Asymmetric bankruptcy methods for resolving transboundary water allocation conflicts

Abstract

The present invention belongs to the field of cross-border water resource allocation decision-making, and relates to an asymmetric bankruptcy method for resolving cross-border water resource allocation conflicts, including: 1) collecting basic data information of the cross-border water resource allocation system; 2) describing the cross-border water resource allocation problem as a bankruptcy game problem with non-transferable benefits; 3) constructing a cross-border water resource allocation stakeholder negotiation power-related indicator system; 4) calculating the weights of stakeholder negotiation power-related indicators; 5) calculating the stakeholder asymmetric negotiation power coefficient; 6) determining the water right at the negotiation breakdown point; 7) performing cross-border water resource allocation. The present invention provides an asymmetric bankruptcy method for resolving cross-border water resource allocation conflicts, which can resolve cross-border water resource allocation conflicts and provide fair and reasonable water allocation.

Description

Technical Field

[0001] The invention belongs to the field of cross-border water resource allocation decision-making and relates to an asymmetric bankruptcy method for solving cross-border water resource allocation conflicts. Background Art

[0002] The high-quality development of the economy and society depends on the sustainable support of water resources. Generally, transboundary water resources have the attributes of quasi-public goods, so geopolitical disputes caused by the competition for water resources are relatively common worldwide. When transboundary water resources are in short supply, how to quickly formulate an effective water resource allocation plan to resolve conflicts between stakeholders has become a current research hotspot. At present, there are many theories, technologies and methods in the literature on transboundary water resource allocation to optimize water resource allocation and resolve water resource allocation conflicts, such as social welfare maximization method, compromise planning and target planning based on operations research, and cooperative game method. However, the first two types of optimization methods based on the planner's perspective need to assume perfect cooperation and effective compensation mechanisms between stakeholders during implementation, so they may fail in the actual transboundary water resource management. The allocation method based on cooperative game requires that the water use utility information of stakeholders is transparent and reliable and that cooperation must be able to generate gains, so its operability is restricted.

[0003] When the available supply of transboundary water resources cannot meet the total amount of water resources declared by the stakeholders, and the water resource allocation problem is difficult to be transformed into a cooperative game problem with transferable benefits in the short term, the bankruptcy theory-based method can provide policymakers with a quick and easy-to-understand water resource allocation plan. However, traditional bankruptcy rules usually allocate water resources only based on the declared water volume of the stakeholders, without considering other characteristic factors such as water volume contribution, economic and social status, water use benefits and degree of environmental damage. Therefore, it is usually difficult for stakeholders to reach an effective water resource sharing agreement. In addition, considering that the current water consumption may not be suitable as the starting point for stakeholders to negotiate when allocating transboundary water resources, and the traditional bankruptcy theory rules may not guarantee the basic water demand of stakeholders with smaller declared water volumes. Summary of the invention

[0004] In order to solve the above technical problems existing in the background technology, the present invention provides an asymmetric bankruptcy method for solving cross-border water resource allocation conflicts and providing fair and reasonable water allocation.

[0005] To achieve the above object, the present invention adopts the following technical solution:

[0006] An asymmetric bankruptcy method for resolving cross-border water resource allocation conflicts, characterized in that: the asymmetric bankruptcy method for resolving cross-border water resource allocation conflicts comprises the following steps:

[0007] S1) Collect basic data information on the transboundary water resources allocation system, including the stakeholders involved, the total allocable water resources, the water resources declared by the stakeholders, and basic data related to the negotiation power; the basic data related to the negotiation power includes climate, geography, hydrology, environment and socio-economic data;

[0008] S2) describing the transboundary water resources allocation problem as a bankruptcy game problem where the benefits cannot be transferred based on the stakeholders involved in the transboundary water resources allocation system, the total allocable water resources, and the water resources declared by the stakeholders in the basic data information in step S1);

[0009] S3) constructing an indicator system related to the negotiation power of stakeholders in cross-border water resources allocation based on the basic data related to the negotiation power in the basic data information in step S1);

[0010] S4) calculating the weights of the indicators related to the negotiation power of the stakeholders in cross-border water resources allocation based on the results of the determination of the indicator system related to the negotiation power of the stakeholders in step S3);

[0011] S5) calculating the asymmetric negotiation power coefficient of the stakeholder based on the calculation result of the weight of the relevant index of the negotiation power of the stakeholder in step S4);

[0012] S6) Based on the basic data information in step 1), the stakeholders involved in the transboundary water resources allocation system, the total allocable water resources and the water resources declared by the stakeholders, combined with the minimum initial water rights of the bankruptcy game and the basic living water needs of the stakeholders, determine the water rights at the negotiation breaking point;

[0013] S7) allocating cross-border water resources based on the negotiation power coefficient of the interest subject calculated in step S5) and the negotiation breakdown point water right determined in step S6).

[0014] Preferably, the specific implementation method of step S2) recorded in the present invention is: according to the relevant definition of bankruptcy theory, a cross-border water bankruptcy problem is directly described as: there is a finite set of interest entities N = [1, 2, ..., n], each interest entity has a reasonable declared water volume wc = (wc1, wc2, ..., wc n ),when When , the transboundary water resources allocation system is considered to have water bankruptcy; E is the amount of water resources that can be allocated by the transboundary water resources allocation system, and E∈R + , where R + is a set of positive real numbers; is the sum of the declared water resources; based on the Pareto efficiency constraints, the declared boundedness constraints and the non-negativity constraints, combined with the declared water resources of the stakeholders, the bankruptcy theory rules are used to fully allocate the limited water resources to the stakeholders; among them, the Pareto efficiency constraint means that the allocable water of the cross-border water resources allocation system must be fully allocated to the stakeholders; the declared boundedness constraint means that the water allocation obtained by all stakeholders does not exceed their declared water volume; the non-negativity constraint means that the water allocation obtained by all stakeholders is greater than or equal to 0.

[0015] Preferably, the specific implementation method of step S3) recorded in the present invention is to combine the principles of fairness and reasonableness and not causing significant damage, comprehensively consider the differences of stakeholders in climate, geography, hydrology, environment and socio-economic aspects, and construct an indicator system related to the negotiation power of stakeholders; the indicators covered by the principle of fairness and reasonableness include basin area, multi-year average runoff, annual average precipitation, future water demand, population size, current water consumption, per capita GDP, water resource productivity and effective utilization coefficient of agricultural irrigation water; the indicators covered by the principle of not causing significant damage include ecological environmental flow in the river, sewage discharge into the river and forest coverage.

[0016] Preferably, the specific implementation of step S4) recorded in the present invention is:

[0017] S401) Determine the weights of the indicators related to the negotiation power of the stakeholders;

[0018] S402) Calculate the subjective weights of the relevant indicators of the negotiation power of the stakeholders by using the analytic hierarchy process;

[0019] S403) using entropy method to calculate the objective weights of the indicators related to the negotiation power of the stakeholders;

[0020] S404) uses a subjective and objective combined weight method to calculate the weight value of the stakeholder negotiation power index based on the result of step S402) and the result of step S403).

[0021] Preferably, the specific implementation of step S402) recorded in the present invention is:

[0022] S4021) The stakeholders of the transboundary water resources allocation system negotiate power-related indicators, and combine the number of stakeholders to construct an initial indicator matrix C:

[0023]

[0024] in:

[0025] c ijis the actual value of the negotiation power-related index j∈M=[1,2,...,m] of the interest subject i∈N=[1,2,...,n];

[0026] N is the set of stakeholders;

[0027] M is a set of indicators related to the negotiation power of stakeholders;

[0028] n is the number of stakeholders;

[0029] m is the number of indicators related to the negotiating power of stakeholders;

[0030] S4022) The indicators in the initial indicator matrix C are compared pairwise, and the relative importance of the indicators is assigned using a 1-9 scale method to form an indicator judgment matrix A that can express the decision maker's preference:

[0031]

[0032] in:

[0033] a jj′ is the importance scale value of index j relative to index j′∈M, satisfying: a jj′ >0, a jj′ =1 / a j′j (j≠j′) and a jj =1;

[0034] S4023) Based on the indicator judgment matrix A, the geometric mean method is used to calculate the subjective weights of the indicators related to the negotiation power of the stakeholders:

[0035]

[0036]

[0037]

[0038] in:

[0039] m is the number of indicators related to the negotiation power of stakeholders; m′ j It is the product of all elements in the jth row of the indicator judgment matrix A;

[0040] is m′ j The mth root of

[0041] is the subjective weight of the relevant indicator j of the negotiation power of stakeholders in the transboundary water resources allocation system;

[0042] Preferably, the step S402) further comprises, after the step S4023), the following steps:

[0043] S4024) The average value of the remaining characteristic roots other than the maximum eigenvalue of the indicator judgment matrix A is used as an indicator to measure the deviation of the judgment matrix from consistency, that is:

[0044] CI=(λ max -m) / (m-1) (6)

[0045]

[0046] in:

[0047] CI is the consistency test index;

[0048] λ max is the maximum eigenvalue of the indicator judgment matrix A;

[0049] is the subjective weight vector of the indicator;

[0050] is a matrix The jth element in ; the larger the CI value, the greater the degree to which the indicator judgment matrix A deviates from complete consistency; conversely, the better the consistency; when CI = 0, it means that the indicator judgment matrix A has complete consistency, that is, there is no difference in the importance judgment of each indicator; when the CI value is close to 0 and the order m is greater than 2, the consistency ratio CR is used to measure the acceptable range of consistency of the indicator judgment matrix A:

[0051] CR=CI / RI (8)

[0052] in:

[0053] CR is the consistency ratio;

[0054] RI is the average consistency index, which is related to the order of the indicator judgment matrix A;

[0055] If CR≤0.10, it is considered that a certain indicator judgment matrix A has passed the consistency test, otherwise it is adjusted until it meets the consistency requirements.

[0056] Preferably, the specific implementation of step S403) recorded in the present invention is:

[0057] S4031) using the efficacy coefficient method to standardize the data of the initial indicator matrix C;

[0058]

[0059]

[0060]

[0061] in:

[0062] r ij is the standardized value of the negotiation power-related index j∈M=[1,2,...,m] of the stakeholder i∈N=[1,2,...,n];

[0063] and They are the standardized values ​​of the benefit index j and the cost index j′ of the negotiation power related indicators of the interest subject i∈N=[1,2,...,n];

[0064] c ij is the actual value of the negotiation power-related index j∈M=[1,2,...,m] of the interest subject i∈N=[1,2,...,n];

[0065] I B and I C They are the benefit index set and the cost index set;

[0066] ε and ε′ are translation index and scaling index respectively, and ε=10 -4 and ε′=1-ε;

[0067] c maxj and c minj are the maximum and minimum values ​​of the negotiation power-related benefit index j among all stakeholders, respectively;

[0068] c maxj′ and c minj′ are the maximum and minimum values ​​of the negotiation power-related cost index j′ among all stakeholders, respectively;

[0069] S4032) normalizes the index after the standardization process in step S4031):

[0070]

[0071] in:

[0072] p ij is the normalized value of the index j related to the negotiation power of the interest subject;

[0073] r ij is the standardized value of the negotiation power-related index j∈M=[1,2,...,m] of the stakeholder i∈N=[1,2,...,n];

[0074] n is the number of stakeholders;

[0075] S4033) Calculate the information entropy value of the indicator based on the result of step S4032):

[0076]

[0077] in:

[0078] IE j is the information entropy value of the index j related to the negotiation power of the interest subject;

[0079] k is a real constant related to the number of interests n and k>0. Generally, k=1 / ln(n) can ensure IE j is in the range [0,1];

[0080] p ij is the normalized value of the index j related to the negotiation power of the interest subject;

[0081] n is the number of stakeholders;

[0082] ln is the natural logarithm symbol; the smaller the information entropy value of the indicator, the greater its dispersion, the higher its information content, and the more significant its impact on the weight result;

[0083] S4034) Calculate the objective weights of the indicators related to the negotiation power of the stakeholders;

[0084]

[0085] in:

[0086] is the objective weight of the relevant indicator j of the negotiation power of stakeholders in the transboundary water resources allocation system;

[0087] IE j is the information entropy value of the index j related to the negotiation power of the interest subject;

[0088] m is the number of indicators related to the negotiating power of stakeholders.

[0089] Preferably, the specific implementation of step S404) recorded in the present invention is:

[0090] S4041) By introducing the coefficient vector The subjective weight vector of the relevant indicators of the negotiation power of stakeholders and the objective weight vector Perform a linear combination:

[0091]

[0092] in:

[0093] It is the linear weighted vector of subjective and objective weights of the indicators related to the negotiation power of the stakeholders;

[0094] and They are the subjective weight vector and objective weight vector of the indicators related to the negotiation power of the stakeholders;

[0095] T is the transpose symbol of the matrix;

[0096] and are the linear weight coefficients of the subjective weight and objective weight of the indicator, respectively. Here

[0097] S4042) by minimizing the weighted vector and the subjective weight vector of the indicator and the objective weight vector The basic vectors The deviation is used to find the subjective weight vector of the indicator and the objective weight vector The optimal linear weight coefficient vector for effective folding:

[0098]

[0099] in:

[0100] ||·||2 is the norm symbol;

[0101] S4043) According to the differential properties of the matrix, the optimization condition of the optimal linear weight coefficient vector obtained in step S4042) is given:

[0102]

[0103] S4044) Calculate the optimal linear combination coefficients with MatLab The combined coefficient is then normalized:

[0104]

[0105] in:

[0106] and They are the normalized values ​​of the optimal linear combination coefficients of the subjective weights and objective weights of the indicators related to the negotiation power of the stakeholders;

[0107] and They are the optimal linear combination coefficients of the subjective weights and objective weights of the indicators related to the negotiation power of the stakeholders;

[0108] S4045) According to the normalized optimal linear coefficient, the subjective and objective combined weight method based on game theory is used to calculate the weight value of the relevant index of the negotiation power of the interest subject, namely:

[0109]

[0110] in:

[0111] is the weight vector of indicators related to the negotiation power of stakeholders in the transboundary water allocation system;

[0112] It is the weight value of the negotiation power related index j∈M=[1,2,…,m] of the stakeholders in the transboundary water resources allocation system determined by the game theory method.

[0113] Preferably, the specific implementation of step S5) recorded in the present invention is:

[0114] S501) using a vector normative method to derive a normative decision matrix of an initial indicator matrix C;

[0115]

[0116] in:

[0117] N ij is the normalized value of the negotiation power-related index j∈M=[1,2,...,m] of the interest subject i∈N=[1,2,...,n];

[0118] r ij is the standardized value of the negotiation power-related index j∈M=[1,2,...,m] of the stakeholder i∈N=[1,2,...,n];

[0119] n is the number of stakeholders;

[0120] S502) Based on the normalized result of the indicator weights and the initial indicator matrix C, the weighted normalized value of each stakeholder under each indicator is calculated:

[0121]

[0122] Where:

[0123] V ij is the weighted normalized value of the negotiation power-related index j∈M=[1,2,...,m] of the interest subject i∈N=[1,2,...,n];

[0124] is the weight value of the negotiation power related index j∈M=[1,2,...,m] of the interest subject of the transboundary water resources allocation system determined by the game theory method in step S4045);

[0125] S503) calculating the positive ideal value and negative ideal value of the weighted normalized value of the negotiation power-related index of each stakeholder;

[0126]

[0127] in:

[0128] and They are the positive ideal value and negative ideal value of the weighted normalized value of the index j related to the negotiation power of the interest subject;

[0129] N is the set of stakeholders;

[0130] S504) calculating the optimal Euclidean distance and the worst Euclidean distance of the interest subject i∈N=[1,2,...,n] according to the result determined in step S503);

[0131]

[0132] in:

[0133] and They are the optimal Euclidean distance and the worst Euclidean distance of the interest subject i∈N=[1,2,...,n];

[0134] S505) calculating the closeness between the interest subject i∈N=[1,2,...,n] and the negative ideal solution according to the calculation result of step S504);

[0135]

[0136] in:

[0137] is the closeness between the interest subject i∈N=[1,2,...,n] and its negative ideal solution;

[0138] S506) normalizing the closeness between the interest subject i∈N=[1,2,...,n] and its negative ideal solution, and calculating the weight value of the interest subject i∈N=[1,2,...,n];

[0139]

[0140] in:

[0141] ω i is the weight value of the interest subject i∈N=[1,2,...,n];

[0142] S507) determining the negotiation power coefficient of the stakeholder according to the weight value of the stakeholder i∈N=[1,2,...,n] in step S506), wherein the asymmetric negotiation power coefficient of the stakeholder is the weight value of the corresponding scheme;

[0143] ANP i =ω i(26)

[0144] in:

[0145] ANP i is the asymmetric negotiation power coefficient value of interest subject i in the transboundary water resources allocation system.

[0146] Preferably, the specific implementation of step S6) recorded in the present invention is:

[0147]

[0148] bc i =max{0,E-∑ i′∈(N-{i}) wc i′} (28)

[0149] in:

[0150] dp i It is the negotiation breaking point water right of interest subject i;

[0151] bc i It is the minimum initial water right determined by using the bankruptcy game;

[0152] E is the amount of water resources that can be allocated by the transboundary water resources allocation system, and E∈R + , where R + is the set of positive real numbers;

[0153] ∑ i′∈(N-{i}) wc i′ is the sum of water demand of other stakeholders except stakeholder i;

[0154] wc i and wc i′ are the declared water volumes of stakeholders i and i′, respectively, i,i′∈N and i≠i′;

[0155] is the basic water security rate of stakeholder i.

[0156] Preferably, the specific implementation of step S7) recorded in the present invention is:

[0157]

[0158] in:

[0159]

[0160] λ max (N,wc,E)=ANP i ×ρ i (31)

[0161]

[0162] x i (N,wc,E)≤wc i (33)

[0163] x i (N,wc,E)-dp i ≥0 (34)

[0164]

[0165]

[0166]

[0167] λ i (N,wc,E),x i (N,wc,E),ANP i ,ρ i ≥0 (38)

[0168] x i (N,wc,E) is the amount of water resources allocated to stakeholder i, billion m 3 ;

[0169] λ i (N,wc,E) is the weighted water resource gap borne by stakeholder i, billion m 3 ;

[0170] ρ i is the water resource gap borne by stakeholder i, billion m 3 ;

[0171] ANP i is the coefficient value of the asymmetric negotiation power of interest subject i.

[0172] Beneficial effects of the present invention:

[0173] The invention discloses an asymmetric bankruptcy method for solving cross-border water resource allocation conflicts, comprising: collecting basic data information of a cross-border water resource allocation system; describing the cross-border water resource allocation problem as a bankruptcy game problem with non-transferable benefits; constructing a relevant index system of the negotiation power of interest subjects based on the principles of fairness, rationality and not causing major damage; proposing a calculation method for the weight of the relevant index of the negotiation power of interest subjects from the perspective of combining subjective and objective factors; proposing a calculation method for the asymmetric negotiation power coefficient of the interest subjects based on the index weight calculation result; determining the negotiation breaking point water right by combining the minimum initial water right of the bankruptcy game and the basic living water demand of the interest subjects; incorporating the negotiation power coefficient of the interest subjects and the negotiation breaking point water right into the traditional bankruptcy theory rules, proposing an asymmetric bankruptcy method for solving cross-border water resource allocation conflicts, and combining relevant basic data to use the proposed method to carry out cross-border water resource allocation. The present invention takes into account the differences of the interest subjects of the cross-border water resource allocation system in many factors such as climate, geography, hydrology, environment and socio-economics from the perspective of fairness and rationality and the principle of not causing major damage, and combines the bankruptcy game and the basic water demand of the interest subjects to propose an asymmetric bankruptcy method for solving cross-border water resource allocation conflicts. It breaks through the limitations of traditional bankruptcy rules that cannot consider the asymmetry of interest subjects in terms of water contribution, economic society, water use efficiency and degree of environmental damage, and cannot guarantee the basic water demand of interest subjects with small declared water volume, and can provide a fast and easy-to-understand water resource allocation scheme for solving cross-border water resource allocation conflicts. The present invention innovatively combines multi-criteria decision-making technology with traditional bankruptcy theory to form a water resource allocation method that integrates multiple sets of theories, enriching the theoretical system of cross-border water resource allocation decision-making. In view of the fact that traditional bankruptcy rules only allocate water resources based on the declared water volume of interest subjects, the present invention does not consider the influence of other characteristic factors such as water contribution, economic and social status, water use efficiency and degree of environmental damage, and may not guarantee the basic water demand of interest subjects, so as to achieve fair and reasonable allocation of cross-border water resources on the basis of considering the asymmetric negotiation power of interest subjects. BRIEF DESCRIPTION OF THE DRAWINGS

[0174] Figure 1 A flow chart of the asymmetric bankruptcy method proposed by the present invention for resolving conflicts over the allocation of transboundary water resources;

[0175] Figure 2 It is the water gap capacity of the Nanhe River Basin water resources allocation system under the EBM and ABM schemes. DETAILED DESCRIPTION

[0176] According to the attached Figure 1The flowchart of an asymmetric bankruptcy method for solving cross-border water resource allocation conflicts proposed by the present invention can clearly show the implementation process of the present invention. Next, the water resource allocation problem of the Nanhe River Basin across municipal administrative regions in Hubei Province is used as an example to further introduce the technical solution of the present invention, including the following steps:

[0177] The present invention provides an asymmetric bankruptcy method for resolving cross-border water resource allocation conflicts, comprising the following steps:

[0178] S1: Collect basic data and information on the transboundary water allocation system, including the stakeholders involved, the total allocatable water resources, the water resources claimed by the stakeholders, and data on climate, geography, hydrology, environment and socio-economic aspects related to the negotiated power.

[0179] Collect basic data on the water resources allocation system in the Nanhe River Basin of Hubei Province. The main stakeholders include Shennongjia Forest District, Shiyan City and Xiangyang City. The average annual water supply in the basin is 274.73 million m 3 The total water demand of the three stakeholders is 301.32 million m 3 The water demand of Shennongjia Forest Area, Shiyan City and Xiangyang City is 18.13 million m 3 , 113.02 million m 3 and 170.17 million m 3 The indicators and data on climate, geography, hydrology, environment and socio-economic aspects related to the right to negotiate with various stakeholders are shown in Table 1;

[0180] S2: Based on the basic data information such as the stakeholders involved in the transboundary water resources allocation system in step S1), the total allocable water resources and the water resources declared by the stakeholders, the transboundary water resources allocation problem is described as a bankruptcy game problem with non-transferable benefits.

[0181] When the available amount of transboundary water resources cannot meet the total water demand, conflicts may arise between the stakeholders involved due to the competition for water. This situation is very similar to the situation where a company is on the verge of bankruptcy because its remaining assets are not enough to fully repay its debts. Therefore, the bankruptcy theory derived from economics can be used to describe the problem of transboundary water resource allocation as a bankruptcy game problem with non-transferable benefits, and corresponding rules can be used to resolve conflicts in transboundary water resource allocation.

[0182] According to the bankruptcy game theory in economics, the water bankruptcy problem in the Nanhe River Basin of Hubei Province can be directly described as follows: There are three interest groups N = [1, 2, ..., n] (n = 3) in the water resources allocation system of the Nanhe River Basin, namely Shennongjia Forest District, Shiyan City and Xiangyang City. Each interest group has a reasonable declared water volume c = (wc1, wc2, ..., wc n )(The water demand of Shennongjia Forest Area, Shiyan City and Xiangyang City is 18.13 million m3 , 113.02 million m 3 and 170.17 million m 3 ), when the amount of water resources that can be allocated by the transboundary water resources allocation system is E∈R + (E = 274.73 million m 3 ) is less than the sum of the declared water volumes When , the water resource allocation system in the Nanhe River Basin of Hubei Province will go bankrupt. At this time, under the basic constraints of Pareto efficiency, declared boundedness and non-negativity, combined with the declared water volume of the stakeholders, the bankruptcy theory rule can be used to completely divide the limited water resources among the three stakeholders. Among them, the Pareto efficiency constraint condition means that the allocable water volume of the cross-border water resource allocation system must be fully allocated to the stakeholders; the declared boundedness constraint condition means that the water volume allocated to all stakeholders does not exceed their declared water volume; the non-negativity constraint condition means that the water volume allocated to all stakeholders is greater than or equal to 0.

[0183] S3: Based on the basic data information on climate, geography, hydrology, environment, and socio-economics related to the rights of stakeholders to negotiate in step S1), an indicator system related to the rights of stakeholders to negotiate in cross-border water resources allocation is constructed.

[0184] Based on the principles of fairness and reasonableness and not causing major damage, and taking into account the differences among the three stakeholders in the Nanhe River Basin in terms of climate, geography, hydrology, environment, social economy and other factors, a consultation power index system for stakeholders in the water resources allocation system of the Nanhe River Basin is constructed, as shown in the following table:

[0185] Table 1 Index system of consultative power of stakeholders in the water resources allocation system of the Nanhe River Basin in Hubei Province

[0186]

[0187] S4: based on the results of the determination of the relevant indicators of the negotiation power of the stakeholders in the cross-border water resources allocation in step S3), the weights of the relevant indicators of the negotiation power of the stakeholders are calculated;

[0188] S401. Determine the weights of indicators related to the negotiation power of stakeholders.

[0189] The problem of determining the coefficient of the negotiated power of stakeholders in the water resources allocation system of the Nanhe River Basin in Hubei Province is described as a multi-criteria decision-making problem. The three stakeholders in the Nanhe River Basin in Hubei Province are regarded as the schemes to be evaluated in the multi-criteria decision-making problem, and the 12 indicators that affect the negotiated power of stakeholders are regarded as the evaluation criteria of each scheme. In this way, the multi-criteria decision-making technology can be used to determine the weights of the indicators related to the negotiated power of stakeholders.

[0190] S402. Use the analytic hierarchy process to calculate the subjective weights of the indicators related to the negotiation power of stakeholders.

[0191] S4021) Based on the relevant indicators of the negotiation power of the stakeholders in the water resources allocation system of the Nanhe River Basin shown in Table 1 in step S3, combined with the number of stakeholders, an initial indicator matrix C of the multi-criteria decision-making problem is constructed:

[0192]

[0193] in:

[0194] c ij is the actual value of the negotiation power-related index j∈M=[1,2,...,m] of the interest subject i∈N=[1,2,...,n];

[0195] N is the set of stakeholders;

[0196] M is a set of indicators related to the negotiation power of stakeholders;

[0197] n is the number of stakeholders;

[0198] m is the number of indicators related to the negotiating power of stakeholders;

[0199] S4022) The indicators in the initial indicator matrix C are compared pairwise, and the relative importance of the indicators is assigned using a 1-9 scale method to form an indicator judgment matrix A that can express the decision maker's preference:

[0200]

[0201] in:

[0202] a jj′ is the importance scale value of index j relative to index j′∈M, satisfying: a jj′ >0, a jj′ =1 / a j′j (j≠j′) and a jj =1;

[0203] S4023) Based on the indicator judgment matrix A, the geometric mean method is used to calculate the subjective weights of the indicators related to the negotiation power of the stakeholders:

[0204]

[0205]

[0206]

[0207] in:

[0208] m is the number of indicators related to the negotiation power of stakeholders; m′ jIt is the product of all elements in the jth row of the indicator judgment matrix A;

[0209] is m′ j The mth root of

[0210] is the subjective weight of the index j related to the negotiation power of the stakeholders in the water resources allocation system of the Nanhe River Basin, and the results are shown in Table 2;

[0211] Preferably, the step S402) further comprises, after the step S4023), the following steps:

[0212] S4024) The average value of the remaining characteristic roots other than the maximum eigenvalue of the indicator judgment matrix A is used as an indicator to measure the deviation of the judgment matrix from consistency, that is:

[0213] CI=(λ max -m) / (m-1) (6)

[0214]

[0215] in:

[0216] CI is the consistency test index (CI of the present invention = 0.0392);

[0217] λ max is the maximum eigenvalue of the index judgment matrix A (λ max =12.4317);

[0218] is the subjective weight vector of the indicator;

[0219] is a matrix The jth element in ; the larger the CI value, the greater the degree to which the indicator judgment matrix A deviates from complete consistency; conversely, the better the consistency; when CI = 0, it means that the indicator judgment matrix A has complete consistency, that is, there is no difference in the importance judgment of each indicator; when the CI value is close to 0 and the order m is greater than 2, the consistency ratio CR is used to measure the acceptable range of consistency of the indicator judgment matrix A:

[0220] CR=CI / RI (8)

[0221] in:

[0222] CR is the consistency ratio (CR of the present invention = 0.0263);

[0223] RI is the average consistency index, which is related to the order of the index judgment matrix A (RI = 1.49 in the present invention);

[0224] If CR≤0.10, it is considered that a certain indicator judgment matrix A has passed the consistency test, otherwise it is adjusted until it meets the consistency requirements.

[0225] After calculation, CR < 0.10, indicating that the indicator judgment matrix A constructed by the present invention has passed the consistency test, and the calculation results of the subjective weights of the indicators related to the negotiation power of the stakeholders in the water resources allocation system of the Nanhe River Basin are effective and reasonable.

[0226] S403) using entropy method to calculate the objective weights of the indicators related to the negotiation power of the stakeholders;

[0227] S4031) using the efficacy coefficient method to standardize the data of the initial indicator matrix C;

[0228]

[0229]

[0230]

[0231] in:

[0232] r ij is the standardized value of the negotiation power-related index j∈M=[1,2,...,m] of the stakeholder i∈N=[1,2,...,n];

[0233] and They are the standardized values ​​of the benefit index j and the cost index j′ of the negotiation power related indicators of the interest subject i∈N=[1,2,...,n], combined with step S3, where the benefit index refers to the basin area, multi-year average runoff, annual average precipitation, future water demand, population size, current water consumption, effective utilization coefficient of farmland irrigation water and ecological environment flow in the river; the cost index refers to per capita GDP, water resources productivity and sewage discharge into the river;

[0234] c ij is the actual value of the negotiation power-related index j∈M=[1,2,...,m] of the interest subject i∈N=[1,2,...,n];

[0235] I B and I C They are the benefit indicator set and the cost indicator set. The benefit indicator set is composed of the basin area, multi-year average runoff, annual average precipitation, future water demand, population size, current water consumption, effective utilization coefficient of farmland irrigation water and ecological environment flow in the river; the cost indicator set is composed of per capita GDP, water resource productivity and sewage discharge into the river.

[0236] ε and ε′ are translation index and scaling index respectively, and ε=10-4 and ε′=1-ε;

[0237] c maxj and c minj are the maximum and minimum values ​​of the negotiation power-related benefit index j among all stakeholders, respectively;

[0238] c maxj′ and c minj′ are the maximum and minimum values ​​of the negotiation power-related cost index j′ among all stakeholders respectively; S4032) normalizes the index after the standardization process in step S4031):

[0239]

[0240] in:

[0241] p ij is the normalized value of the index j related to the negotiation power of the interest subject;

[0242] r ij is the standardized value of the negotiation power-related index j∈M=[1,2,...,m] of the stakeholder i∈N=[1,2,...,n];

[0243] n is the number of stakeholders; S4033) calculates the information entropy value of the indicator based on the result of step S4032):

[0244]

[0245] in:

[0246] IE j is the information entropy value of the index j related to the negotiation power of the interest subject;

[0247] k is a real constant related to the number of interests n and k>0. Generally, k=1 / ln(n) can ensure IE j is in the range [0,1];

[0248] p ij is the normalized value of the index j related to the negotiation power of the interest subject;

[0249] n is the number of stakeholders;

[0250] ln is the natural logarithm symbol; the smaller the information entropy value of the indicator, the greater its dispersion, the higher its information content, and the more significant its impact on the weight result;

[0251] S4034) Calculate the objective weights of the indicators related to the negotiation power of the stakeholders;

[0252]

[0253] in:

[0254] is the objective weight of the relevant indicator j of the negotiation power of stakeholders in the transboundary water resources allocation system;

[0255] IE j is the information entropy value of index j;

[0256] m is the number of evaluation criteria.

[0257] The objective weights of the indicators related to the negotiation power of stakeholders in the water resources allocation system of the Nanhe River Basin can be calculated by combining formula (13) and formula (14). The results are shown in Table 2.

[0258] S404) uses a subjective and objective combined weight method to calculate the weight value of the stakeholder negotiation power index based on the result of step S402) and the result of step S403).

[0259] S4041) By introducing the coefficient vector The subjective weight vector of the relevant indicators of the negotiation power of stakeholders and the objective weight vector Perform a linear combination:

[0260]

[0261] in:

[0262] It is the linear weighted vector of subjective and objective weights of the indicators related to the negotiation power of the stakeholders;

[0263] and They are the subjective weight vector and objective weight vector of the indicators related to the negotiation power of the stakeholders;

[0264] T is the transpose symbol of the matrix;

[0265] and are the linear weight coefficients of the subjective weight and objective weight of the indicator, respectively. Here

[0266] S4042) by minimizing the weighted vector and the subjective weight vector of the indicator and the objective weight vector The basic vectors The deviation is used to find the subjective weight vector of the indicator and the objective weight vector The optimal linear weight coefficient vector for effective folding:

[0267]

[0268] in:

[0269] ||·||2 is the norm symbol;

[0270] S4043) According to the differential properties of the matrix, the optimization condition of the optimal linear weight coefficient vector obtained in step S4042) is given:

[0271]

[0272] S4044) Calculate the optimal linear combination coefficients with MatLab The combined coefficient is then normalized:

[0273]

[0274] in:

[0275] and They are the normalized values ​​of the optimal linear combination coefficients of the subjective weights and objective weights of the indicators related to the negotiation power of the stakeholders;

[0276] and They are the optimal linear combination coefficients of the subjective weights and objective weights of the indicators related to the negotiation power of the stakeholders;

[0277] S4045) According to the normalized optimal linear coefficient, the subjective and objective combined weight method based on game theory is used to calculate the weight value of the relevant index of the negotiation power of the interest subject, namely:

[0278]

[0279] in:

[0280] is the weight vector of indicators related to the negotiation power of stakeholders in the transboundary water allocation system;

[0281] is the weight value of the negotiation power-related index j∈M=[1,2,...,m] of the interest subjects in the transboundary water resources allocation system determined by the game theory method;

[0282] After calculation, the optimal linear combination coefficient of subjective and objective weights based on game theory is After normalization, we get Then, the normalized optimal linear coefficient Substituting into formula (15), formula (19) can be used to obtain the weight vector of the relevant indicators of the negotiation power of the stakeholders in the water resources allocation system of the Nanhe River Basin based on the subjective and objective combined weight method of game theory: The results are shown in Table 2.

[0283] Table 2 Calculation results of weights of indicators related to the negotiation power of stakeholders in the water resources allocation system of the Nanhe River Basin Unit: dimensionless

[0284]

[0285] S5) based on the calculation results of the weights of the relevant indicators of the negotiation power of the stakeholders in step S4), the TOPSIS method is used to calculate the asymmetric negotiation power coefficients of the stakeholders in the water resources allocation system of the Nanhe River Basin;

[0286] S501) using a vector normative method to derive a normative decision matrix of an initial indicator matrix C;

[0287]

[0288] in:

[0289] N ij is the normalized value of the negotiation power-related index j∈M=[1,2,...,m] of the interest subject i∈N=[1,2,...,n];

[0290] r ij is the standardized value of the negotiation power-related index j∈M=[1,2,...,m] of the stakeholder i∈N=[1,2,...,n];

[0291] n is the number of stakeholders;

[0292] S502) Based on the normalized result of the indicator weights and the initial indicator matrix C, the weighted normalized value of each stakeholder under each indicator is calculated:

[0293]

[0294] Where:

[0295] V ij is the weighted normalized value of the negotiation power-related index j∈M=[1,2,...,m] of the interest subject i∈N=[1,2,...,n];

[0296] is the weight value of the negotiation power related index j∈M=[1,2,...,m] of the interest subject of the transboundary water resources allocation system determined by the game theory method in step S4045;

[0297] S503) calculating the positive ideal value and negative ideal value of the weighted normalized value of the negotiation power-related index of each stakeholder;

[0298]

[0299] in:

[0300] and They are the positive ideal value and negative ideal value of the weighted normalized value of the index j related to the negotiation power of the interest subject;

[0301] N is the set of stakeholders;

[0302] S504) calculating the optimal Euclidean distance and the worst Euclidean distance of the interest subject i∈N=[1,2,...,n] according to the result determined in step S503);

[0303]

[0304] in:

[0305] and They are the optimal Euclidean distance and the worst Euclidean distance of the interest subject i∈N=[1,2,...,n];

[0306] S505) calculating the closeness between the interest subject i∈N=[1,2,...,n] and the negative ideal solution according to the calculation result of step S504);

[0307]

[0308] in:

[0309] is the closeness between the interest subject i∈N=[1,2,...,n] and its negative ideal solution;

[0310] S506) normalizing the closeness between the interest subject i∈N=[1,2,...,n] and its negative ideal solution, and calculating the weight value of the interest subject i∈N=[1,2,...,n];

[0311]

[0312] in:

[0313] ω i is the weight value of the interest subject i∈N=[1,2,...,n];

[0314] S507) determining the negotiation power coefficient of the stakeholder according to the weight value of the stakeholder i∈N=[1,2,...,n] in step S506), the asymmetric negotiation power coefficient of the stakeholder is the weight value of the corresponding scheme;

[0315] ANP i =ω i (26)

[0316] in:

[0317] ANP i is the asymmetric negotiation power coefficient value of interest subject i in the transboundary water resources allocation system.

[0318] In order to determine the size of the negotiation power of the interest subject of the water resources allocation system in the Nanhe River Basin, the present invention requires that the larger the coefficient value, the larger the negotiation power value. Therefore, the original TOPSIS method is adjusted to a certain extent, that is, the farther away from its negative ideal solution, the greater the weight. After calculation, the negotiation power coefficient value of the interest subject of the water resources allocation system in the Nanhe River Basin of Hubei Province is shown in Table 3.

[0319] Table 3. Coefficients of negotiation power of stakeholders in the water resources allocation system of the Nanhe River Basin Unit: dimensionless

[0320]

[0321] S6) Based on the basic data information of the stakeholders involved in the cross-border water resources allocation system in step 1), the total allocable water resources and the water resources declared by the stakeholders, combined with the minimum initial water rights of the bankruptcy game and the basic living water needs of the stakeholders, determine the water rights at the negotiation breakdown point;

[0322] Considering that the current water consumption may not be suitable as the starting point water right for the negotiation of cross-border water resources allocation by the interest subject; at the same time, the traditional bankruptcy theory rules may not guarantee the basic water demand of the interest subject with a small declared water volume. The present invention combines the minimum initial water right of the bankruptcy game and the basic water demand of the interest subject to determine the water right at the breaking point of the negotiation.

[0323]

[0324] bc i =max{0,E-∑ i′∈(N-{i}) wc i′} (28)

[0325] in:

[0326] dp i It is the negotiation breaking point water right of interest subject i;

[0327] bc i It is the minimum initial water right determined by using the bankruptcy game;

[0328] E is the amount of water resources that can be allocated by the transboundary water resources allocation system, and E∈R + , where R + is the set of positive real numbers;

[0329] ∑ i′∈(N-{i}) wc i′is the sum of water demand of other stakeholders except stakeholder i;

[0330] wc i and wc i′ are the declared water volumes of stakeholders i and i′, respectively, i,i′∈N and i≠i′;

[0331] is the basic water security rate of interest subject i;

[0332] It is predicted that the basic living water consumption in Shennongjia Forest District, Shiyan City and Xiangyang City in the Nanhe River Basin water resources allocation system is 0.0311 billion m 3 , 15.36 million m 3 and 21.05 million m 3 , combined with the water demand of the three stakeholders, their basic water use guarantee rate vector can be calculated And determine the basic water demand of the three stakeholders. Then, combined with the water demand of each stakeholder in the water resources allocation system of the Nanhe River Basin and the total amount of allocable water resources, the minimum initial water rights of the bankruptcy game of the three stakeholders can be calculated using formula (26). Finally, using formula (27), that is, outsourcing the basic water demand of the stakeholder and the minimum initial water rights of the bankruptcy game, the negotiation breaking point water rights of Shennongjia Forest District, Shiyan City and Xiangyang City can be obtained. The results are shown in Table 4.

[0333] Table 4 Negotiation breakdown points of the stakeholders in the water resources allocation system of the Nanhe River Basin Water rights unit: billion m 3

[0334]

[0335] S7) Based on the negotiation power coefficient of the interest subject calculated in step S5) and the negotiation breakdown point water right determined in step S6), an asymmetric bankruptcy method for resolving cross-border water resource allocation conflicts is proposed, and cross-border water resource allocation is carried out based on the basic data collected in step 1).

[0336] Traditional bankruptcy rules usually allocate water resources only based on the declared water resources of the stakeholders, without considering the impact of other characteristic factors such as water contribution, economic and social status, water use efficiency and degree of environmental damage on the water allocation results, and cannot guarantee the basic water demand of stakeholders with smaller declared water quantities. Therefore, when water bankruptcy occurs in the cross-border water resource allocation system, it is usually difficult for stakeholders to reach an effective water resource sharing agreement. To this end, the present invention proposes an asymmetric bankruptcy method for resolving cross-border water resource allocation conflicts from the perspective of water resource gap allocation, so as to ensure that the basic water demand of all stakeholders is guaranteed, so that the stakeholders with higher negotiation power can share the water resource gap as little as possible. The proposed asymmetric bankruptcy method for resolving cross-border water resource allocation conflicts is described by formula (29)-formula (38).

[0337]

[0338] in:

[0339]

[0340] λ max (N,wc,E)=ANP i ×ρ i (31)

[0341]

[0342] x i (N,wc,E)≤wc i (33)

[0343] x i (N,wc,E)-dp i ≥0 (34)

[0344]

[0345]

[0346]

[0347] λ i (N,wc,E),x i (N,wc,E),ANP i ,ρ i ≥0 (38)

[0348] x i (N,wc,E) is the amount of water resources allocated to stakeholder i, billion m 3 ;

[0349] λ i(N,wc,E) is the weighted water resource gap borne by stakeholder i, billion m 3 ;

[0350] ρ i is the water resource gap borne by stakeholder i, billion m 3 ;

[0351] ANP i is the coefficient value of the asymmetric negotiation power of interest subject i.

[0352] Formula (31) comprehensively considers the differences in climate, geography, hydrology, environment, socio-economics and other factors among stakeholders in the transboundary water resources allocation system in the form of negotiation power coefficients; Formula (33) is a boundedness constraint to ensure that the water allocation of stakeholders does not exceed their water demand; Formula (34) is an individual rationality condition to ensure the basic water demand of stakeholders; Formula (35) is a Pareto efficiency constraint to ensure that the limited water resources are fully allocated; Formula (36) is the basic prerequisite for the formation of the water bankruptcy problem in the transboundary water resources allocation system; Formula (38) is a non-negativity constraint to ensure that the proposed method has a feasible solution.

[0353] On the basis of the calculation results in the previous steps, combined with relevant basic data information, the current water use ratio method, the equal negotiation power method (traditional bankruptcy method) and the method proposed in this invention are used to allocate water resources in the Nanhe River Basin. The results are shown in Table 5.

[0354] Table 5 Water resources allocation results of Nanhe River Basin in Hubei Province Unit: billion m 3

[0355]

[0356] Note: The CUR scheme is a water allocation scheme based on the current water use ratio method; the EBM scheme is an allocation scheme based on the equal negotiation power method; the ABM scheme is a scheme based on the method proposed by the present invention.

[0357] From the results in Table 5, it can be seen that under the CUR scheme, the water allocation of Shiyan City exceeds its declared water volume, that is, it does not meet the demand boundedness constraint condition. Therefore, it is unscientific and unreasonable to allocate water resources in the Nanhe River Basin based on the current water use ratio. The EBM scheme and the ABM scheme meet the basic constraints such as Pareto efficiency, declared boundedness and non-negativity, and can ensure that the water volume obtained by the three stakeholders in the Nanhe River Basin exceeds their negotiation breakdown point water rights, thus meeting the individual rationality condition. However, compared with the ABM scheme, the EBM scheme fails to comprehensively consider the differences in many factors such as climate, geography, hydrology, environment and socio-economic factors among the stakeholders in the water resources allocation system of the Nanhe River Basin when allocating water, and therefore fails to reflect the principle of fairness and rationality of cross-border water resources allocation and not causing major damage.

[0358] In order to further explore the effectiveness of the proposed method, the water gap capacity of the Nanhe River Basin water resources allocation system under the EBM scheme and the ABM scheme was compared. Figure 2 .Depend on Figure 2 It can be seen that under the EBM scheme, the negotiation power coefficients of the three stakeholders in the Nanhe River Basin water resources allocation system are the same, and water resources are allocated only based on their declared water volume. Therefore, the water volume gap borne by the three stakeholders is the same, which is 8.86 million m 3 However, under the ABM scheme, due to the comprehensive consideration of other characteristic factors of the stakeholders in addition to the declared water volume, the water volume gaps borne by the three stakeholders in the Nanhe River Basin water resources allocation system are different. The water volume gaps borne by Shennongjia Forest District, Shiyan City and Xiangyang City are 0.1312 billion m3 and 0.276 billion m3, respectively. 3 , 70.2 million m 3 and 0.0645 billion m 3 In addition, Figure 2 (b) It can be seen that the size of the water gap borne by the three stakeholders in the water resources allocation system of the Nanhe River Basin is inversely proportional to the size of their asymmetric negotiation power coefficients. That is, Xiangyang City has the smallest water gap (0.0645) due to its largest negotiation power coefficient value (0.4149).

[0359] In summary, the present invention proposes an asymmetric bankruptcy method for resolving cross-border water resource allocation conflicts, which can break through the limitations of traditional bankruptcy rules that cannot take into account the asymmetry of stakeholders in terms of water contribution, economic society, water use efficiency and degree of environmental damage, and cannot guarantee the basic water demand of stakeholders with smaller declared water volume, and can provide a fast and easy-to-understand water resource allocation plan for resolving cross-border water resource allocation conflicts.

Claims

1. An asymmetric bankruptcy method for resolving transboundary water resource allocation conflicts, characterized by: The asymmetric bankruptcy method for resolving transboundary water resource allocation conflicts comprises the following steps: S1) Collect basic data information on the transboundary water resources allocation system, including the stakeholders involved, the total allocable water resources, the water resources declared by the stakeholders, and basic data related to the negotiation power; the basic data related to the negotiation power includes climate, geography, hydrology, environment and socio-economic data; S2) Based on the stakeholders involved in the cross-border water resources allocation system of the basic data information in step S1), the total allocable water resources and the water resources declared by the stakeholders, the cross-border water resources allocation problem is described as a bankruptcy game problem where the benefits cannot be transferred; the specific implementation method of step S2) is: according to the relevant definition of bankruptcy theory, a cross-border water bankruptcy problem is directly described as: there is a finite set of stakeholders N = [1,2,...,n], and each stakeholder has a reasonable declared water volume wc = (wc1,wc2,...,wc n ),when When , the transboundary water resources allocation system is considered to have water bankruptcy; E is the amount of water resources that can be allocated by the transboundary water resources allocation system, and E∈R + , where R + is a set of positive real numbers; is the sum of declared water resources; based on the Pareto efficiency constraint, declared boundedness constraint and non-negativity constraint, combined with the declared water resources of the stakeholders, the bankruptcy theory rule is used to fully allocate the limited water resources to the stakeholders; among them, the Pareto efficiency constraint means that the allocable water of the cross-border water resources allocation system must be fully allocated to the stakeholders; the declared boundedness constraint means that the water allocation obtained by all stakeholders does not exceed their declared water; the non-negativity constraint means that the water allocation obtained by all stakeholders is greater than or equal to 0; S3) constructing an indicator system related to the negotiation power of stakeholders in cross-border water resources allocation based on the basic data related to the negotiation power in the basic data information in step S1); S4) calculating the weights of the indicators related to the negotiation power of the stakeholders in cross-border water resources allocation based on the results of the determination of the indicator system related to the negotiation power of the stakeholders in step S3); S5) calculating the asymmetric negotiation power coefficient of the stakeholder based on the calculation result of the weight of the relevant index of the negotiation power of the stakeholder in step S4); The specific implementation of step S5) is: S501) using a vector normative method to derive a normative decision matrix of an initial indicator matrix C; in: N ij is the normalized value of the negotiation power-related index j∈M=[1,2,...,m] of the interest subject i∈N=[1,2,...,n]; r ij is the standardized value of the negotiation power-related index j∈M=[1,2,...,m] of the stakeholder i∈N=[1,2,...,n]; n is the number of stakeholders; S502) Based on the normalized result of the indicator weights and the initial indicator matrix C, the weighted normalized value of each stakeholder under each indicator is calculated: Where: V ij is the weighted normalized value of the negotiation power-related index j∈M=[1,2,...,m] of the interest subject i∈N=[1,2,...,n]; is the weight value of the negotiation power-related index j∈M=[1,2,...,m] of the interest subjects in the transboundary water resources allocation system determined by the game theory method; S503) calculating the positive ideal value and negative ideal value of the weighted normalized value of the negotiation power-related index of each stakeholder; in: and They are the positive ideal value and negative ideal value of the weighted normalized value of the index j related to the negotiation power of the interest subject; N is the set of stakeholders; S504) calculating the optimal Euclidean distance and the worst Euclidean distance of the interest subject i∈N=[1,2,...,n] according to the result determined in step S503); in: and They are the optimal Euclidean distance and the worst Euclidean distance of the interest subject i∈N=[1,2,...,n]; S505) calculating the closeness between the interest subject i∈N=[1,2,...,n] and the negative ideal solution according to the calculation result of step S504); in: is the closeness between the interest subject i∈N=[1,2,...,n] and its negative ideal solution; S506) normalizing the closeness between the interest subject i∈N=[1,2,...,n] and its negative ideal solution, and calculating the weight value of the interest subject i∈N=[1,2,...,n]; in: ω i is the weight value of the interest subject i∈N=[1,2,...,n]; S507) determining the negotiation power coefficient of the stakeholder according to the weight value of the stakeholder i∈N=[1,2,...,n] in step S506), wherein the asymmetric negotiation power coefficient of the stakeholder is the weight value of the corresponding scheme; ANP i =ω i (26) in: ANP i is the asymmetric negotiation power coefficient value of interest subject i in the transboundary water resources allocation system; S6) Based on the basic data information in step 1), the stakeholders involved in the transboundary water resources allocation system, the total allocable water resources and the water resources declared by the stakeholders, combined with the minimum initial water rights of the bankruptcy game and the basic living water needs of the stakeholders, determine the water rights at the negotiation breaking point; The specific implementation of step S6) is: bc i =max{0,E-∑ i′∈(N-{i}) wc i′ } (28) in: dp i It is the negotiation breaking point water right of interest subject i; bc i It is the minimum initial water right determined by using the bankruptcy game; E is the amount of water resources that can be allocated by the transboundary water resources allocation system, and E∈R + , where R + is the set of positive real numbers; ∑ i′∈(N-{i}) wc i′ is the sum of water demand of other stakeholders except stakeholder i; wc i and wc i′ are the declared water volumes of stakeholders i and i′, respectively, i,i′∈N and i≠i′; is the basic water security rate of interest subject i; S7) allocating cross-border water resources based on the negotiation power coefficient of the interest subject calculated in step S5) and the negotiation breaking point water right determined in step S6); The specific implementation of step S7) is: in: λ max (N,wc,E)=ANP i ×ρ i (31) x i (N,wc,E)≤wc i (33) x i (N,wc,E)-dp i ≥0 (34) λ i (N,wc,E),x i (N,wc,E),ANP i ,ρ i ≥0 (38) x i (N,wc,E) is the amount of water resources allocated to stakeholder i, billion m 3 ; λ i (N,wc,E) is the weighted water resource gap borne by stakeholder i, billion m 3 ; ρ i is the water resource gap borne by stakeholder i, billion m 3 ; ANP i is the coefficient value of the asymmetric negotiation power of interest subject i.

2. The asymmetric bankruptcy method for resolving cross-border water resource allocation conflicts according to claim 1, characterized in that: The specific implementation method of step S3) is to combine the principles of fairness and reasonableness and not causing major damage, comprehensively consider the differences of stakeholders in climate, geography, hydrology, environment and socio-economic aspects, and construct an indicator system related to the negotiation power of stakeholders; the indicators covered by the principle of fairness and reasonableness include basin area, multi-year average runoff, annual average precipitation, future water demand, population size, current water consumption, per capita GDP, water resource productivity and effective utilization coefficient of agricultural irrigation water; the indicators covered by the principle of not causing major damage include ecological environmental flow in the river, sewage discharge into the river and forest coverage rate.

3. The asymmetric bankruptcy method for resolving cross-border water resource allocation conflicts according to claim 2 is characterized by: The specific implementation of step S4) is: S401) Determine the weights of the indicators related to the negotiation power of the stakeholders; S402) Calculate the subjective weights of the relevant indicators of the negotiation power of the stakeholders by using the analytic hierarchy process; S403) using entropy method to calculate the objective weights of the indicators related to the negotiation power of the stakeholders; S404) uses a subjective and objective combined weight method to calculate the weight value of the stakeholder negotiation power index based on the result of step S402) and the result of step S403).

4. The asymmetric bankruptcy method for resolving cross-border water resource allocation conflicts according to claim 3 is characterized by: The specific implementation of step S402) is: S4021) The stakeholders of the transboundary water resources allocation system negotiate power-related indicators, and combine the number of stakeholders to construct an initial indicator matrix C: in: c ij is the actual value of the negotiation power-related index j∈M=[1,2,...,m] of the interest subject i∈N=[1,2,...,n]; N is the set of stakeholders; M is a set of indicators related to the negotiation power of stakeholders; n is the number of stakeholders; m is the number of indicators related to the negotiating power of stakeholders; S4022) The indicators in the initial indicator matrix C are compared pairwise, and the relative importance of the indicators is assigned using a 1-9 scale method to form an indicator judgment matrix A that can express the decision maker's preference: in: a jj′ is the importance scale value of index j relative to index j′∈M, satisfying: a jj′ >0, a jj′ =1 / a j′j (j≠j′) and a jj =1; S4023) Based on the indicator judgment matrix A, the geometric mean method is used to calculate the subjective weights of the indicators related to the negotiation power of the stakeholders: in: m is the number of indicators related to the negotiation power of stakeholders; m′ j It is the product of all elements in the jth row of the indicator judgment matrix A; is m′ j The mth root of It is the subjective weight of the index j related to the negotiation power of stakeholders in the transboundary water resources allocation system.

5. The asymmetric bankruptcy method for resolving cross-border water resource allocation conflicts according to claim 4, characterized in that: The step S402) further includes, after the step S4023): S4024) The average value of the remaining characteristic roots other than the maximum eigenvalue of the indicator judgment matrix A is used as an indicator to measure the deviation of the judgment matrix from consistency, that is: CI=(λ max -m) / (m-1) (6) in: CI is the consistency test index; λ max is the maximum eigenvalue of the indicator judgment matrix A; is the subjective weight vector of the indicator; is a matrix The jth element in ; the larger the CI value, the greater the degree to which the indicator judgment matrix A deviates from complete consistency; conversely, the better the consistency; when CI = 0, it means that the indicator judgment matrix A has complete consistency, that is, there is no difference in the importance judgment of each indicator; when the CI value is close to 0 and the order m is greater than 2, the consistency ratio CR is used to measure the acceptable range of consistency of the indicator judgment matrix A: CR=CI / RI (8) in: CR is the consistency ratio; RI is the average consistency index, which is related to the order of the indicator judgment matrix A; If CR≤0.10, it is considered that a certain indicator judgment matrix A has passed the consistency test, otherwise it is adjusted until it meets the consistency requirements.

6. The asymmetric bankruptcy method for resolving transboundary water resource allocation conflicts according to claim 5, characterized in that: The specific implementation of step S403) is: S4031) using the efficacy coefficient method to standardize the data of the initial indicator matrix C; in: r ij is the standardized value of the negotiation power-related index j∈M=[1,2,...,m] of the stakeholder i∈N=[1,2,...,n]; and They are the standardized values ​​of the benefit index j and the cost index j′ of the negotiation power related indicators of the interest subject i∈N=[1,2,...,n]; c ij is the actual value of the negotiation power-related index j∈M=[1,2,...,m] of the interest subject i∈N=[1,2,...,n]; I B and I C They are the benefit index set and the cost index set; ε and ε′ are translation index and scaling index respectively, and ε=10 -4 and ε′=1-ε; c maxj and c minj are the maximum and minimum values ​​of the negotiation power-related benefit index j among all stakeholders, respectively; c maxj′ and c minj′ are the maximum and minimum values ​​of the negotiation power-related cost index j′ among all stakeholders, respectively; S4032) normalizes the index after the standardization process in step S4031): in: p ij is the normalized value of the index j related to the negotiation power of the interest subject; r ij is the standardized value of the negotiation power-related index j∈M=[1,2,...,m] of the stakeholder i∈N=[1,2,...,n]; n is the number of stakeholders; S4033) Calculate the information entropy value of the indicator based on the result of step S4032): in: IE j is the information entropy value of the index j related to the negotiation power of the interest subject; k is a real constant related to the number of benefits n and k>0, let k=1 / ln(n), then IE can be guaranteed j is in the range [0,1]; p ij is the normalized value of the index j related to the negotiation power of the interest subject; n is the number of stakeholders; ln is the natural logarithm symbol; S4034) Calculate the objective weights of the indicators related to the negotiation power of the stakeholders; in: is the objective weight of the relevant indicator j of the negotiation power of stakeholders in the transboundary water resources allocation system; IE j is the information entropy value of the index j related to the negotiation power of the interest subject; m is the number of indicators related to the negotiating power of stakeholders.

7. The asymmetric bankruptcy method for resolving transboundary water resource allocation conflicts according to claim 6, characterized in that: The specific implementation of step S404) is: S4041) By introducing the coefficient vector The subjective weight vector of the relevant indicators of the negotiation power of stakeholders and the objective weight vector Perform a linear combination: in: It is the linear weighted vector of subjective and objective weights of the indicators related to the negotiation power of the stakeholders; and They are the subjective weight vector and objective weight vector of the indicators related to the negotiation power of the stakeholders; T is the transpose symbol of the matrix; and are the linear weight coefficients of the subjective weight and objective weight of the indicator, respectively. Here S4042) by minimizing the weighted vector and the subjective weight vector of the indicator and the objective weight vector The basic vectors The deviation is used to find the subjective weight vector of the indicator and the objective weight vector The optimal linear weight coefficient vector for effective folding: in: ||·||2 is the norm symbol; S4043) According to the differential properties of the matrix, the optimization condition of the optimal linear weight coefficient vector obtained in step S4042) is given: S4044) Calculate the optimal linear combination coefficients with MatLab The combined coefficient is then normalized: in: and They are the normalized values ​​of the optimal linear combination coefficients of the subjective weights and objective weights of the indicators related to the negotiation power of the stakeholders; and They are the optimal linear combination coefficients of the subjective weights and objective weights of the indicators related to the negotiation power of the stakeholders; S4045) According to the normalized optimal linear coefficient, the subjective and objective combined weight method based on game theory is used to calculate the weight value of the relevant index of the negotiation power of the interest subject, namely: in: is the weight vector of indicators related to the negotiation power of stakeholders in the transboundary water allocation system; It is the weight value of the negotiation power related index j∈M=[1,2,…,m] of the stakeholders in the transboundary water resources allocation system determined by the game theory method.

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