Multi-attribute decision-making method for emergency rescue scheme of water conservancy project based on improved CoCoSo method

Abstract

This invention discloses a multi-attribute decision-making method for emergency rescue schemes in water conservancy projects based on an improved CoCoSo method. The method includes the following steps: establishing an evaluation index system for emergency rescue schemes in water conservancy projects; calculating the weights of each index using the hesitant fuzzy Boltzmann Method (BWM); constructing and defuzzifying a hesitant fuzzy decision matrix; and calculating the scores of each alternative emergency rescue scheme using the improved CoCoSo method, wherein an adaptive weighting factor is introduced to adjust the weight ratio of the three aggregation strategy values ​​in the CoCoSo method. This invention organically integrates the hesitant fuzzy language terminology set, the Boltzmann Boltzmann Method (BWM), and the adaptive CoCoSo method, preserving the disagreement and hesitation information of the expert group in emergency decision-making. Furthermore, by introducing an adaptive weighting factor, the weights of the geometric mean and arithmetic mean of the three aggregation strategy values ​​in the CoCoSo method are adjusted according to the degree of data dispersion, improving the accuracy, reliability, and robustness of emergency rescue scheme selection.

Description

Technical Field

[0001] This invention belongs to the field of water conservancy engineering decision analysis technology, specifically relating to a multi-attribute decision-making method for water conservancy engineering emergency rescue schemes based on the improved CoCoSo method. Background Technology

[0002] Water conservancy projects are crucial infrastructure for national economic and social development, playing a vital role in flood control, water supply, power generation, and navigation. However, these projects face numerous unforeseen risks during operation, such as catastrophic floods, dam failures, landslides, and secondary disasters caused by earthquakes. In the event of such emergencies, the rapid activation of scientifically effective emergency response plans is crucial for minimizing casualties, reducing property damage, preventing secondary disasters, and ensuring the safety of downstream areas. Therefore, the optimal decision-making process for emergency response plans in water conservancy projects has become a core issue in the field of water conservancy project management.

[0003] Decision-making regarding emergency rescue plans for water conservancy projects typically involves multiple conflicting evaluation indicators. For example: rescue timeliness requires the fastest possible emergency response; disaster site control capability reflects the effectiveness of rescue measures in containing the danger; the social impact of the disaster involves the degree of impact on the lives of surrounding residents, the ecological environment, and social order; economic costs include the consumption of rescue materials, equipment deployment costs, and post-disaster recovery costs; post-disaster recovery capabilities relate to post-disaster reconstruction and risk mitigation; and the utilization of machinery and equipment evaluates the dispatch efficiency and applicability of existing emergency equipment. These indicators often have different dimensions and evaluation standards, and there may be trade-offs between them, making the optimal plan a typical multi-attribute decision-making problem.

[0004] In actual decision-making, experts often face a highly uncertain environment when evaluating the performance of various options under different indicators. On the one hand, the evolution of emergencies in water conservancy projects is sudden, complex, and dynamic, making it difficult for experts to obtain completely accurate information. On the other hand, different experts may give different judgments on the same option due to differences in professional background, experience, and risk preferences, and even hesitate within their own judgments. Traditional precise numerical scoring methods cannot effectively express this uncertainty and disagreement. In recent years, the Hesitant Fuzzy Linguistic Term Set (HFLTS) has been proposed and applied to the field of multi-attribute decision-making. It allows experts to use multiple consecutive linguistic terms to express their evaluations, thereby preserving the experts' hesitation information. However, existing research lacks effective methods for aggregating HFLTS evaluation information from multiple experts. Common simple averaging or voting mechanisms often lose important information in group disagreements, leading to distorted decision results.

[0005] In multi-attribute decision-making methods, commonly used approaches include the Analytic Hierarchy Process (AHP), the Top-Down Scheme (TOPSIS), and the Viktor's Principle of Multi-Objective Optimization (VIKOR). Among these, the CoCoSo (Combined Compromise Solution) method has gained attention in recent years. It obtains the final ranking by calculating weighted sums and weighted products and combining three different aggregation strategies (arithmetic mean strategy, relative advantage strategy, and compromise balance strategy), exhibiting good comprehensiveness and flexibility. However, traditional CoCoSo methods typically use a simple arithmetic mean or a fixed-weight geometric mean to process the final score, failing to consider the distribution characteristics of the evaluation data itself. In practical emergency rescue decision-making in water conservancy projects, the evaluation data of different schemes under various indicators may exhibit different degrees of dispersion. When data fluctuations are large, the geometric mean can better reflect the impact of extreme values; when data is relatively concentrated, the arithmetic mean better reflects the overall trend. Fixed-weight aggregation methods lack adaptability and are difficult to dynamically adjust according to data characteristics, thus affecting the accuracy and robustness of the decision.

[0006] Furthermore, determining the weights of the indicators is a crucial step affecting the quality of decision-making. Traditional subjective weighting methods (such as direct scoring and pairwise comparison) are easily influenced by expert subjective preferences and struggle to handle hesitant or ambiguous information. The Best Worst Method (BWM) reduces the number of comparisons and improves the consistency of weight calculation by only performing pairwise comparisons between the best and worst indicators. However, the traditional BWM method requires experts to provide precise comparison values ​​and cannot handle hesitant or ambiguous linguistic information.

[0007] In summary, existing multi-attribute decision-making methods for emergency rescue schemes in water conservancy projects have the following shortcomings: (1) the high uncertainty of evaluation information and the failure to effectively express and aggregate expert hesitation information; (2) the lack of ability to process hesitant and fuzzy information in the calculation of indicator weights; and (3) the fixed weight ratio of the aggregation strategy in the CoCoSo method, which cannot be adaptively adjusted according to the degree of data dispersion. Therefore, there is an urgent need for a multi-attribute decision-making method that can integrate hesitant and fuzzy linguistic information, scientifically calculate indicator weights, and has adaptive aggregation capabilities, in order to improve the accuracy, reliability, and robustness of the selection of emergency rescue schemes for water conservancy projects. Summary of the Invention

[0008] The purpose of this invention is to overcome the shortcomings of the prior art and provide a multi-attribute decision-making method for emergency rescue schemes in water conservancy projects based on the improved CoCoSo method. This method combines hesitant fuzzy logic (BWM) with the adaptive CoCoSo method, which can effectively handle the high uncertainty of evaluation information and adaptively adjust the weight ratio of the aggregation strategy according to the degree of data dispersion, thereby improving the accuracy, reliability and robustness of the decision results.

[0009] A multi-attribute decision-making method for emergency rescue schemes in water conservancy projects based on an improved CoCoSo method includes the following steps: Step S1: Construct a decision-making indicator system for emergency rescue plans for water conservancy projects; Step S2: The hesitant fuzzy BWM method is used to calculate the weight of each indicator. Multiple experts are invited to determine the best and worst indicators from the indicators. The hesitant fuzzy language terminology set is used for evaluation. The best comparison vector and the worst comparison vector are constructed. The hesitant fuzzy language terms are converted into numerical intervals. The interval number comparison vector is constructed. Finally, the hesitant fuzzy interval weight of each indicator is obtained by solving the nonlinear optimization model and converted into the final precise weight. Step S3: Invite multiple experts to evaluate the performance of each alternative under various evaluation indicators using a set of hesitant fuzzy language terms. Use the min-upper and max-lower operators to aggregate the evaluation information of multiple experts, construct a hesitant fuzzy decision matrix, and then defuzzify it to obtain an accurate decision matrix. Step S4: Standardize the exact decision matrix to obtain the standardized decision matrix; Step S5: Calculate the population mean and population standard deviation of the standardized values ​​using the standardized decision matrix, and then determine the adaptive weighting factor; Step S6: Calculate the comprehensive score of each candidate scheme using the adaptive CoCoSo method. Combine the precise weights obtained in step S2 to calculate the weighted sum and weighted product of each candidate scheme, as well as the values ​​of the three aggregation strategies. Weight the geometric mean and arithmetic mean of the three aggregation strategy values ​​using the adaptive weighting factors to obtain the final comprehensive score of each candidate scheme. The scheme with the highest score is the optimal scheme.

[0010] Furthermore, in step S1, the evaluation indicators of the decision-making indicator system for emergency rescue plans for water conservancy projects include: selection of rescue timeliness, disaster site control, disaster social impact, economic cost, post-disaster treatment, and utilization of machinery and equipment.

[0011] Furthermore, in step S2, the set of hesitant and ambiguous language terms is specifically defined as: Definition 1: A set of hesitant and fuzzy semantic terms It is a semantic set ordered subsets ;set up , If it is a semantic variable, then , For two hesitant fuzzy sets with different granularities; Assuming experts Treatment of evaluation items An evaluation was conducted, resulting in a set of hesitant and fuzzy terms. , and They represent the first k The evaluation by experts The lower and upper bounds of the set are determined using expert evaluation information from the min-upper and max-lower operators. The steps are as follows: Calculate the optimal semantic evaluation of the lower bound set and the worst semantic evaluation of the upper bound set of HFLTS:

[0012]

[0013] The semantic evaluation information is integrated to determine the aggregation result:

[0014] in: , , and These represent the upper and lower bounds of the semantic interval, respectively. Use a binary semantic group To represent the decision-maker's linguistic evaluation information, among which Represents a predefined set of language evaluations One of the language assessment levels, This indicates the decision-maker's language evaluation information relative to the language evaluation level. deviation, ; Definition 2. Let there be a set S of semantic evaluation terms, For any semantic evaluation term, its corresponding binary semantics can be obtained through a transformation function. get:

[0015] Definition 3 Let the result of the semantic term set S be the set operation, and let , The binary semantics corresponding to β can be derived from the function get:

[0016]

[0017] Where: round is the rounding operator; Conversely, make For binary semantic information, there exists an inverse function. Convert this information into the corresponding numerical value. ,Right now:

[0018]

[0019] Furthermore, in step S2, the index weights are calculated using the Hesitant Fuzzy Boolean Method (BWM), and the specific process includes: Step 1: In the indicator set In the process, the optimal indicators were determined through expert discussion. And worst-case indicator ; Step Two: Experts evaluate based on a set of hesitant and fuzzy semantic terms to determine the optimal index. Compared to other indicators The degree of preference is used to construct a comparison vector. ,in 1,2, Indicates the optimal index Other indicators The degree of preference is compared. Similarly, determine the degree of preference for all other indicators. Compared to the worst indicator The degree of preference is used to construct a comparison vector. ,in

[0020] Indicates other indicators With worst indicators The degree of preference compared; Step 3: Using the formula The constructed comparison vector is transformed to obtain the corresponding binary semantics, and then the formula is applied. The binary semantic information is converted into corresponding precise numerical values ​​to obtain the comparison vector. and ;

[0021]

[0022] in: Indicates the optimal index Compared to other indicators The degree of preference, Indicates other indicators With worst indicators Compared to the degree of preference, and These represent the lower bound and the upper bound, respectively. Step 4: Calculate the weight of each indicator: Establish a hesitant fuzzy BWM linear optimization model to minimize the bias ξ:

[0023] According to the model use Solving for the interval weight vector

[0024] ;

[0025] Build an optimization model To obtain the final precise weights ; in: For the allowable deviation, These are the optimal indicators. The lower and upper bounds of the weights, The worst indicators The lower and upper bounds of the weights, The first The lower and upper bounds of the weights of each indicator. The first The lower and upper bounds of the weights of each indicator. For the first The final precise weight of each indicator,

[0026] For the first The interval weights of each indicator, The first The lower and upper bounds of the weights of each indicator interval.

[0027] Furthermore, in step S3, a hesitant fuzzy decision matrix is ​​constructed and defuzzified to obtain an accurate decision matrix. The specific process includes: Suppose there are m alternative solutions. n evaluation indicators , Experts ; Let the semantic term set be ,Specialize Home Regarding the plan In terms of indicators The evaluation results are represented as a set of hesitant and fuzzy semantic terms. The set is S A non-empty set, for example: This indicates that experts hesitated between "slightly worse", "average", and "slightly better"; remember and They represent the firstk The lower bound (i.e., the expert's most pessimistic assessment) and upper bound (i.e., the expert's most optimistic assessment) of HFLTS obtained from the evaluations of the experts are as follows:

[0028] For each scheme and indicators ,remember To compile all expert evaluation information, follow these steps:

[0029]

[0030] in: For experts k The given lower bound of HFLTS is the most pessimistic assessment. For experts k The upper bound of HFLTS is given, which is the most optimistic evaluation; This represents the optimal semantic evaluation among all expert lower bound sets, i.e., max-lower; This represents the worst semantic evaluation among all expert upper bound sets, i.e., the min-upper. The semantic evaluation information is integrated to determine the aggregation result:

[0031] in: , , and These represent the upper and lower bounds of the semantic interval, respectively. This indicates that the experts have a positive view of the plan. In terms of indicators The final hesitant and fuzzy semantic evaluation results; Transform semantic intervals into numerical intervals: Semantic term set is Introducing binary semantic transformation function and its inverse function semantic range Convert to numerical range : Define conversion function : ; Define the inverse transformation function : For binary semantics have:

[0032] Lower bound of semantic interval and the Upper Realm Apply the conversions separately:

[0033] Thus, the numerical range is obtained. ,satisfy ; By summing up the numerical ranges for all options and indicators, we obtain the initial hesitant fuzzy decision matrix. :

[0034] Use the midpoint method to divide the interval numbers Convert to exact value :

[0035] Finally, the exact decision matrix is ​​obtained. :

[0036] Furthermore, in step S4, the specific steps for transforming the exact decision matrix into a standardized matrix include: Perform precise decision matrix Standardization process: Standardized formula for efficiency indicators:

[0037] Standardized formula for cost indicators:

[0038] Obtain the standardized decision matrix:

[0039] in: The number of alternative options, To evaluate the number of indicators, Indicates the first The first alternative is in the... The original evaluation values ​​under each indicator .

[0040] Furthermore, in step S5, the determination of the adaptive weighting factor specifically includes the following process: Through standardized decision matrix Calculate the population mean of all standardized values. and population standard deviation :

[0041]

[0042] Define the adaptive weighting factor α:

[0043] in: For the number of decision options, To evaluate the number of indicators, These are the standardized values ​​within the standardized matrix; , .

[0044] Furthermore, in step S6, the adaptive CoCoSo method is used to calculate the comprehensive score of each alternative solution. The specific process includes: The final precise weights of each index are calculated using the hesitant fuzzy BWM method. Calculate the weighted sum of each alternative in turn. Weighted product The three aggregation strategies are used to obtain the comprehensive score for each solution. And determine the optimal solution based on the scores; Calculate the weighted sum :

[0045] Calculate the weighted product :

[0046] in: The final precise weights calculated in step S2 satisfy... , ,when At that time, it was agreed ,when At that time, calculated through an index, For the number of decision options, To evaluate the number of indicators, These are the standardized values ​​within the standardized matrix; Calculate the values ​​for the three aggregation strategies: Strategy 1, the formula for calculating the arithmetic mean strategy value:

[0047] Strategy 2, the formula for calculating the relative advantage strategy:

[0048] Where: Assumption and In the evaluation of emergency rescue plans for actual water conservancy projects, it is naturally satisfied that at least one plan's weighted sum and weighted product are positive; Strategy 3, the formula for calculating the compromise and balance strategy:

[0049] in: This is the balance coefficient, and its value range is... ; Calculate the final overall score : Values ​​of the three aggregation strategies With adaptive weighting factor Combination:

[0050] Sort all alternative solutions in descending order of their values, and the one with the highest score is the optimal solution.

[0051] Compared with the prior art, the beneficial effects of the present invention are: 1. This invention employs a Hesitant Fuzzy Language Term Set (HFLTS) to allow experts to evaluate the performance of alternative solutions under various indicators. Experts can use multiple consecutive linguistic terms to express their judgments, thus avoiding the information distortion caused by forcing experts to provide a single numerical value in traditional precise scoring methods. Based on this, this invention aggregates the experts' evaluation information through min-upper and max-lower operators, ultimately forming a semantic range representing the group consensus. This aggregation method preserves the degree of disagreement among experts while avoiding the excessive influence of extreme individual evaluations, making the group evaluation results more robust and realistic.

[0052] 2. This invention combines a hesitant fuzzy language terminology set with BWM (Optimal-Worst Method) to propose a hesitant fuzzy BWM. Experts only need to determine the optimal and worst indicators and provide their hesitant fuzzy comparison preferences to construct an interval comparison vector. By solving a nonlinear optimization model, the hesitant fuzzy interval weights of each indicator are obtained. Then, by minimizing the deviation between the precise weights and the interval weights through an optimization model, the interval weights are transformed into the final precise weights. Compared with traditional BWM, this method has the following advantages: ① It reduces the number of comparisons by experts, lowering the cognitive burden; ② It can handle the hesitant information in the expert's comparison preferences, avoiding the errors caused by forcing fuzzy judgments to be precise; ③ The optimization model ensures the consistency of weights and improves the reliability of weight calculation.

[0053] 3. Traditional CoCoSo methods typically calculate the final composite score by performing a simple arithmetic average or a fixed-weight geometric average of the three aggregation strategies (arithmetic mean strategy, relative advantage strategy, and compromise balance strategy), ignoring the distribution characteristics of the evaluation data itself. This invention innovatively defines an adaptive weighting factor. ,in To standardize the population standard deviation of all data in the decision matrix, This is the overall mean. This factor reflects the relative dispersion of the data: when the data fluctuates significantly ( When relatively large, When the score is close to 1, the final score is more based on the geometric mean of the three strategy values ​​(sensitive to extreme values, which can amplify differences); when the data is relatively concentrated ( When relatively small, Approaching zero, the final score is more heavily weighted towards the arithmetic mean of the three strategy values ​​(resulting in a smoother and more robust approach). This adaptive weighted combination method allows the decision-making model to flexibly adjust the weight ratio of the aggregation strategy based on specific evaluation data, avoiding decision biases that may result from fixed weights. Consequently, in highly uncertain scenarios such as emergency rescue in water conservancy projects, it significantly improves the accuracy, reliability, and robustness of the scheme ranking. Attached Figure Description

[0054] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0055] Figure 1 A flowchart illustrating a multi-attribute decision-making method for emergency rescue schemes in water conservancy projects based on an improved CoCoSo method, provided as an embodiment of the present invention; Figure 2 A schematic diagram of the evaluation index system provided in the embodiments of the present invention; Detailed Implementation To more fully disclose the technical content of this invention and facilitate understanding and implementation by those skilled in the art, the technical solutions in the embodiments of this invention will be clearly and completely described below with reference to the accompanying drawings. It should be understood that the embodiments shown herein are merely illustrative and do not constitute a limitation on the scope of this invention. Any other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort fall within the protection scope of this invention.

[0056] The embodiments of the present invention will be further described in detail below with reference to the accompanying drawings. Please refer to... Figure 1 , Figure 2 As shown, this invention proposes a multi-attribute decision-making method for emergency rescue schemes in water conservancy projects based on an improved CoCoSo method. The specific steps are as follows: Step S1: Construct a decision-making index system for emergency rescue plans for water conservancy projects, selecting six attributes as evaluation indicators: rescue timeliness, disaster site control, social impact of the disaster, economic cost, post-disaster handling, and utilization of machinery and equipment. The selection of these six indicators fully considers the entire process and multi-dimensional decision-making needs of emergency response to sudden emergencies in water conservancy projects (such as dam failure, overtopping, and seepage). Rescue timeliness reflects the speed and time window of the emergency response, and is the primary factor determining the magnitude of disaster losses; disaster site control reflects the direct containment capability of the rescue plan, which is related to technical effectiveness; social impact of the disaster measures the negative impact of the rescue operation on downstream residents, the ecological environment, and social order, reflecting the social acceptability of the plan; economic cost assesses the human, financial, and material input required for the rescue and subsequent compensation costs, ensuring the economic rationality of the plan; post-disaster handling considers the convenience of post-disaster recovery and reconstruction and risk elimination, which is related to long-term safety; and utilization of machinery and equipment evaluates the dispatch efficiency and applicability of existing emergency equipment, reflecting the level of resource utilization. These six indicators comprehensively cover the typical decision-making criteria for selecting emergency rescue plans for water conservancy projects from six core dimensions: time response, technical effectiveness, social impact, economic cost, subsequent recovery, and resource utilization. They are highly representative and practical.

[0057] Step S2: The hesitant fuzzy BWM method is used to calculate the weight of each indicator. Multiple experts are invited to determine the best and worst indicators from the indicators. The hesitant fuzzy language terminology set is used for evaluation. The best comparison vector and the worst comparison vector are constructed. The hesitant fuzzy language terms are converted into numerical intervals. The interval number comparison vector is constructed. Finally, the hesitant fuzzy interval weight of each indicator is obtained by solving the nonlinear optimization model and converted into the final precise weight. The specific definition of the hesitant and ambiguous language terminology set is as follows: Definition 1: A set of hesitant and fuzzy semantic terms It is a semantic set ordered subsets .set up , If it is a semantic variable, then , For two hesitant fuzzy sets with different granularities.

[0058] Assuming experts Treatment of evaluation items An evaluation was conducted, resulting in a set of hesitant and fuzzy terms. , and They represent the first k The evaluation by experts The lower and upper bounds of the set are determined using expert evaluation information from the min-upper and max-lower operators. The steps are as follows: (1) Calculate the optimal semantic evaluation of the lower bound set and the worst semantic evaluation of the upper bound set of HFLTS.

[0059]

[0060]

[0061] (2) Integrate semantic evaluation information to determine the aggregation result.

[0062]

[0063] in: , , and These represent the upper and lower bounds of the semantic interval, respectively. In the HFLTS computation process, the concept of binary semantics is introduced to convert semantic evaluation terms into precise numerical values. The binary semantics computation process is relatively simple, and the results are more accurate. It mainly uses a binary semantic group. To represent the decision-maker's linguistic evaluation information, among which Represents a predefined set of language evaluations One of the language assessment levels, This indicates the decision-maker's language evaluation information relative to the language evaluation level. deviation, ; Definition 2: Let there be a set S of semantic evaluation terms, For any semantic evaluation term, its corresponding binary semantics can be obtained through a transformation function. get;

[0064] Definition 3 Let the result of the semantic term set S be the set operation, and let , The binary semantics corresponding to β can be derived from the function get;

[0065]

[0066] Where: round is the rounding operator; Conversely, make For binary semantic information, there exists an inverse function. Convert this information into the corresponding numerical value. ,Right now

[0067]

[0068] Table 1. Semantic and Numerical Index of Hesitant and Ambiguous Semantic Terms

[0069] The Hesitant Fuzzy Language Term Set (HFLTS) allows experts to evaluate the performance of alternatives across various metrics. Experts can use multiple consecutive language terms to express their judgments, thus avoiding the information distortion caused by forcing experts to provide a single numerical value in traditional precise scoring methods. Based on this, this invention achieves this through min... upper and max The lower operator aggregates expert evaluations to form a semantic range representing the group consensus. This aggregation method preserves the degree of disagreement among experts while avoiding the excessive influence of extreme individual evaluations, making the group evaluation results more robust and accurate.

[0070] The above definition provides a complete mathematical tool for processing hesitant and ambiguous linguistic information, enabling the uncertainty and disagreement in expert evaluation to be reasonably preserved and transmitted in subsequent calculations.

[0071] The indicator weights are calculated using Hesitant Fuzzy Wave Model (BWM), specifically as follows: Step 1: In the indicator set In the process, the optimal indicators were determined through expert discussion. And worst-case indicator .

[0072] Step Two: Experts evaluate based on a set of hesitant and fuzzy semantic terms to determine the optimal index. Compared to other indicators The degree of preference is used to construct a comparison vector. ,in 1,2, Indicates the optimal index Other indicators The degree of preference is compared. Similarly, determine the degree of preference for all other indicators. Compared to the worst indicator The degree of preference is used to construct a comparison vector. in

[0073] Indicates other indicators With worst indicators The degree of preference compared to the other.

[0074] Step 3: Using the formula The constructed comparison vector is transformed to obtain the corresponding binary semantics, and then the formula is applied. The binary semantic information is converted into corresponding precise numerical values ​​to obtain the comparison vector. and .

[0075]

[0076]

[0077] in: Indicates the optimal index Compared to other indicators The degree of preference, Indicates other indicators With worst indicators Compared to the degree of preference, and These represent the lower bound and the upper bound, respectively. Step 4: Calculate the weights of each indicator and establish a hesitant fuzzy Bragg wiggler linear optimization model to minimize the deviation ξ:

[0078] According to the model use Solving for the interval weight vector

[0079] .

[0080]

[0081] Build an optimization model To obtain the final precise weights .

[0082] in: For the allowable deviation, These are the optimal indicators. The lower and upper bounds of the weights, The worst indicators The lower and upper bounds of the weights, The first The lower and upper bounds of the weights of each indicator. The first The lower and upper bounds of the weights of each indicator. For the first The final precise weight of each indicator,

[0083] For the first The interval weights of each indicator, The first The lower and upper bounds of the weights of each indicator interval.

[0084] This paper proposes a hesitant fuzzy BWM method by combining a hesitant fuzzy language terminology set with BWM (optimal-worst method). Experts only need to determine the optimal and worst indicators and provide their hesitant fuzzy comparison preferences to construct an interval comparison vector. By solving a nonlinear optimization model, the hesitant fuzzy interval weights of each indicator are obtained. Then, by minimizing the deviation between the precise weights and the interval weights through an optimization model, the interval weights are transformed into the final precise weights. Compared with traditional BWM, this method has the following advantages: ① It reduces the number of comparisons by experts (only comparisons with the optimal and worst indicators are required), reducing cognitive burden; ② It can handle hesitant information in expert comparison preferences, avoiding errors caused by forcing fuzzy judgments to be precise; ③ The optimization model ensures the consistency of weights and improves the reliability of weight calculation.

[0085] Step S3: Construct a hesitant fuzzy decision matrix and defuzzify it to obtain an accurate decision matrix. The specific process is as follows: Suppose there are m alternative solutions. n evaluation indicators , Experts .

[0086] Let the semantic term set be ,Specialize Home Regarding the plan In terms of indicators The evaluation results are represented as a set of hesitant and fuzzy semantic terms. The set is S A non-empty set, for example: This indicates that experts hesitated between "slightly worse", "average", and "slightly better".

[0087] remember and They represent the first k The lower bound (i.e., the expert's most pessimistic assessment) and upper bound (i.e., the expert's most optimistic assessment) of HFLTS obtained from the evaluations of 10 experts. That is:

[0088] For each scheme and indicators ,remember To compile all expert evaluation information, follow these steps:

[0089]

[0090] in: For experts k The given lower bound of HFLTS is the most pessimistic assessment. For experts k The upper bound of HFLTS is given, which is the most optimistic evaluation; This represents the optimal semantic evaluation among all expert lower bound sets, i.e., max-lower; This represents the worst semantic evaluation among all expert upper bound sets, i.e., the min-upper. The semantic evaluation information is integrated to determine the aggregation result:

[0091] in: , , and These represent the upper and lower bounds of the semantic interval, respectively. This indicates that the experts have a positive view of the plan. In terms of indicators The final hesitant and fuzzy semantic evaluation results.

[0092] Transform semantic intervals into numerical intervals: Semantic term set is Introducing binary semantic transformation function and its inverse function semantic range Convert to numerical range : Define conversion function : ; Define the inverse transformation function : For binary semantics have:

[0093] Lower bound of semantic interval and the Upper Realm Apply the conversions separately:

[0094] Thus, the numerical range is obtained. ,satisfy ; By summing up the numerical ranges for all options and indicators, we obtain the initial hesitant fuzzy decision matrix. :

[0095] Use the midpoint method to divide the interval numbers Convert to exact value :

[0096] Finally, the exact decision matrix is ​​obtained. :

[0097] Step S4: The specific steps for transforming the exact decision matrix into a standardized matrix include: To ensure a unified evaluation standard for all indicators under different criteria, a precise decision matrix is ​​generated using standardized formulas for benefit-type and cost-type indicators. Standardization process: Standardized formula for efficiency indicators (the larger the better):

[0098] Standardized formula for cost indicators (the smaller the better):

[0099] Obtain the standardized decision matrix:

[0100] in: The number of alternative options, To evaluate the number of indicators, Indicates the first The first alternative is in the... The original evaluation values ​​for each indicator (the range of values ​​is determined by the defuzzification result, usually 100%) (or the numerical value after binary semantic transformation).

[0101] Step S5: Determining the adaptive weighting factor, specifically: The adaptive weighting factor α is based on the standardized decision matrix. The degree of dispersion of all standardized values ​​is determined by the standardized decision matrix. Calculate the population mean of all standardized values. and population standard deviation :

[0102]

[0103] Define the adaptive weighting factor α:

[0104] in: For the number of decision options, The number of evaluation indicators. The standardized values ​​are those within the standardized matrix. , ; When the standardized value has a high degree of dispersion ( When (large), When the standardized values ​​are close to 1, the final score focuses more on the geometric mean, improving discrimination; when the standardized values ​​are concentrated in a certain range ( Hour, Approaching 0, it places more emphasis on the arithmetic mean, thus enhancing stability.

[0105] Step S6: Calculate the comprehensive score of each alternative using the adaptive CoCoSo method, specifically: The final precise weights of each index are calculated using the hesitant fuzzy BWM method. Calculate the weighted sum of each alternative in turn. Weighted product The three aggregation strategies are used to obtain the comprehensive score for each solution. And determine the optimal solution based on the scores; The weighted sum reflects the weighted linear comprehensive performance of the alternatives on each indicator. The weighted sum is calculated as follows: :

[0106] The weighted product reflects the nonlinear comprehensive performance of alternatives across various indicators, emphasizing the balance among indicators. The weighted product is calculated as follows. :

[0107] in: The precise weights calculated in step S2 satisfy... ,when At that time, it was agreed ,when At that time, calculated through an index, For the number of decision options, To evaluate the number of indicators, These are the standardized values ​​within the standardized matrix; Calculate the values ​​for the three aggregation strategies: Strategy 1, the formula for calculating the arithmetic mean strategy value:

[0108] This strategy directly adds the weighted sum to the weighted product, reflecting the overall advantage of the alternatives.

[0109] Strategy 2, Formula for calculating the relative advantage strategy value:

[0110] This strategy highlights the lead of the alternative relative to the worst benchmark by dividing by the minimum value.

[0111] Where: Assumption and This condition is naturally satisfied in the evaluation of emergency rescue plans for actual water conservancy projects (at least one plan has a positive weighted sum and weighted product). Strategy 3, the formula for calculating the value of the compromise balance strategy:

[0112] in: This is the balance coefficient, and its value range is... The present invention takes This indicates that the weighted sum and the weighted product are given equal importance.

[0113] Calculate the final overall score : Values ​​of the three aggregation strategies With adaptive weighting factor Combination:

[0114] Sort all alternative solutions in descending order of their values, and the one with the highest score is the optimal solution.

[0115] Traditional CoCoSo methods typically calculate the final composite score by performing a simple arithmetic average or a fixed-weight geometric average of the three aggregation strategy values ​​(arithmetic mean strategy, relative advantage strategy, and compromise balance strategy), ignoring the distribution characteristics of the evaluation data itself. This invention innovatively defines an adaptive weighting factor. ,in To standardize the population standard deviation of all data in the decision matrix, This is the overall mean. This factor reflects the relative dispersion of the data: when the data fluctuates significantly ( When relatively large, When the score is close to 1, the final score is more based on the geometric mean of the three strategy values ​​(sensitive to extreme values, which can amplify differences); when the data is relatively concentrated ( When relatively small, Approaching zero, the final score is more heavily weighted towards the arithmetic mean of the three strategy values ​​(resulting in a smoother and more robust approach). This adaptive weighted combination method allows the decision-making model to flexibly adjust the weight ratio of the aggregation strategy based on specific evaluation data, avoiding decision biases that may result from fixed weights. Consequently, in highly uncertain scenarios such as emergency rescue in water conservancy projects, this significantly improves the accuracy of scheme ranking.

[0116] Water conservancy project emergencies are characterized by their suddenness, dynamism, and incomplete information. Traditional decision-making methods either force experts to provide precise scores, leading to information distortion, or employ fixed aggregation strategies that cannot adapt to different data distributions. This invention addresses both of these core issues simultaneously through hesitant fuzzy language expression and the adaptive CoCoSo method. In practical applications, this method can output a clear ranking of solutions, with the highest-scoring solution being the optimal emergency rescue plan, providing scientific, objective, and interpretable support for emergency command and decision-making in water conservancy projects.

[0117] Implementation Cases During the pouring of sloping concrete for the section from the downstream of the right bank secondary dam to the tailrace tunnel outlet at a hydropower station, a formwork ruptured on the upstream side as the concrete was being prepared for placement. The entire volume of concrete surged from the ruptured formwork onto the downstream face of the prepared concrete placement area, causing it to collapse and resulting in a concrete collapse accident with significant casualties. Following the accident, the project management immediately activated its emergency response plan for production safety.

[0118] Based on the actual situation of the engineering cases, four emergency rescue plans were developed and studied, and a set of plans was compiled. Based on comprehensive analysis and actual research, the timeliness of rescue was selected. ), disaster site control ( ), social impact of disasters ( ), economic costs ( ), aftermath handling ), mechanical equipment utilization Indicator set Construct a decision-making indicator system for emergency rescue plans for water conservancy projects.

[0119] The index weights are calculated using the Hesitant Fuzzy Boolean Method (BWM). By six senior experts Through discussion, the optimal indicator for the emergency rescue plan was determined to be disaster site control. The worst-case indicator is the economic cost (). The hesitant fuzzy semantic set is used to evaluate the comparison between attributes. The semantic set is... .expert The evaluation information provided by the hesitant fuzzy semantic set is shown in Tables 2 and 3. Each element in the table represents the comparison index of other attributes. and The degree of superiority or inferiority.

[0120] Table 2 Optimal Indicators For other indicators Preference comparison

[0121] Table 3 Other Indicators For the worst indicator Preference comparison

[0122] By formula (1) (3) The expert evaluation information was collected, and the results are shown in Table 4.

[0123] Table 4. Results of expert evaluation information aggregation based on comparisons between evaluation indicators.

[0124] Finally, the binary semantic method is adopted, based on formula (7). (8) The semantic interval numbers were converted into numerical interval numbers, and the results are shown in Table 5.

[0125] Table 5. Expert evaluation information expressed in numerical ranges.

[0126] Based on the data in Table 5, the interval weight vector is solved using MATLAB according to the mathematical model (11):

[0127]

[0128] Then, using model (12), the weight interval values ​​are converted into precise values, and the precise weights of each indicator are calculated as follows:

[0129] The following table can be obtained: Table 6: Results of Precise Weights for Indicators

[0130] Multiple experts were invited to evaluate the performance of each alternative under various evaluation indicators using a hesitant fuzzy language terminology set. The evaluation information from multiple experts was aggregated using the min-upper and max-lower operators to construct a hesitant fuzzy decision matrix, which was then defuzzified to obtain a precise decision matrix. The expert panel based its decisions on six indicators. Four emergency rescue plans An evaluation is conducted, and the evaluation result is represented by a hesitant fuzzy set, with the semantic set being... Through formula (13) (16) Gather expert information. The gathered expert semantic interval evaluation information is shown in the following table: Table 7. Expert Semantic Interval Evaluation Information After Gathering

[0131] By formula (17) (19) Transform the semantic interval into a numerical interval and establish an initial hesitant fuzzy decision matrix. :

[0132] Use formula (20) to divide the interval numbers Convert to exact value To obtain the exact decision matrix :

[0133] The precise decision matrix is ​​obtained through formulas (22) and (23). Transform into a standardized decision matrix : Among them, the timeliness of rescue ( ), disaster site control ( ), aftermath handling ), mechanical equipment utilization ) is a benefit-type indicator; social impact of disasters ( ), economic costs ( () is a cost-type indicator.

[0134]

[0135] The population mean of all standardized values ​​is calculated using formulas (25) and (26). and population standard deviation :

[0136]

[0137] Define the adaptive weighting factor α:

[0138] in: , .

[0139] Then, the adaptive CoCoSo method is used to calculate the comprehensive score of each alternative, specifically: The final precise weights of each index are calculated using the hesitant fuzzy BWM method. Calculate the weighted sum of each alternative in turn. Weighted product The three aggregation strategies are used to obtain the comprehensive score for each solution. The optimal solution is determined based on the scores.

[0140] Precise weights :

[0141] Because each solution has its own... And the corresponding weight The situation led to all Therefore, all Replace with The weighted sums are calculated using formulas (28) and (29) respectively. and weighted product :

[0142]

[0143] By formula (30) (32) Calculate the values ​​for the three aggregation strategies: Strategy 1, Arithmetic Mean Strategy Calculation Value:

[0144] Strategy 2, Calculated value of relative advantage strategy:

[0145] Strategy 3, Compromise Balance Strategy Calculation Value:

[0146] Calculate the final overall score : Values ​​of the three aggregation strategies With adaptive weighting factor Combine the calculations to determine the score for each solution:

[0147]

[0148]

[0149] Sort all alternative solutions in descending order of their values, and the one with the highest score is the optimal solution.

[0150] because The sorting of the solutions can be obtained as follows:

[0151] Based on the calculation results of the embodiments of the present invention, a multi-attribute decision-making method combining the hesitant fuzzy BWM method and the adaptive CoCoSo method is used to optimize the emergency rescue schemes for water conservancy projects. The final comprehensive score ranking of each alternative scheme is as follows: That is, the plan This represents the optimal emergency rescue plan. The results are consistent with the actual situation, verifying the effectiveness and practicality of the method proposed in this invention.

[0152] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. The specific examples used in the description are intended to facilitate understanding of the technical ideas and core points of the present invention, and do not constitute any form of limitation on the embodiments. For those skilled in the art, without departing from the essential spirit of the present invention, evaluation indicators, weighting coefficients, or decision parameters can be flexibly adjusted for different application scenarios; such reasonable modifications should be considered reasonable extensions of the content of the present invention. Therefore, the scope of protection of the present invention should be determined by the precise wording of the claims. All equivalent transformations or optimizations made based on the technical teachings of the present invention, as long as they do not exceed the scope defined by the claims, should fall within the scope of protection of the present invention.

Claims

1. A multi-attribute decision-making method for emergency rescue schemes in water conservancy projects based on an improved CoCoSo method, characterized in that, Includes the following steps: Step S1: Construct a decision-making indicator system for emergency rescue plans for water conservancy projects; Step S2: The hesitant fuzzy BWM method is used to calculate the weight of each indicator. Multiple experts are invited to determine the best and worst indicators from the indicators. The hesitant fuzzy language terminology set is used for evaluation. The best comparison vector and the worst comparison vector are constructed. The hesitant fuzzy language terms are converted into numerical intervals. The interval number comparison vector is constructed. Finally, the hesitant fuzzy interval weight of each indicator is obtained by solving the nonlinear optimization model and converted into the final precise weight. Step S3: Invite multiple experts to evaluate the performance of each alternative under various evaluation indicators using a set of hesitant fuzzy language terms. Use the min-upper and max-lower operators to aggregate the evaluation information of multiple experts, construct a hesitant fuzzy decision matrix, and then defuzzify it to obtain an accurate decision matrix. Step S4: Standardize the exact decision matrix to obtain the standardized decision matrix; Step S5: Calculate the population mean and population standard deviation of the standardized values ​​using the standardized decision matrix, and then determine the adaptive weighting factors; Step S6: Calculate the comprehensive score of each candidate scheme using the adaptive CoCoSo method. Combine the precise weights obtained in step S2 to calculate the weighted sum and weighted product of each candidate scheme, as well as the values ​​of the three aggregation strategies. Weight the geometric mean and arithmetic mean of the three aggregation strategy values ​​using the adaptive weighting factors to obtain the final comprehensive score of each candidate scheme. The scheme with the highest score is the optimal scheme.

2. The multi-attribute decision-making method for emergency rescue schemes in water conservancy projects based on the improved CoCoSo method as described in claim 1, characterized in that, In step S1, the evaluation indicators of the decision-making indicator system for emergency rescue plans for water conservancy projects include: the selection of rescue timeliness, disaster site control, disaster social impact, economic cost, post-disaster treatment, and utilization of machinery and equipment.

3. The multi-attribute decision-making method for emergency rescue schemes in water conservancy projects based on the improved CoCoSo method as described in claim 1, characterized in that, In step S2, the set of hesitant and ambiguous language terms is specifically defined as follows: Definition 1: A set of hesitant and fuzzy semantic terms It is a semantic set ordered subsets ;set up , If it is a semantic variable, then , For two hesitant fuzzy sets with different granularities; Assuming experts Treatment of evaluation items The evaluation yielded a set of hesitant and fuzzy terms. , and They represent the first k The evaluation by experts The lower and upper bounds of the set are determined using expert evaluation information from the min-upper and max-lower operators. The steps are as follows: Calculate the optimal semantic evaluation of the lower bound set and the worst semantic evaluation of the upper bound set of HFLTS: The semantic evaluation information is integrated to determine the aggregation result: in: , , and These represent the upper and lower bounds of the semantic interval, respectively. Use a binary semantic group To represent the decision-maker's linguistic evaluation information, among which Represents a predefined set of language evaluations One of the language assessment levels, This indicates the decision-maker's language evaluation information relative to the language evaluation level. deviation, ; Definition 2. Let there be a semantic evaluation term set S, For any semantic evaluation term, its corresponding binary semantics can be obtained through a transformation function. get: Definition 3 Let the result of the semantic term set S be the set operation, and let , The binary semantics corresponding to β can be derived from the function get: Where: round is the rounding operator; Conversely, make For binary semantic information, there exists an inverse function. Convert this information into the corresponding numerical value. ,Right now: 。 4. The multi-attribute decision-making method for emergency rescue schemes in water conservancy projects based on the improved CoCoSo method as described in claim 3, characterized in that, In step S2, the index weights are calculated using the Hesitant Fuzzy Boolean Method (BWM). The specific process includes: Step 1: In the indicator set In the process, the optimal indicators were determined through expert discussion. And worst-case indicator ; Step Two: Experts evaluate based on a set of hesitant and fuzzy semantic terms to determine the optimal index. Compared to other indicators The degree of preference is used to construct a comparison vector. ,in 1,2, Indicates the optimal index Other indicators Compare the degree of preference; similarly, determine the degree of preference for all other indicators. Compared to the worst indicator The degree of preference is used to construct a comparison vector. ,in Indicates other indicators With worst indicators The degree of preference compared; Step 3: Using the formula The constructed comparison vector is transformed to obtain the corresponding binary semantics, and then the formula is applied. The binary semantic information is converted into corresponding precise numerical values ​​to obtain the comparison vector. and ; in: Indicates the optimal index Compared to other indicators The degree of preference, Indicates other indicators With worst indicators Compared to the degree of preference, and These represent the lower bound and the upper bound, respectively. Step 4: Calculate the weight of each indicator: Establish a hesitant fuzzy BWM linear optimization model to minimize the bias ξ: According to the model use Solving for the interval weight vector ； Build an optimization model To obtain the final precise weights ; in: For the allowable deviation, These are the optimal indicators. The lower and upper bounds of the weights, The worst indicators The lower and upper bounds of the weights, The first The lower and upper bounds of the weights of each indicator. The first The lower and upper bounds of the weights of each indicator. For the first The final precise weight of each indicator, For the first The interval weights of each indicator, The first The lower and upper bounds of the weights of each indicator interval.

5. The multi-attribute decision-making method for emergency rescue schemes in water conservancy projects based on the improved CoCoSo method as described in claim 1, characterized in that, In step S3, a hesitant fuzzy decision matrix is ​​constructed and then defuzzified to obtain an accurate decision matrix. The specific process includes: Suppose there are m alternative solutions. n evaluation indicators , Experts ; Let the semantic term set be ,Specialize Home Regarding the plan In indicators The evaluation results are represented as a set of hesitant and fuzzy semantic terms. The set is S A non-empty set, for example: This indicates that experts hesitated between "slightly worse", "average", and "slightly better"; remember and They represent the first k The lower bound (i.e., the expert's most pessimistic assessment) and upper bound (i.e., the expert's most optimistic assessment) of HFLTS obtained from the evaluations of the experts are as follows: For each scheme and indicators ,remember To compile all expert evaluation information, follow these steps: in: For experts k The given lower bound of HFLTS is the most pessimistic assessment. For experts k The upper bound of HFLTS is given, which is the most optimistic evaluation; This represents the optimal semantic evaluation among all expert lower bound sets, i.e., max-lower; This represents the worst semantic evaluation among all expert upper bounds, i.e., the min-upper. The semantic evaluation information is integrated to determine the aggregation result: in: , , and These represent the upper and lower bounds of the semantic interval, respectively. This indicates that the experts have a positive view of the plan. In indicators The final hesitant and fuzzy semantic evaluation results; Transform semantic intervals into numerical intervals: Semantic term set is Introducing binary semantic transformation function and its inverse function semantic range Convert to numerical range : Define conversion function : ; Define the inverse transformation function : For binary semantics have: Lower bound of semantic interval and the Upper Realm Apply the conversions separately: Thus, the numerical range is obtained. ,satisfy ; By summing up the numerical ranges for all options and indicators, we obtain the initial hesitant fuzzy decision matrix. : Use the midpoint method to divide the interval numbers Convert to exact value : Finally, the exact decision matrix is ​​obtained. : 。 6. The multi-attribute decision-making method for emergency rescue schemes in water conservancy projects based on the improved CoCoSo method as described in claim 1, characterized in that, In step S4, the specific steps for transforming the exact decision matrix into a standardized matrix include: Perform precise decision matrix Standardization process: Standardized formula for efficiency indicators: Standardized formula for cost indicators: Obtain the standardized decision matrix: in: The number of alternative options, To evaluate the number of indicators, Indicates the first The first alternative is in the The original evaluation values ​​under each indicator .

7. The multi-attribute decision-making method for emergency rescue schemes in water conservancy projects based on the improved CoCoSo method as described in claim 1, characterized in that, In step S5, the determination of the adaptive weighting factor specifically includes the following process: Through standardized decision matrix Calculate the population mean of all standardized values. and population standard deviation : Define the adaptive weighting factor α: in: For the number of decision options, To evaluate the number of indicators, These are the standardized values ​​within the standardized matrix; ， 。 8. The multi-attribute decision-making method for emergency rescue schemes in water conservancy projects based on the improved CoCoSo method as described in claim 1, characterized in that, In step S6, the adaptive CoCoSo method is used to calculate the comprehensive score of each alternative solution. The specific process includes: The final precise weights of each indicator are calculated using the hesitant fuzzy BWM method. Calculate the weighted sum of each alternative in turn. Weighted product The three aggregation strategies are used to obtain the comprehensive score for each solution. And determine the optimal solution based on the scores; Calculate the weighted sum : Calculate the weighted product : in: The final precise weights calculated in step S2 satisfy... , ,when At that time, it was agreed ,when At that time, calculated through an index, For the number of decision options, To evaluate the number of indicators, These are the standardized values ​​within the standardized matrix; Calculate the values ​​for the three aggregation strategies: Strategy 1, the formula for calculating the arithmetic mean strategy value: Strategy 2, the formula for calculating the relative advantage strategy: Where: Assumption and In the evaluation of emergency rescue plans for actual water conservancy projects, it is naturally satisfied that at least one plan's weighted sum and weighted product are positive; Strategy 3, the formula for calculating the compromise and balance strategy: in: This is the balance coefficient, and its value range is... ; Calculate the final overall score : Values ​​of the three aggregation strategies With adaptive weighting factor Combination: Sort all alternative solutions in descending order of their values, and the one with the highest score is the optimal solution.

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