2.0; Normalizing the total participation yields the dynamic weight vector: w=(1.7 / 5.2,1.5 / 5.2,2.0 / 5.2)≈(0.3269,0.2885,0.3846).
[0026] Step 3: Calculate the payoff of the alliance in the fuzzy cooperative game; For each possible alliance, the maximum value range is extracted using a lower bound priority rule, and the weighted range return is calculated using dynamic weights. Taking the large alliance {X, Y, Z} as an example: c1 takes max([0.6,0.7],[0.7,0.9],[0.5,0.6])=[0.7,0.9]; c2 takes max([0.8,0.9],[0.7,0.7],[0.5,0.7])=[0.8,0.9]; c3 takes max([0.3,0.5],[0.6,0.7],[0.7,0.8]) = [0.7,0.8]; Calculate the weighted returns: 0.3269*[0.7,0.9]+0.2885*[0.8,0.9]+0.3846*[0.7,0.8]=[0.7288,0.8615].
[0027] Step 4: Hesitant fuzzy Shapley value assignment; Using the interval subtraction formula The marginal contribution is calculated one by one and multiplied by the factorial weight of the corresponding combination, then summed. The allocation result is obtained after rigorous model calculation as described above: Supplier X: [0.2151, 0.2708]; Manufacturer Y: [0.2766, 0.3169]; Retailer Z: [0.2371, 0.2737]; The allocation results strictly satisfy the requirement that the sum of the Shapley values of all participants equals the overall revenue range of the large alliance (satisfying the efficiency axiom), providing a fair and scientific quantitative basis for cost sharing and profit distribution in this supply chain.
[0028] Results verification and analysis: Adding the benefits of the three together, we get: [0.2151,0.2708]+[0.2766,0.3169]+[0.2371,0.2737]≈[0.7288,0.8614]; The results are in strict agreement with the total revenue of the grand pool, proving that the model satisfies the efficiency axiom. Manufacturers receive the highest allocation due to their greatest contribution to supply chain stability, while retailers receive the lowest, demonstrating fair allocation. This invention, while preserving multiple uncertainties (range fluctuations), assigns dynamic weights based on attribute participation and combines them with the fuzzy Shapley mechanism, effectively overcoming the loss of uncertainty information caused by traditional single-valued methods, and providing a scientifically sound decision support basis for supply chain game theory.
[0029] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.
Claims
1. A method for distributing payoffs in hesitant fuzzy cooperative games based on participation weights, characterized in that, Includes the following steps: Step 1: Obtain the evaluation data of cooperative game participants under multi-dimensional attributes, construct the hesitant fuzzy evaluation matrix of participants and attributes, and perform data cleaning and multi-value interval processing on the hesitant fuzzy evaluation matrix based on the preset outlier removal criteria. Step 2: For the cleaned attribute range data, traverse all possible alliance combinations, calculate the local participation degree of each attribute in different alliance combinations, and aggregate the total participation degree of each attribute accordingly, and then construct a dynamic weight vector based on participation degree. Step 3: Based on the dynamic weight vector and the participants' interval performance on each attribute, the feature function under different degrees of fuzzy alliance cooperation is calculated using the interval lower limit priority comparison rule to determine the interval revenue of each alliance; Step 4: Based on the interval returns of each alliance, construct a hesitant fuzzy Shapley value allocation model, and use the interval subtraction rule to calculate the weighted marginal contribution of each participant to the alliance, so as to obtain the final return allocation result or risk assessment indicator.
2. The method for distributing payoffs in hesitant fuzzy cooperative games based on participation weights as described in claim 1, characterized in that, In step 1, the outlier removal criteria and multi-value interval processing specifically include: For any set of attribute values in the hesitant fuzzy evaluation matrix, calculate its mean. and standard deviation ; Compare the attribute values in the collection If it exists Then determine the attribute value. These are outliers and should be removed. Convert the hesitant fuzzy set after removing outliers into interval value form. ,in and These represent the minimum and maximum values in the filtered set, respectively.
3. The method for distributing payoffs in hesitant fuzzy cooperative games based on participation weights as described in claim 1, characterized in that, In step 2, the method for constructing the dynamic weight vector specifically includes: For any alliance and attributes The alliance All members in the attribute The values are merged to form a set, and the local participation degree is defined. The difference between the maximum and minimum values of the set: （1） in, For the maximum value operator of a set, For the minimum value operator of a set, For the union operator, For participants In attributes The set of evaluation values on; Computed properties Total participation It represents the local participation of all non-air alliances. sum; Total participation The attributes are calculated by performing normalization processing. Dynamic weights : （2） in, For the first Total participation of each attribute This represents the total number of dimensions / number of attributes.
4. The method for distributing payoffs in hesitant fuzzy cooperative games based on participation weights according to claim 3, characterized in that, In step 3, the specific method for calculating the characteristic function and the alliance interval return is as follows: Define the characteristic function of hesitant fuzzy cooperative games. for: （3） in, For interval weighted summation operators, To select the alliance The operator representing the maximum interval of a member on a specific attribute; The max operation follows the rule of prioritizing the lower limit of the interval: if the lower limits of the participants' intervals are different, the interval with the larger lower limit is selected; if the lower limits are the same, the interval with the larger upper limit is selected.
5. The method for distributing payoffs in hesitant fuzzy cooperative games based on participation weights according to claim 4, characterized in that, In step 4, the hesitant fuzzy Shapley value assignment model is specifically as follows: Calculate participants Fuzzy Shapley values : （4） in, The total number of participants. For those who do not include participants any of the sub-alliances, The set consisting of all participants.
6. The method for distributing payoffs in hesitant fuzzy cooperative games based on participation weights according to claim 1, characterized in that, In step 4, the interval subtraction operation rule is defined as follows: for any two fuzzy numbers and ,in For fuzzy numbers The lower limit of the interval, For fuzzy numbers The upper limit of the interval, For fuzzy numbers The lower limit of the interval, For fuzzy numbers The upper limit of the interval; Its marginal contribution from subtraction is .