SF-CPT-GRA-based emergency plan generation method for water supply emergencies

Abstract

The invention discloses a water supply emergency emergency plan generation method based on SF-CPT-GRA, and the method comprises the steps: constructing a spherical fuzzy lumped decision matrix of a water supply emergency emergency disposal scheme, and obtaining a standardized score of the spherical fuzzy lumped decision matrix of the water supply emergency emergency disposal scheme; according to the water supply emergency event emergency disposal scheme spherical fuzzy lumped decision matrix, obtaining each attribute weight; processing each attribute at the same time; obtaining a conversion probability weight according to each attribute weight; according to the grey correlation among the alternative schemes, performing foreground analysis on subjective values brought by the alternative schemes on attributes of the alternative schemes; according to the foreground analysis and the conversion probability weight, obtaining accumulated foreground analysis of each alternative scheme; and obtaining an alternative scheme sequence of each decision maker according to the accumulated foreground value. According to the method, comprehensive analysis of complex decision problems can be realized, psychology of decision makers is considered, preferences of different decision makers are integrated, and the problems of uncertainty and inconsistency of group decision information of a water supply emergency plan are solved.

Description

Technical Field

[0001] The present invention relates to the field of emergency disaster prevention, and in particular to a method for generating an emergency plan for water supply emergencies based on SF-CPT-GRA. Background Art

[0002] Emergency decision-making for water supply emergencies is an important measure to ensure water supply safety and improve the emergency response mechanism. In order to improve the level of emergency disposal decision-making, relevant scholars have carried out research on the theory and method of generating emergency plans for water supply emergencies. Existing methods for generating emergency plans for water supply emergencies mostly use fuzzy theory to find historical cases that are most similar to the target case. They mainly rely on the screening and analysis of historical cases, and the emergency plans presented in documents have the problem of insufficient use of historical cases. In order to further enrich the data source for emergency disposal of water supply emergencies, factors such as disposal effect, timeliness, scheduling feasibility and risk are considered. Therefore, formulating emergency disposal plans and refining water source switching and engineering scheduling plans are technical problems that need to be solved urgently in this invention. Summary of the Invention

[0003] The present invention aims to propose a method for generating emergency plans for water supply emergencies based on SF-CPT-GRA. Through the three-stage architecture of "fuzzy processing → risk correction → association optimization", the emergency response plan decision generation for water supply emergencies is realized for each decision maker.

[0004] The present invention proposes a method for generating an emergency plan for water supply emergencies based on SF-CPT-GRA, comprising the following steps:

[0005] Determine the spherical fuzzy decision model of the emergency response plan for water supply emergencies for each decision maker. The input of the model is the fuzzy evaluation information of each alternative plan and each attribute, and the output is the spherical fuzzy decision matrix of the emergency response plan for water supply emergencies.

[0006] According to the spherical fuzzy decision model matrix of the water supply emergency response plan, a spherical fuzzy lumped decision matrix of the water supply emergency response plan is constructed, and a standardized score of the spherical fuzzy lumped decision matrix of the water supply emergency response plan is obtained;

[0007] According to the spherical fuzzy lumped decision matrix of the water supply emergency response plan, the weight of each attribute is obtained; at the same time, each attribute is processed, including:

[0008] i) Calculate the spherical fuzzy ideal solution of each attribute;

[0009] ii) obtaining the distance between each alternative solution and the spherical fuzzy ideal solution of each attribute based on the spherical fuzzy ideal solution of each attribute; and obtaining the grey correlation between the alternative solutions based on the distance;

[0010] Obtaining a conversion probability weight based on the attribute weights; and performing a prospect analysis of the subjective value of the alternatives in terms of their attributes based on the grey correlations between the alternatives;

[0011] Obtaining a cumulative prospect analysis of each alternative plan based on the prospect analysis and the conversion probability weight;

[0012] Based on the cumulative prospect analysis of each alternative plan, the ranking of alternative plans for each decision maker is obtained.

[0013] In some embodiments, the method further includes normalizing the spherical fuzzy decision model of the water supply emergency response plan. The matrix of the spherical fuzzy decision model of the water supply emergency response plan after normalization is as shown in the following formula:

[0014]

[0015] Where, represents the normalized decision matrix of the rth decision maker, n, t, and p represent the number of alternatives and decision makers, respectively. Respectively The membership, non-membership and hesitation of the decision maker are: e represents the e-th alternative, a represents the a-th attribute, and r represents the r-th decision maker. Represents the normalized decision matrix V r The elements in It represents the decision information of the rth decision maker on the eth alternative on the ath attribute based on the spherical fuzzy set; Indicates when When it is a cost indicator The spherical fuzzy number obtained by conversion is Represent the original evaluation of membership, non-membership and hesitation, Represents the tth attribute.

[0016] In some embodiments, the spherical fuzzy lumped decision matrix of the water supply emergency response plan is C=(c ea ) n×t ,in:

[0017]

[0018] In the formula, δ=(δ1, δ2,..., δ p ) T represents the weight vector of the p-th decision maker, is the comprehensive membership, which indicates the degree of group’s affirmation of scheme e on attribute a; is the comprehensive non-membership degree, which indicates the degree of group’s rejection of scheme e on attribute a. It represents the comprehensive hesitation degree, indicating the degree of uncertainty of the group towards the solution e on the attribute a; c ea represents the comprehensive evaluation result of the e-th solution and the a-th attribute in the spherical fuzzy set total decision matrix C, respectively represent the membership degree, non-membership degree and hesitation degree of the r-th decision maker's normalized decision matrix. SWAM represents the spherical weighted arithmetic mean operator, which is defined as follows:

[0019]

[0020] In the formula, is a spherical fuzzy number, represents a set of spherical fuzzy sets, ω = (ω1, ω2,..., ω m ) T is the corresponding weight vector, the spherical weighted arithmetic mean operator.

[0021] In some embodiments, the standardized scoring of the spherical fuzzy set total decision matrix of the emergency disposal plan for water supply emergencies is as follows:

[0022]

[0023] In the formula, represents the score of the spherical fuzzy set total decision matrix c of the emergency disposal plan for water supply emergencies ea of c ea represents the standardized score of c ea of c represents the minimum score corresponding to the attribute a among all alternative solutions, represents the maximum score corresponding to the attribute a among all alternative solutions.

[0024] In some embodiments, obtaining the weights of each attribute according to the spherical fuzzy set total decision matrix of the emergency disposal plan for water supply emergencies further includes the following steps:

[0025] Determine the correlation coefficient between each attribute as follows:

[0026]

[0027] In the formula, γ aj represents the correlation coefficient between the a-th attribute and the j-th attribute, k ea represents the standardized score of the e-th alternative solution on the a-th attribute, k ej represents the standardized score of the e-th alternative solution on the j-th attribute, e = 1, 2,..., n, and n is the total number of alternative solutions;

[0028] Calculate the standard deviation of each attribute as shown in the following formula:

[0029]

[0030] In the formula, σ a represents the standard deviation of the a-th type of attribute;

[0031] Calculate the degree of deviation of each attribute as shown in the following formula:

[0032]

[0033] In the formula, J a represents the degree of deviation of the a-th type of attribute;

[0034] Calculate the weight of each attribute as shown in the following formula:

[0035]

[0036] In the formula, represents the weight of the a-th type of attribute.

[0037] In some embodiments, the calculation of the spherical fuzzy ideal solution of each attribute further includes calculating the spherical fuzzy positive ideal solution S + and the spherical fuzzy negative ideal solution S - , as shown in the following formula:

[0038]

[0039] In the formula, a = 1, 2,..., t; S + is the spherical fuzzy positive ideal solution, representing the optimal value combination of each attribute among all alternative solutions, is the a-th element in the vector of S + , representing the spherical fuzzy positive ideal solution of the a-th attribute, is the membership degree in the spherical fuzzy positive ideal solution of the a-th attribute, is the non-membership degree in the spherical fuzzy positive ideal solution of the a-th attribute, is the hesitation degree in the spherical fuzzy positive ideal solution of the a-th attribute, a is the index of the attribute, and t is the total number of attributes;

[0040]

[0041] In the formula, a = 1, 2,..., t, S - is the spherical fuzzy negative ideal solution, representing the worst value combination of each attribute among all alternative solutions, is the a-th element in the vector of S - , representing the spherical fuzzy negative ideal solution of the a-th attribute, The membership degree in the spherical fuzzy negative ideal solution for the a-th attribute The non-membership degree in the spherical fuzzy negative ideal solution for the a-th attribute The hesitation degree in the spherical fuzzy negative ideal solution for the a-th attribute, where a is the index of the attribute and t is the total number of attributes

[0042] In some embodiments, the distances between each alternative and the spherical fuzzy ideal solutions of each attribute include calculating the distances between each alternative and the spherical fuzzy positive ideal solutions of each attribute and the distances between each alternative and the spherical fuzzy negative ideal solutions of each attribute, as shown in the following formula:

[0043]

[0044] In the formula, represents the distance between the e-th alternative decision plan of the a-th type of attribute and the spherical fuzzy positive ideal solution SF-PIS of the a-th type of attribute; represents the distance between the e-th alternative of the a-th type of attribute and the spherical fuzzy negative ideal solution SF-NIS of the a-th type of attribute.

[0045] In some embodiments, the grey correlation between each alternative further includes calculating the grey correlation coefficients between each alternative and SF-PIS and SF-NIS:

[0046]

[0047] In the formula, represents the grey correlation coefficient between the e-th alternative on the a-th type of attribute and the spherical fuzzy positive ideal solution SF-PIS of the a-th type of attribute, represents the grey correlation coefficient between the e-th alternative on the a-th type of attribute and the spherical fuzzy negative ideal solution SF-NIS of the a-th type of attribute, and ρ represents the recognition coefficient; represents the minimum value of the distances among all plans e and all attributes a, represents the maximum value of the distances among all plans e and all attributes a.

[0048] In some embodiments, the prospect analysis of the subjective value brought by each alternative on its attributes according to the grey correlation between each alternative further includes:

[0049] Establish a positive prospect matrix H + and a negative prospect matrix H - , as shown in the following formula:

[0050]

[0051] In the formula, $V^+(a,e)$ represents the positive prospect value of the $e$-th solution on the $a$-th attribute, indicating the subjective value of "benefit" brought by this solution on this attribute; $V^-(a,e)$ represents the negative prospect value of the $e$-th solution on the $a$-th attribute, indicating the subjective value of "loss" brought by this solution on this attribute; $\beta$ is the benefit risk attitude parameter; $\gamma$ is the loss risk attitude parameter; $\lambda$ is the loss aversion coefficient, which amplifies the subjective value of loss and reflects the aversion to loss.

[0052] In some embodiments, the obtaining of the cumulative prospect analysis of each alternative solution according to the prospect analysis and the transformation probability weights further includes calculating the cumulative prospect value, as shown in the following formula:

[0053]

[0054] In the formula, $V^C(e)$ represents the cumulative prospect value of the $e$-th alternative solution, $V^+(a,e)$ represents the positive prospect value of the $e$-th solution on the $a$-th attribute, indicating the subjective value of "benefit" brought by this solution on this attribute; $w^+(p(a,e))$ and $w^-(p(a,e))$ represent the benefit probability weight and loss probability weight after considering the decision maker's risk attitude.

[0055] The present invention is implemented by the following technical solutions:

[0056] 1) Comprehensive analysis of complex decision-making problems, especially suitable for modern management scenarios that need to deal with uncertainty, behavioral biases and information deficiencies at the same time. Its core value lies in combining mathematical rigor with the reality of human behavior to provide decision-making support closer to actual needs; further, considering the psychological and behavioral characteristics of decision makers' bounded rationality, effectively integrating the preference information of different decision makers, and solving problems such as information uncertainty and inconsistency in group decision-making of water supply emergency plans. This method is simple to calculate, highly operable, and the calculation process conforms to the actual situation of decision-making.

[0057] 2) The spherical fuzzy ideal solution technology (SF) adopted by the present invention helps to process multi-dimensional fuzzy information. Through the spherical fuzzy set, the model can simultaneously process the uncertainty information of three dimensions: membership degree, non-membership degree and hesitation degree, which is more comprehensive than the traditional fuzzy set; therefore, it is applicable to decision-making problems with complex evaluation criteria, differences in expert opinions or fuzzy data itself.

[0058] 3) The cumulative prospect theory (CPT) adopted by the present invention helps to integrate risk preferences and behavioral factors. Using the cumulative prospect theory, psychological characteristics such as decision makers' risk aversion and loss aversion are incorporated into the model, and objective probabilities are transformed into weighted decision weights; therefore, in high-risk decision-making such as emergency management, it more realistically reflects the impact of human irrational behavior on the results.

[0059] 4) The grey relational analysis (GRA) adopted by the present invention helps to analyze and process small-sample and incomplete information data, and quantifies the degree of closeness to the ideal solution through the correlation degree quantification scheme. Therefore, it is applicable to problem scenarios with limited data and reduces the interference of information loss on decision-making. Description of the Drawings

[0060] Figure 1 is the flowchart of the method for generating an emergency response plan for water supply emergencies based on SF-CPT-GRA of the present invention;

[0061] Figure 2 is the schematic diagram of the water conveyance of the alternative plan. Among them, the light-colored pipeline indicates that the pipeline is not conveying water, and the dark-colored pipeline indicates that the pipeline is conveying water; (A) Alternative plan (1), (B) Alternative plan (2), (C) Alternative plan (3), (D) Alternative plan (4). Detailed Embodiments

[0062] The following will further describe in detail the specific embodiments of the present invention with reference to the drawings.

[0063] As Figure 1 shown, the method for generating an emergency response plan for water supply emergencies based on SF-CPT-GRA of the present invention specifically includes the following steps:

[0064] Let represent the set of alternative plans, represent the set of attributes, represent the set of decision-makers, and δ=(δ1, δ2,..., δ p ) T represent the weight vector of the pth decision-maker. represent the decision matrix of the rth decision-maker based on the spherical fuzzy set, where are the membership degree, non-membership degree, and hesitation degree respectively. The main steps of the method are as Figure 1 shown.

[0065] Step 1: The decision-maker determines the spherical fuzzy decision model for the emergency response plan of the water supply emergency: The input of the model is the set of alternative response plans and the fuzzy evaluation information of the decision-maker on the plan attributes, and the output of the model is the spherical fuzzy decision matrix. Among them is the membership degree, indicating the degree to which an element belongs to a set, with a value range of [0,1]. The higher the membership degree, the higher the degree to which the element belongs to the set, and in decision-making, it indicates a higher degree of affirmation of a certain attribute of the plan; is the non-membership degree, indicating the degree to which an element does not belong to a set, with a value range of [0,1]. The higher the non-membership degree, the higher the degree to which the element does not belong to the set, and in decision-making, it reflects a higher degree of negation of a certain attribute of the plan; The hesitation degree, denoted as, represents the decision maker's uncertainty about whether an element belongs to a set. Its value range is [0, 1]. The higher the hesitation degree, the lower the consistency of the decision maker's judgment on the alternative in this attribute, and the greater the uncertainty of the decision. The spherical fuzzy set adopts a 9 - evaluation scale, from "Extremely high (EH)" to "Extremely low (EL)". Each semantics corresponds to a triple composed of membership degree, non - membership degree, and hesitation degree. "Extremely high (EH)" corresponds to (0.9, 0.1, 0.1), and "Extremely low (EL)" corresponds to (0.1, 0.9, 0.1). This correspondence provides a standardized way to describe the fuzziness of evaluations, making the understanding and expression of the same concept by different decision makers relatively unified.

[0066] Take the evaluation scale of the emergency response plan for water supply emergencies based on spherical fuzzy sets as spherical fuzzy decision - making information. As shown in Table 1, it is the evaluation scale of the emergency response plan for water supply emergencies based on spherical fuzzy sets.

[0067] Table 1

[0068]

[0069] Step 2: Construct a normalized decision - making matrix for the emergency response plan of water supply emergencies: Perform normalization pre - processing on the evaluation indicators in the spherical fuzzy decision - making model of the emergency response plan for water supply emergencies constructed in Step 1, aiming to eliminate the differences in magnitude and unit of different attributes, and obtain the normalized spherical fuzzy decision - making model matrix of the emergency response plan for water supply emergencies for each decision maker as shown in the following formula:

[0070]

[0071] In the formula, represents the normalized decision - making matrix of the r - th decision maker. n, t, and p represent the number of alternative plans (such as the plan of starting A and aborting B and the plan of starting B and aborting A, etc.), attributes (such as timeliness and disposal effect, etc.), and decision makers respectively. are respectively 's membership degree, non - membership degree, and hesitation degree. e represents the e - th alternative plan, a represents the a - th attribute, r represents the r - th decision maker. represents the element in the normalized decision - making matrix V r used to describe the spherical fuzzy number. represents the decision - making information of the r - th decision maker based on the spherical fuzzy set for the e - th alternative plan on the a - th attribute. represents when is a cost - type index, the spherical fuzzy number obtained by converting A cost - type index refers to an attribute where the smaller the index value, the better, such as riskiness. In this case, it is necessary to exchange Membership degree and non - membership degree, respectively represent the membership degree, non - membership degree and hesitation degree of the original evaluation, which are given by the decision - maker according to the evaluation scale. represents the \(t\) - th attribute, and is used to judge whether the attribute is a benefit - type or a cost - type.

[0072] Step 3: Construct the spherical fuzzy set total decision - making matrix for the emergency disposal plan of water supply emergencies: Summarize the normalized decision - making matrices of each decision - maker for the emergency disposal plan of water supply emergencies. The summarized decision - making matrix of each decision - maker is expressed as Use the spherical weighted arithmetic average method to construct the spherical fuzzy set total decision - making matrix for the emergency disposal plan of water supply emergencies. The spherical fuzzy set total decision - making matrix for the emergency disposal plan of water supply emergencies is expressed as \(C=(c_{ea})\) ea ) n×t , where:

[0073]

[0074] In the formula, \(\delta = (\delta_1,\delta_2,\cdots,\delta_p)\) p ) T represents the weight vector of the \(p\) - th decision - maker. is the comprehensive membership degree, indicating the degree of affirmation of the group for plan \(e\) on attribute \(a\); is the comprehensive non - membership degree, indicating the degree of negation of the group for plan \(e\) on attribute \(a\). is the comprehensive hesitation degree, indicating the degree of uncertainty of the group for plan \(e\) on attribute \(a\); \(c_{ea}\) ea represents the comprehensive evaluation result of the \(e\) - th plan and the \(a\) - th attribute in the spherical fuzzy set total decision - making matrix \(C\). respectively represent the membership degree, non - membership degree and hesitation degree of the normalized decision - making matrix of the \(r\) - th decision - maker. SWAM represents the spherical weighted arithmetic average operator. Let is a spherical fuzzy number. represents a set of spherical fuzzy sets, \(\omega = (\omega_1,\omega_2,\cdots,\omega_p)\) m ) T is the corresponding weight vector, where The spherical weighted arithmetic average operator is defined as follows:

[0075]

[0076] Step 4: Based on the CRITIC method, determine the weights of the attributes of the above - mentioned plans. The attribute weights are expressed as \((a = 1,2,\cdots,t)\);

[0077] The CRITIC method calculates the weights of attributes based on the correlation between attributes. The basic idea is that if two attributes are highly correlated, the information they provide is repetitive, so their importance is relatively low. The steps to calculate the attribute weights using the CRITIC method are as follows:

[0078] 4.1: Standardize the spherical fuzzy set total decision matrix C = (c ea ) n×t of the emergency response plan for water supply emergencies to obtain the standardized scores of the spherical fuzzy set total decision matrix of the emergency response plan for water supply emergencies, as shown in the following formula:

[0079]

[0080] In the formula, represents the score of the spherical fuzzy set total decision matrix c ea of the emergency response plan for water supply emergencies, k ea represents the standardized score of c ea , represents the minimum score corresponding to attribute a among all alternative plans, represents the maximum score corresponding to attribute a among all alternative plans.

[0081] 4.2: Determine the correlation coefficient between each attribute, as shown in the following formula:

[0082]

[0083] In the formula, γ aj represents the correlation coefficient between the a-th type of attribute and the j-th type of attribute, k ea represents the standardized score of the e-th alternative plan on the a-th attribute, k ej represents the standardized score of the e-th alternative plan on the j-th attribute, e = 1, 2,..., n, where n is the total number of alternative plans.

[0084] 4.3: Calculate the standard deviation of each attribute, as shown in the following formula:

[0085]

[0086] In the formula, σ a represents the standard deviation of the a-th type of attribute;

[0087] 4.4: Calculate the deviation degree of each attribute, as shown in the following formula:

[0088]

[0089] In the formula, J a represents the deviation degree of the a-th type of attribute;

[0090] 4.5: Calculate the weights of each attribute as shown in the following formula:

[0091]

[0092] In the formula, represents the weight of the a-th type of attribute.

[0093] Step 5: Calculate the spherical fuzzy positive ideal solutions (SF-PIS) S + and the spherical fuzzy negative ideal solutions (SF-NIS) S - as shown in the following formula:

[0094]

[0095] In the formula, a = 1, 2,..., t. S + is the spherical fuzzy positive ideal solution, which is a vector. Each element corresponds to the ideal solution of an attribute. It represents the optimal value combination of each attribute among all alternative solutions and is the theoretical best solution reference point; is the a-th element in the S + vector, representing the spherical fuzzy positive ideal solution of the a-th attribute; is the membership degree in the spherical fuzzy positive ideal solution of the a-th attribute, and its value is the maximum value of this attribute among all alternative solutions (e = 1, 2,..., n); ; is the non-membership degree in the spherical fuzzy positive ideal solution of the a-th attribute, and its value is the minimum value of the non-membership degree of this attribute among all alternative solutions; ; is the hesitation degree in the spherical fuzzy positive ideal solution of the a-th attribute, and its value is the minimum value of the hesitation degree of this attribute among all alternative solutions; a is the index of the attribute, with a value range of [1, t], and t is the total number of attributes.

[0096]

[0097] In the formula, a = 1, 2,..., t. S - is the spherical fuzzy negative ideal solution, which is a vector. Each element corresponds to the negative ideal solution of an attribute. It represents the worst value combination of each attribute among all alternative solutions and is another reference point for evaluating the quality of the solution; is the -The a-th element in the vector represents the spherical fuzzy negative ideal solution of the a-th attribute; is the membership degree in the spherical fuzzy negative ideal solution of the a-th attribute, and its value is the minimum value of this attribute among all alternative solutions (e = 1, 2,..., n); The minimum value; is the non-membership degree in the spherical fuzzy negative ideal solution of the a-th attribute, and its value is the maximum value of the non-membership degree of this attribute among all alternative solutions; The maximum value; is the hesitation degree in the spherical fuzzy negative ideal solution of the a-th attribute, and its value is the maximum value of the hesitation degree of this attribute among all alternative solutions; The maximum value; a is the index of the attribute, with a value range of [1, t], where t is the total number of attributes.

[0098] Step 6: Calculate the distances between each alternative solution and the spherical fuzzy positive ideal solution SF-PIS of each attribute and the distances between each alternative solution and the spherical fuzzy negative ideal solution SF-NIS of each attribute respectively, as shown in the following formula:

[0099]

[0100] In the formula, represents the distance between the e-th alternative decision solution of the a-th attribute and the spherical fuzzy positive ideal solution SF-PIS of the a-th attribute. The smaller this distance value is, the closer the alternative solution is to the ideal state in this attribute; represents the distance between the e-th alternative solution of the a-th attribute and the spherical fuzzy negative ideal solution SF-NIS of the a-th attribute. The smaller this distance value is, the closer the alternative solution is to the worst state in this attribute.

[0101] Step 7: Use the grey relational analysis method to determine the grey relational coefficients between each alternative solution and SF-PIS and SF-NIS according to formulas (14) and (15):

[0102]

[0103] In the formula, represents the grey relational coefficient between the e-th alternative solution on the a-th attribute and the spherical fuzzy positive ideal solution SF-PIS of the a-th attribute, represents the grey relational coefficient between the e-th alternative solution on the a-th attribute and the spherical fuzzy negative ideal solution SF-NIS of the a-th attribute; ρ represents the identification coefficient, usually taking ρ ∈ [0, 1]; represents the minimum value of the distances among all solutions e and all attributes a, represents the maximum value of the distances among all solutions e and all attributes a.

[0104] Step 8: Establish the positive prospect matrix H according to the value function+ and the negative prospect matrix H - , as shown in the following formula:

[0105]

[0106] In the formula, is the positive prospect value of the e-th alternative on the a-th attribute, representing the subjective value of "benefit" brought by this alternative on this attribute; is the negative prospect value of the e-th alternative on the a-th attribute, representing the subjective value of "loss" brought by this alternative on this attribute; β is the benefit risk attitude parameter (usually β ≤ 1, reflecting the diminishing marginal benefit and the decision maker's risk aversion towards benefits); γ is the loss risk attitude parameter (usually γ ≤ 1, reflecting the diminishing marginal loss and the decision maker's risk seeking towards losses); λ is the loss aversion coefficient, amplifying the subjective value of losses and reflecting the aversion to losses.

[0107] Step 9: Calculate the transformed probability weights and Convert the attribute weights calculated by the CRITIC method in Step 4 into transformed probability weights considering the decision maker's risk attitude, as shown in the following formula:

[0108] When the decision maker faces benefits, the transformed probability weights are calculated by Equation (18):

[0109]

[0110] When the decision maker faces losses, the transformed probability weights are calculated by Equation (19):

[0111]

[0112] In the formula, represents the curvature parameter of the probability weight function in the benefit scenario, usually is used to describe the decision maker's non-linear processing of benefit probabilities; λ represents the curvature parameter of the probability weight function in the loss scenario, usually λ ∈ (0,1), and is used to describe the decision maker's non-linear processing of loss probabilities.

[0113] Step 10: Calculate the cumulative prospect value, as shown in the following formula:

[0114]

[0115] In the formula, represents the cumulative prospect value of the e-th alternative, is the positive prospect value of the e-th alternative on the a-th attribute, representing the subjective value of "benefit" brought by this alternative on this attribute; represents the benefit probability weight and loss probability weight considering the decision maker's risk attitude.

[0116] Step 11: Sort all alternative solutions according to the cumulative prospect value The larger the cumulative prospect value , the better the comprehensive disposal effect of the alternative solution.

[0117] In summary, the method for generating an emergency plan for water supply emergencies based on SF-CPT-GRA of the present invention is an overall phased refined decision-making process.

[0118] In the first stage, (spherical fuzzy SF) is adopted: initially screen the solutions and calculate the closeness degree of each solution to the fuzzy ideal solution.

[0119] In the second stage, (prospect theory CPT) is adopted: adjust the closeness degree according to the risk preference to generate a prospect value matrix.

[0120] In the third stage (grey relational analysis GRA): calculate the grey relational degree based on the prospect value to determine the final ranking.

[0121] The advantages of the present invention are: gradually integrating objective data and subjective behavior, and balancing rational analysis and actual decision-making psychology.

[0122] . Robustness in complex environments: The model maintains stability in an environment with fuzzy information, insufficient data, and coexisting risks, and outputs reliable decision-making suggestions. In the selection of emergency plans for natural disasters, it can not only handle the uncertainty of rescue efficiency (fuzzy set), but also consider the decision-maker's risk aversion to casualties (CPT), and finally associate the optimal plan through a small amount of historical data (GRA).

[0123] The present invention takes the supporting project of the South-to-North Water Diversion Project as the research object. Assume that an emergency occurs in the western main line or a certain river pumping station; the water supply mode is river diversion water supply, a certain river pumping station supplies water to three major water plants in the urban area, a certain village pumping station supplies water to the Jinbin Water Plant, and reverse supplies river diversion water to a certain village area through a certain canal water supply connection project, etc.; the event level is level IV, the duration is 3 - 7 days, the event time is in March, the event location is the western main line, the cause of the event is pipeline leakage in the western main line, and the event impact is the interruption of water transmission in the western main line and the inability of a certain river pumping station to supply water to three major water plants in the urban area. Consult experts in the water supply industry, relevant professional departments, and universities to form an emergency decision-making group for water supply emergencies, carry out pre-evaluation of disposal plans, and formulate four alternative plans for water source switching and project scheduling, such as Figure 2 shown. The urban water supply in Tianjin mainly relies on the Luanhe River water diversion and the middle route of the South-to-North Water Diversion Project. Limited by research space, region, and focus, this study does not consider the emergency scheduling of water sources such as the Yellow River diversion water, reclaimed water, and desalinated seawater for the time being.

[0124] Alternative plan (1) It is to supply water to three water plants in the urban area emergently by using the water source from the Luanhe River Diversion Project. Stop the water supply from a certain river pumping station to the three water plants in the urban area; activate the water source from the Luanhe River Diversion Project (initially using the water discharged from the Erwangzhuang Reservoir), and supply water to the three water plants in the urban area through a certain pumping station; store the surplus water from the South-to-North Water Diversion Project in the reservoir and conduct ecological water replenishment.

[0125] Alternative Plan (2) It is to supply water to three water plants in the urban area emergently by using the Erwangzhuang Reservoir. Stop the water supply from a certain river pumping station to the three water plants in the urban area; activate the water discharged from the Erwangzhuang Reservoir and a certain pumping station to supply water to the three water plants in the urban area; store the surplus water from the South-to-North Water Diversion Project in the reservoir and conduct ecological water replenishment.

[0126] Alternative Plan (3) It is to supply water to three water plants in the urban area emergently by using a certain canal water supply connection project. Stop the water supply from a certain river pumping station to the three water plants in the urban area; increase the water supply flow of a certain canal water supply connection project and supply water to the three water plants in the urban area through a certain pumping station.

[0127] Alternative Plan (4) It is to supply water to three water plants in the urban area emergently by using a certain reservoir and blending with the water from the Luanhe River Diversion Project. Stop the water supply from a certain river pumping station to the three water plants in the urban area; after activating the water discharged from a certain reservoir and blending it with the water from the Luanhe River Diversion Project, supply water to the three water plants in the urban area through a certain pumping station; store the surplus water from the South-to-North Water Diversion Project in the reservoir and conduct ecological water replenishment.

[0128] Step 1: Using the evaluation scale shown in Table 1, respectively evaluate the four indicators of each plan: timeliness Disposal effect Dispatch feasibility and risk to formulate an emergency disposal plan for water supply emergencies through the proposed method.

[0129] Table 2 Decision Maker Evaluation Matrix Table

[0130]

[0131] Step 2: Construct a normalized decision matrix according to Equation (1), as shown in Tables 3 to 5. Table 3 is the decision maker evaluation matrix table. Table 4 is the decision maker evaluation matrix table. Table 5 is the decision maker evaluation matrix table.

[0132] Table 3

[0133]

[0134] Table 4

[0135]

[0136]

[0137] Table 5

[0138]

[0139] Step 3: Aggregate the evaluation matrices of each decision maker, and construct the spherical fuzzy set total decision matrix of the emergency response plan for water supply emergencies as shown in Equation (2). The spherical fuzzy group decision matrix is shown in Table 6.

[0140] Table 6

[0141]

[0142] Step 4: Determine the attribute weights using the CRITIC method according to Equations (4) to (9). The calculation process is shown in Tables 7 to 11. Table 7 shows the normalized score matrix table. Table 8 shows the attribute correlation coefficient matrix table. Table 9 shows the standard deviation σ a matrix table. Table 10 shows the attribute deviation degree J a matrix table. Table 11 shows the attribute weight ω a matrix table.

[0143] Table 7

[0144]

[0145] Table 8

[0146]

[0147] Table 9

[0148]

[0149] Table 10

[0150]

[0151] Table 11

[0152]

[0153] Step 5: Calculate the SF-PIS and SF-NIS of each type of attribute according to Equations (10) and (11). Table 12 shows the attribute weight matrix table.

[0154] Table 12

[0155]

[0156] Step 6: Calculate the distances between each alternative and SF-PIS and SF-NIS according to equations (12) and (13), as shown in Tables 13 and 14. Table 13 shows the distances between the alternative and SF-PIS. Table 14 shows the distances between the alternative and SF-NIS.

[0157] Table 13

[0158]

[0159] Table 14

[0160]

[0161] Step 7: Using the grey relational analysis method, determine the grey relational coefficients (assuming ρ = 0.5) between each alternative and the SF-PIS and SF-NIS according to Equations (14) and (15), as shown in Tables 15 and 16. Table 15 shows the grey relational coefficient matrix between the alternatives and the SF-PIS. Table 16 shows the grey relational coefficient matrix between the alternatives and the SF-NIS.

[0162] Table 15

[0163]

[0164] Table 16

[0165]

[0166] Step 8: According to equations (16) and (17), construct the positive foreground matrix H + and the negative foreground matrix H - , as shown in Tables 17 and 18. Table 17 shows the positive foreground matrix table. Table 18 shows the negative foreground matrix table.

[0167] Table 17

[0168]

[0169] Table 18

[0170]

[0171]

[0172] Step 9: Calculate the transformed probability weight according to formula (18) and formula (19) and The probability weights are shown in Table 19. Matrix table. As shown in Table 20, the probability weights Matrix table.

[0173] Table 19

[0174]

[0175] Table 20

[0176]

[0177] Step 10: Calculate the cumulative prospect value according to Equation (20).

[0178] Step 11: According to the cumulative prospect value sort all alternative solutions. The larger the cumulative prospect value is, the better the comprehensive performance of the alternative solution. As shown in Table 21, the cumulative prospect values of alternative solutions and their rankings. The optimal emergency response plan is The worst emergency response plan is

[0179] Table 21

[0180]

[0181] An example of the SF-CPT-GRA method is that an emergency occurs at the West Main Line or a certain river pumping station. The time of the water supply emergency is in March. The cause of the event is the leakage of the pipeline of the West Main Line. The water supply mode is to draw water from the Yangtze River, that is, a certain river pumping station supplies water to three major water plants in the urban area, a certain village pumping station supplies water to the Jinbin Water Plant, and the diverted Yangtze River water is supplied back to a certain village area through a certain canal connection project, etc.

[0182] Emergency response plan refers to using a certain canal water supply connection project to supply emergency water to three water plants in the urban area. Before the emergency of the West Main Line or a certain river pumping station occurs, the diverted Yangtze River water is being supplied back to a certain village area through a certain canal connection project; after the emergency occurs, the certain canal connection project usually cannot significantly increase the water conveyance flow, and the water conveyance capacity may not be able to meet the total water demand of the three major water plants in the urban area.

[0183] Emergency response plan refers to using a certain village reservoir and the blended Luanhe water to supply emergency water to three water plants in the urban area. Considering two types of water supply sources, namely the regulated reservoir and the externally diverted water source, taking into account certain timeliness, treatment effect and dispatching feasibility, and having relatively low operation risks. To sum up, the optimal emergency response plan is The worst emergency response plan is The calculation results of this method are basically reasonable and in line with the actual engineering application.

[0184] The above is a detailed introduction to a method for generating an emergency response plan for water supply emergencies based on SF-CPT-GRA provided by this application. It should be noted that the present invention is not limited to the above method steps and calculation processes. The above specific implementation manners are merely illustrative and not restrictive. Those skilled in the art can make formal changes and modifications to the present invention under the inspiration of the present invention without departing from the purpose of the present invention and the protection scope of the claims, and these all fall within the protection scope of the present invention.

Claims

1. A method for generating an emergency response plan for water supply emergencies based on SF-CPT-GRA, characterized in that Including the following steps: Determine the spherical fuzzy decision-making model for the emergency response plan of water supply emergencies for each decision maker. The input of this model is the fuzzy evaluation information of each alternative plan and each attribute, and the output is the spherical fuzzy decision matrix of the emergency response plan for water supply emergencies; According to the spherical fuzzy decision-making model matrix of the emergency response plan for water supply emergencies, construct a spherical fuzzy aggregated decision matrix for the emergency response plan for water supply emergencies, and obtain the standardized score of the spherical fuzzy aggregated decision matrix of the emergency response plan for water supply emergencies; According to the spherical fuzzy aggregated decision matrix of the emergency response plan for water supply emergencies, obtain the weights of each attribute; meanwhile, the processing of each attribute includes: i) Calculate the spherical fuzzy ideal solution of each attribute; ii) According to the spherical fuzzy ideal solution of each attribute, obtain the distance between each alternative plan and the spherical fuzzy ideal solution of each attribute; according to the distance, obtain the grey correlation between each alternative plan; According to the weights of each attribute, obtain the transformation probability weights; and, according to the grey correlation between each alternative plan, conduct a prospect analysis of the subjective value brought by each alternative plan in its attributes; According to the prospect analysis and the transformation probability weights, obtain the cumulative prospect analysis of each alternative plan; According to the cumulative prospect analysis of each alternative plan, obtain the ranking of alternative plans for each decision maker.

2. The method for generating an emergency response plan for water supply emergencies based on SF-CPT-GRA according to claim 1, wherein, Further include normalizing the spherical fuzzy decision-making model for the emergency response plan of water supply emergencies. The spherical fuzzy decision-making model matrix of the emergency response plan of water supply emergencies after normalization is shown as follows: In the formula, represents the normalized decision matrix of the r-th decision maker, where n, t, and p represent the number of alternative solutions, criteria, and decision makers respectively, respectively represent the membership degree, non-membership degree, and hesitation degree of denotes the normalized decision matrix V r in the elements, represents the decision-making information of the r-th decision maker on the e-th alternative solution for the a-th criterion based on spherical fuzzy sets; represents when is a cost-type criterion for the spherical fuzzy number obtained by conversion, respectively represent the membership degree, non-membership degree, and hesitation degree of the original evaluation, represents the t-th criterion.

3. A method for generating an emergency response plan for water supply emergencies based on SF-CPT-GRA according to claim 1, characterized in that, The spherical fuzzy comprehensive decision matrix of the emergency response plan for water supply emergencies is C = (c ea ) n×t , where: where δ = (δ1, δ2,..., δ p ) T represents the weight vector of the p-th decision maker, is the comprehensive membership degree, indicating the degree of affirmation of the group for the alternative e on the attribute a; is the comprehensive non-membership degree, indicating the degree of negation of the group for the alternative e on the attribute a, is the comprehensive hesitation degree, indicating the degree of uncertainty of the group for the alternative e on the attribute a; c ea represents the comprehensive evaluation result of the e-th alternative and the a-th attribute in the spherical fuzzy set total decision matrix C, respectively represent the membership degree, non-membership degree and hesitation degree of the r-th decision maker's normalized decision matrix. SWAM represents the spherical weighted arithmetic mean operator, and is defined as shown in the following formula: wherein, is a spherical fuzzy number, represents a set of spherical fuzzy sets, ω = (ω1, ω2,..., ω m ) T is the corresponding weight vector, spherical weighted arithmetic mean operator.

4. A method for generating an emergency response plan for water supply emergencies based on SF-CPT-GRA according to claim 1, characterized in that, The standardized score of the spherical fuzzy aggregated decision matrix of the emergency response plan for water supply emergencies is shown as follows: In the formula, represents the spherical fuzzy set total decision matrix c of the emergency response plan for water supply emergencies ea score of, k ea represents the standardized score of c ea , represents the minimum score corresponding to attribute a among all alternative plans, represents the maximum score corresponding to attribute a among all alternative plans.

5. A method for generating an emergency response plan for water supply emergencies based on SF-CPT-GRA according to claim 1, characterized in that, The step of obtaining the weights of each attribute according to the spherical fuzzy aggregated decision matrix of the emergency response plan for water supply emergencies further includes the following steps: Determine the correlation coefficient between each attribute, as shown in the following formula: where γ aj represents the correlation coefficient between the a-th type of attribute and the j-th type of attribute, k ea represents the standardized score of the e-th alternative on the a-th attribute, and k ej represents the standardized score of the e-th alternative on the j-th attribute, where e = 1, 2,..., n and n is the total number of alternatives; Calculate the standard deviation of each attribute, as shown in the following formula: where, σ a represents the standard deviation of the a-th type of attribute; Calculate the deviation degree of each attribute, as shown in the following formula: where J a represents the degree of deviation of the a-th type of attribute; Calculate the weights of each attribute, as shown in the following formula: In the formula, represents the weight of the a-th type of attribute.

6. The method for generating an emergency response plan for water supply emergencies based on SF-CPT-GRA according to claim 1, wherein, The calculation of the spherical fuzzy ideal solution for each attribute further includes calculating the spherical fuzzy positive ideal solution $S$ for each type of attribute + and the spherical fuzzy negative ideal solution $S$ - , as shown in the following formula: In the formula, S + is the spherical fuzzy positive ideal solution, representing the optimal value combination of each attribute among all alternative solutions. is the ath element in the S + vector, representing the spherical fuzzy positive ideal solution of the ath attribute. is the membership degree in the spherical fuzzy positive ideal solution of the ath attribute. is the non-membership degree in the spherical fuzzy positive ideal solution of the ath attribute. is the hesitation degree in the spherical fuzzy positive ideal solution of the ath attribute, a is the index of the attribute, and t is the total number of attributes. In the formula, S - is the spherical fuzzy negative ideal solution, representing the worst value combination of each attribute among all alternative solutions, is the ath element in the S - vector, representing the spherical fuzzy negative ideal solution of the ath attribute, is the membership degree in the spherical fuzzy negative ideal solution of the ath attribute, is the non-membership degree in the spherical fuzzy negative ideal solution of the ath attribute, is the hesitation degree in the spherical fuzzy negative ideal solution of the ath attribute, a is the index of the attribute, and t is the total number of attributes.

7. A method for generating an emergency response plan for water supply emergencies based on SF-CPT-GRA according to claim 1, characterized in that, The distance between each alternative plan and the spherical fuzzy ideal solution of each attribute includes calculating the distance between each alternative plan and the spherical fuzzy positive ideal solution of each attribute and the distance between each alternative plan and the spherical fuzzy negative ideal solution of each attribute, as shown in the following formula: Wherein, represents the distance between the e-th alternative decision-making scheme of the a-th type of attribute and the spherical fuzzy positive ideal solution SF-PIS of the a-th type of attribute; represents the distance between the e-th alternative scheme of the a-th type of attribute and the spherical fuzzy negative ideal solution SF-NIS of the a-th type of attribute.

8. A method for generating an emergency response plan for water supply emergencies based on SF-CPT-GRA according to claim 1, characterized in that The grey correlation between each alternative plan further includes calculating the grey correlation coefficients between each alternative plan and SF-PIS and SF-NIS; In the formula, represents the grey correlation coefficient between the e-th alternative and the spherical fuzzy positive ideal solution SF-PIS of the a-th attribute on the a-th attribute, represents the grey correlation coefficient between the e-th alternative and the spherical fuzzy negative ideal solution SF-NIS of the a-th attribute on the a-th attribute, and ρ represents the identification coefficient; represents the minimum value of the distances among all alternatives e and all attributes a, represents the maximum value of the distances among all alternatives e and all attributes a.

9. A method for generating an emergency response plan for water supply emergencies based on SF-CPT-GRA according to claim 1, characterized in that, The step of conducting a prospect analysis of the subjective value brought by each alternative plan in its attributes according to the grey correlation between each alternative plan further includes: Establish the positive foreground matrix H + and the negative foreground matrix H - , as shown in the following formula: In the formula, is the positive prospect value of the e-th solution on the a-th attribute, representing the subjective value of "benefit" brought by the solution on this attribute; is the negative prospect value of the e-th solution on the a-th attribute, representing the subjective value of "loss" brought by the solution on this attribute; β is the benefit risk attitude parameter; γ is the loss risk attitude parameter; λ is the loss aversion coefficient, which amplifies the subjective value of loss and reflects the aversion to loss.

10. A method for generating an emergency response plan for water supply emergencies based on SF-CPT-GRA, characterized in that, The step of obtaining the cumulative prospect analysis of each alternative plan according to the prospect analysis and the transformation probability weights further includes calculating the cumulative prospect value, as shown in the following formula: In the formula, represents the cumulative prospect value of the e-th alternative, is the positive prospect value of the e-th alternative on the a-th attribute, indicating the subjective value of "benefit" brought by this alternative on this attribute; represents the benefit probability weight and loss probability weight after considering the decision maker's risk attitude.

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