VIKOR-based unmanned / manned aerial vehicle earthquake rescue scheme decision-making system and method

Abstract

The invention relates to the field of unmanned aerial vehicles, and discloses a VIKOR-based unmanned / manned vehicle earthquake rescue scheme decision-making system and method, and the method comprises the steps: calculating the optimal evaluation value and the missing evaluation value of a selection scheme in an expert evaluation decision-making matrix, forming an aggregated evaluation decision-making matrix, carrying out the normalization processing of the aggregated evaluation decision-making matrix, and carrying out the calculation of the optimal evaluation value and the missing evaluation value of a selection scheme. Calculating a comprehensive regret perception utility value of each scheme, and forming a perception value matrix; a fusion weighting method is adopted, a subjective weighting method and an objective weighting method are combined, the weight of each attribute is determined, the subjective weight and the objective weight are fused through a multiplication normalization method, and the fusion weight of each attribute is obtained; using an improved VIKOR method to obtain an optimal scheme to a worst scheme; and outputting a final decision result. According to the method, the improved VIKOR method is used for sorting the evaluation decision results, and the optimal rescue scheme can be screened out more accurately.

Description

Technical Field

[0001] The present invention relates to the field of unmanned aerial vehicles, and specifically to an unmanned / manned aircraft earthquake rescue plan decision-making system and method based on VIKOR. Background Art

[0002] With the rapid development of unmanned aerial vehicle technology and its wide application in various fields, it has shown great potential in earthquake rescue scenarios. Unmanned aerial vehicles can quickly reach some complex areas that are difficult for people to enter and perform tasks such as disaster situation reconnaissance and material delivery. However, manned aircraft also have irreplaceable advantages in rescue, such as being able to carry more rescue personnel and materials and perform more complex rescue operations. Therefore, the rescue method combining unmanned / manned aircraft has gradually attracted attention.

[0003] Currently, when an earthquake disaster occurs in a complex terrain area, the decision-making of unmanned / manned aircraft rescue plans faces many challenges. On the one hand, existing decision-making methods often rely too much on a single factor, such as only considering one aspect of rescue cost, rescue efficiency, etc., while ignoring the influence of other important factors. On the other hand, in the face of decisions with strong subjectivity, existing methods lack consideration of the regret psychology of decision-makers and cannot well intervene in objective factors. For example, in the decision-making of multi-attribute rescue plans, the decision result may be unsatisfactory due to the subjective hesitation or inaccurate judgment of decision-makers, affecting the rescue efficiency and accuracy.

[0004] Traditional decision-making methods also have deficiencies in dealing with fuzzy information. In earthquake rescue scenarios, a lot of information is fuzzy and uncertain, such as the complexity of the geographical environment, the utilization rate of resources, etc. These information are difficult to be represented by precise numerical values. When existing decision-making methods deal with this fuzzy information, they often adopt simple approximation methods, resulting in a deviation between the decision result and the actual situation. Summary of the Invention

[0005] The purpose of the present invention is to overcome the deficiencies of the prior art and provide an unmanned / manned aircraft earthquake rescue plan decision-making method based on VIKOR, including the following steps: Step 1, calculate the advantage evaluation value and disadvantage evaluation value of the selected plan in the expert evaluation decision matrix, aggregate the expert decision-making information by using the PFULPWAA operator to form an aggregated evaluation decision matrix, perform normalization processing on the aggregated evaluation decision matrix, compare the sample reference point values of each attribute in each stage according to the normalized evaluation decision matrix, calculate the regret perception utility value of each attribute in each stage, calculate the comprehensive regret perception utility value of each plan according to the regret perception utility value and the probability of each stage occurring, and form a perception value matrix; Step 2: The combined weighting method is adopted, combining the subjective weighting method and the objective weighting method to determine the weights of each attribute. The multiplication normalization method is used to fuse the subjective and objective weights to obtain the combined weights of each attribute; Step 3: Use the improved VIKOR method to calculate the positive ideal solution and negative ideal solution of each alternative; according to the positive ideal solution and negative ideal solution, calculate the minimum individual regret degree and maximum group benefit of each solution; according to the minimum individual regret degree and maximum group benefit, obtain the compromise ranking value of each solution; according to the compromise ranking value, arrange the solutions in descending order to obtain the optimal solution to the worst solution; Step 4: Output the final decision result, where the decision result includes the ranking of different rescue plans in each rescue stage and the optimal rescue plan.

[0006] Furthermore, calculate the advantage evaluation value and disadvantage evaluation value of the selected solutions in the expert evaluation decision matrix, and use the PFULPWAA operator to aggregate the expert decision information to form the aggregated evaluation decision matrix, including: Calculate the advantage evaluation value of the selected solutions in the expert evaluation decision matrix: Indicates that in stage, the evaluation decision value of the scoring expert for the i-th solution under the j-th attribute; Then it represents that in stage, the membership degree of the scoring expert's evaluation decision score value for the i-th solution under the j-th attribute, Indicates that in stage, the non-membership degree of the scoring expert's evaluation decision score value for the i-th solution under the j-th attribute; Is an element of the linguistic variable and takes the value of the number of dimensions selected for solution selection in the evaluation decision matrix; And represent the upper and lower limits of the entire evaluation decision matrix; Calculate the evaluation value of the disadvantage matrix of the selected solutions in the expert evaluation decision matrix: Aggregate the expert decision information using the PFULPWAA operator: Where ; Represents the disadvantage matrix under each stage, Represents the cumulative addition of the defect matrix in each stage.

[0007] Furthermore, the normalization process of the aggregated evaluation decision matrix includes: Represents the set of solutions, : Represents the set of index attributes, where Is a subscript parameter, Represents the set of evaluation dimensions.

[0008] Furthermore, according to the normalized evaluation decision matrix, compare the sample reference point values of each attribute in each stage, calculate the regret perception utility values of each attribute in each stage, and calculate the comprehensive regret perception utility value of each solution according to the regret perception utility value and the probability of each stage occurring, and form a perceived value matrix, including: According to the normalized evaluation decision matrix Compare the sample reference point values of each attribute in each stage, and then determine the sample reference point of each attribute in each stage according to the sample reference value , using the following formula: : Represents the maximum perceived value; Calculate the regret perception utility values of the sample points of each attribute in each stage Given the probability of each stage occurring The comprehensive regret perception utility value of each solution , and build a perceived value matrix according to the calculation results , the calculation formula is as follows: In the t stage, the satisfaction-regret perception utility of each solution is calculated as follows: In the formula Represents The regret value of solution In Attribute, Represents the regret aversion coefficient; The probability that all stages in the decision-making process occur in the solution: The comprehensive utility of the decision-making solution is calculated as follows: Where Denote the result of solution \(i\) under criterion \(j\); Denote the probability of the occurrence of an event; and are parameters used to adjust the shape of the function and are positive real numbers.

[0009] Furthermore, the fusion weighting method is adopted, combining the subjective weighting method and the objective weighting method to determine the weights of each attribute. The multiplicative normalization method is used to fuse the subjective and objective weights to obtain the fusion weights of each attribute, including: Determine the subjective weight based on the preference ratio method: Let denote the attribute The ratio preference value for attribute is established, and the following matrix is used to solve the weight values of each attribute: where ; Solve the model to obtain the subjective weight vector of the attribute as: ; Calculate the objective weight of the matrix based on the maximum deviation method: The formula for the maximum deviation calculation method is as follows: where denotes the objective weight of attribute ; Use the multiplicative normalization method to fuse the subjective and objective weights, and its calculation formula is as follows: where denotes the fusion weight of attribute ; is the number of weight assignment methods; denotes the product of the subjective and objective weight fusions; denotes the cumulative sum of the products of the subjective and objective weight fusions.

[0010] Furthermore, the improved VIKOR method is used to calculate the positive ideal solution and the negative ideal solution of each alternative solution; according to the positive ideal solution and the negative ideal solution, calculate the minimum individual regret degree and the maximum group benefit of each solution; according to the minimum individual regret degree and the maximum group benefit, obtain the compromise ranking value of each solution; arrange the solutions in descending order according to the compromise ranking value to obtain the optimal solution to the worst solution, including: Positive ideal solution and negative ideal solution The solution formulas are as follows: Calculation scheme Individual regret degree and maximum group benefit : Calculate the compromise ranking value of each scheme , and the formula is as follows: In the formula, represents the risk coefficient, and the value of the risk coefficient is . When the risk coefficient is close to 1, it means that the decision result approaches the maximum utility value, and when it is close to 0, it means that the decision result approaches the minimum utility value. is the maximum value, is the minimum value; is the maximum value, is the minimum value.

[0011] The unmanned / manned aircraft earthquake rescue plan decision-making system based on VIKOR applies the above-mentioned unmanned / manned aircraft earthquake rescue plan decision-making method based on VIKOR, including: A data acquisition module, which is used to collect the evaluation data of civil aviation domain experts on the unmanned / manned aircraft rescue plans under different attributes, including the scores of different rescue plans under each attribute in each rescue stage, as well as the membership degree and non-membership degree information corresponding to the scores; A decision matrix construction module, which is used to construct a two-dimensional Pythagorean fuzzy uncertain language evaluation decision matrix according to the collected data, process and transform the collected data through mathematical algorithms and formulas, perceive decision information from multiple dimensions, and optimize the PT decision matrix; A weight determination module, which is used to determine the weights of each attribute, combines the subjective weighting method and the objective weighting method by using the fusion weighting method, and calculates and processes through corresponding algorithms and formulas to obtain the fusion weights of each attribute; A plan ranking module, which improves the VIKOR method based on the regret theory, calculates the positive ideal plan and negative ideal plan of each alternative plan, calculates the minimum individual regret degree and maximum group benefit of each plan by using the positive ideal plan and negative ideal plan, and ranks the plans according to the compromise ranking value; A result output module, which is used to output the final decision result, including the ranking of different rescue plans in each rescue stage and the selection of the optimal rescue plan.

[0012] The beneficial effects of the present invention are as follows: The present invention aims to improve the accuracy of multi-attribute rescue plan decision-making. By integrating subjective weighting methods and objective weighting methods to determine the weights of each attribute, it not only takes into account the professional experience and subjective judgment of decision-makers but also combines objective data and indicators, making the determination of weights more reasonable and accurate. Based on this, the improved VIKOR method is used to rank the evaluation decision results, which can more accurately screen out the optimal rescue plan and provide more scientific and effective decision support for rescue operations. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 FIG. is a schematic flow chart of a method for making a decision on an unmanned / manned aircraft earthquake rescue plan based on VIKOR; Figure 2 FIG. is a schematic implementation diagram of a decision-making system for an unmanned / manned aircraft earthquake rescue plan based on VIKOR. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0014] The technical solution of the present invention will be further described in detail below with reference to the drawings, but the protection scope of the present invention is not limited to the following description.

[0015] The features and performance of the present invention will be further described in detail below with reference to the embodiments.

[0016] As Figure 1 shown, a method for making a decision on an unmanned / manned aircraft earthquake rescue plan based on VIKOR includes the following steps: Step 1: Calculate the merit evaluation value and demerit evaluation value of the selected plan in the expert evaluation decision matrix, aggregate the expert decision information using the PFULPWAA operator to form an aggregated evaluation decision matrix, normalize the aggregated evaluation decision matrix, compare the sample reference point values of each attribute at each stage according to the normalized evaluation decision matrix, calculate the regret perception utility value of each attribute at each stage, calculate the comprehensive regret perception utility value of each plan according to the regret perception utility value and the probability of each stage, and form a perceived value matrix; Step 2: Use a fusion weighting method to combine subjective weighting methods and objective weighting methods to determine the weights of each attribute, and use the multiplication normalization method to fuse the subjective and objective weights to obtain the fusion weights of each attribute; Step 3: Use the improved VIKOR method to calculate the positive ideal solution and negative ideal solution of each alternative plan; according to the positive ideal solution and negative ideal solution, calculate the minimum individual regret degree and maximum group benefit of each plan; according to the minimum individual regret degree and maximum group benefit, obtain the compromise ranking value of each plan; arrange the plans in descending order according to the compromise ranking value to obtain the optimal plan to the worst plan; Step 4: Output the final decision result, where the decision result includes the ranking of different rescue plans in each rescue stage and the optimal rescue plan.

[0017] Calculate the advantage evaluation value and disadvantage evaluation value of the selected plan in the expert evaluation decision matrix, and use the PFULPWAA operator to aggregate the expert decision information to form an aggregated evaluation decision matrix, including: Calculate the advantages of the selected plans in the expert evaluation decision matrix Evaluation value: Indicates that in stage, the evaluation decision value of the scoring expert for the i-th plan under the j-th attribute; Then it indicates that in stage, the membership degree of the scoring expert's evaluation decision score value for the i-th plan under the j-th attribute, Indicates that in stage, the non-membership degree of the scoring expert's evaluation decision score value for the i-th plan under the j-th attribute; Is an element of the linguistic variable The value is the number of dimensions selected for plan selection in the evaluation decision matrix; And Represent the upper and lower limits of the entire evaluation decision matrix; Calculate the evaluation value of the disadvantage matrix of the selected plan in the expert evaluation decision matrix : Use the PFULPWAA operator to aggregate the expert decision information: Where ; Represents the disadvantage matrix in each stage, Represents the cumulative addition of the disadvantage matrices in each stage.

[0018] The normalization process for the aggregated evaluation decision matrix includes: Represents the set of plans, : Represents the set of index attributes, where Is the subscript parameter, Represents the set of evaluation dimensions.

[0019] Based on the normalized evaluation decision matrix, compare the sample reference point values of each attribute at each stage, calculate the regret perception utility values of each attribute at each stage, and calculate the comprehensive regret perception utility value of each scheme according to the regret perception utility value and the probability of each stage occurring, and form a perceived value matrix, including: Based on the normalized evaluation decision matrix Compare the sample reference point values of each attribute at each stage, and then determine the sample reference points of each attribute at each stage according to the sample reference values , using the following formula: : represents the maximum perceived value; Calculate the regret perception utility values of the sample points of each attribute at each stage Given the probability of each stage occurring The comprehensive regret perception utility value of each scheme , and build a perceived value matrix according to the calculation results , the calculation formula is as follows: At stage t, the satisfaction-regret perception utility of each scheme is calculated as follows: In the formula represents The regret value of scheme at stage under attribute represents the regret aversion coefficient; The probability of all stages in the decision-making process occurring in the scheme: The comprehensive utility of the decision-making scheme is calculated as follows: Where represents the result of scheme i under criterion j; represents the probability of the event occurring; and are parameters used to adjust the shape of the function and are positive real numbers.

[0020] The above-mentioned method of combining subjective and objective weighting methods is used to determine the weights of each attribute, and the multiplication normalization method is used to fuse the subjective and objective weights to obtain the fused weights of each attribute, including: Determine the subjective weight based on the preference ratio method: Let represent attribute for attribute Based on the ratio preference values, the following matrix is established to solve the weight values of each genus: where ; Solve the model , and the subjective weight vector of the attributes is obtained as: ; Calculate the objective weight of the matrix based on the maximum deviation method: The formula for the maximum deviation calculation method is as follows: where represents the objective weight of attribute ; Use the multiplication normalization method to fuse the subjective and objective weights, and its calculation formula is as follows: where represents the fused weight of attribute ; is the number of weight assignment methods; represents the product of the subjective and objective weight fusions; represents the cumulative sum of the products of the subjective and objective weight fusions.

[0021] Using the improved VIKOR method described above, calculate the positive ideal solution and negative ideal solution of each alternative; According to the positive ideal solution and negative ideal solution, calculate the minimum individual regret degree and maximum group benefit of each solution; According to the minimum individual regret degree and maximum group benefit, obtain the compromise ranking value of each solution; Arrange the solutions in descending order according to the compromise ranking value to obtain the optimal solution to the worst solution, including: Positive ideal solution and negative ideal solution The solution formula is as follows: Calculate the individual regret degree and the maximum group benefit of solution : Calculate the compromise ranking value of each solution , and the formula is as follows: In the formula, represents the risk coefficient, and the value of the risk coefficient is , when the risk coefficient is close to 1, it means that the decision result approaches the maximum utility value, and when it is close to 0, it means that the decision result approaches the minimum utility value. is the maximum value, is the minimum value; is the maximum value, is the minimum value.

[0022] As Figure 2 shown, the unmanned / manned aircraft earthquake rescue plan decision-making system based on VIKOR applies the described unmanned / manned aircraft earthquake rescue plan decision-making method based on VIKOR, including: A data acquisition module, which is used to collect the evaluation data of civil aviation domain experts on the unmanned / manned aircraft rescue plan under different attributes, including the scores of different rescue plans under attributes in each rescue stage, as well as the membership degree and non-membership degree information corresponding to the scores; A decision matrix construction module, which is used to construct a two-dimensional Pythagorean fuzzy uncertain language evaluation decision matrix according to the collected data, process and transform the collected data through mathematical algorithms and formulas, perceive decision-making information from multiple dimensions, and optimize the PT decision matrix; A weight determination module, which is used to determine the weights of each attribute, combines the subjective weighting method and the objective weighting method by using the fusion weighting method, and calculates and processes through corresponding algorithms and formulas to obtain the fusion weights of each attribute; A plan ranking module, which improves the VIKOR method based on the regret theory, calculates the positive ideal plan and negative ideal plan of each alternative plan, calculates the minimum individual regret degree and maximum group benefit of each plan by using the positive ideal plan and negative ideal plan, and ranks the plans according to the compromise ranking value; A result output module, which is used to output the final decision result, including the ranking of different rescue plans in each rescue stage and the selection of the optimal rescue plan.

[0023] Specifically, the unmanned / manned aircraft earthquake rescue plan decision-making system based on the regret theory-VIKOR method proposed by the present invention mainly includes a data acquisition module, a decision matrix construction module, a weight determination module, a plan ranking module and a result output module.

[0024] Detailed description of each module Data acquisition module Function: Responsible for collecting evaluation data of experts in the civil aviation field on unmanned / manned aircraft rescue plans under different attributes. These data include the scores of experts on different rescue plans (unmanned aircraft rescue, manned aircraft rescue, unmanned / manned aircraft cooperative rescue) under attributes (tightness of aircraft quantity, complexity of geographical environment, resource utilization rate, material transportation efficiency) during each rescue stage, including the early search and rescue stage (0 - 24h), the mid-term treatment and rescue stage (24 - 72h), and the late material transportation stage (72 - 168h), as well as the membership degree and non-membership degree information corresponding to the scores.

[0025] Decision Matrix Construction Module Function: Construct a two-dimensional Pythagorean fuzzy uncertain linguistic evaluation decision matrix (2DPUFL - PT - VIKOR) based on the collected data. First, expand the Pythagorean fuzzy linguistic vector into a two-dimensional form to perceive decision information from multiple dimensions and optimize the PT decision matrix.

[0026] Implementation method: Use relevant mathematical algorithms and formulas to process and transform the collected data to construct a decision matrix that meets the requirements.

[0027] Fuzzy Uncertain Linguistic Set Linguistic Variable Definition 1 Let be composed of a group of ordered and finite elements, where the value of is an odd number, represents a linguistic value,

[0028] Fuzzy Uncertain Linguistic Fuzzy uncertain language refers to an imprecise, fuzzy or uncertain language expression. Fuzzy uncertain language shows characteristics such as unclear meaning, uncertain extension, wide application range and diverse expression effects during the expression process.

[0029] Definition 2 Let be a group of linguistic variables composed of ordered variable elements, then the uncertain output variable produced by the parameters within a certain linguistic universe of discourse is defined as a fuzzy uncertain linguistic variable, that is: Pythagorean Fuzzy Uncertain Linguistic Variable Definition 3 Let be a one-dimensional linguistic set, be a given universe of discourse, then the one-dimensional Pythagorean fuzzy uncertain linguistic variable can be expressed as where and and represent the membership degree and non - membership degree of the function. Considering that one - dimensional uncertain variables cannot measure the relationship between numerical values and membership degrees well, the upper and lower limits of the values are considered and a two - dimensional Pythagorean fuzzy uncertain linguistic variable is introduced, that is where and represent the upper and lower limits of the function , and the functions and represent the membership degree and non - membership degree of the function and ; represents 's membership degree with the function . When the value is close to 1, it indicates that the numerical value has a high membership degree (or non - membership degree) with the function . For each , there is . For all , there is . Therefore, the hesitancy degree of the function is called the Pythagorean fuzzy uncertain linguistic variable (PFULV), denoted as: Let and be any two values of the Pythagorean fuzzy uncertain linguistic variable, then the following operation rules are available: (1) (2) (3) (4) .

[0030] PT evaluation decision matrix The PT evaluation decision matrix is a method often used in project management and decision analysis. Its idea is to divide the PT evaluation decision matrix into two parts: the P matrix and the T matrix. Among them, the P matrix is used to represent the advantages of the entire evaluation object, and the T matrix is used to represent the disadvantages of the entire evaluation object. The two together represent the quality of the entire evaluation object. The PT decision matrix consists of multiple rows and columns, where the rows represent influencing factors and the columns represent selection options. The matrix is constructed as follows: Among them represents the evaluation decision score value when facing the first influencing factor and the first selection option.

[0031] The PT evaluation decision matrix is established in the two-dimensional Pythagorean fuzzy uncertain linguistic variable scenario as follows: Among them represents the lower limit value of the evaluation decision score value of the expert for the first scheme under the first attribute in a certain state ( represents the upper limit value); represents the membership degree of the evaluation decision score value of the expert for the first scheme under the first attribute in a certain state ( represents the non-membership degree).

[0032] Step 1: Establish the PT evaluation decision matrix Step 1.1: Aggregate the opinions of decision-making experts (1) Calculate the evaluation value of the advantages of the selected scheme in the expert evaluation decision matrix Evaluation value: In the formula, the evaluation decision matrix considers four dimensions: the upper and lower limits of the expert scoring values, the membership degree of the score to the research scheme, and the non-membership degree when selecting the scheme. Therefore, the value is taken as 4, that is .

[0033] (2) Calculate the evaluation value of the disadvantage matrix of the selected scheme in the expert evaluation decision matrix of: (3) Use the PFULPWAA operator to aggregate expert decision-making information: Step 1.2: Normalize the evaluation decision matrix Step 1.3 Establish the PT evaluation decision matrix According to the normalized evaluation decision matrix Compare the sample reference point values of each attribute at each stage, and then determine the sample reference point of each attribute at each stage according to the sample reference value , and its calculation formula is as follows: Considering the regret psychology generated by experts in decision-making, calculate the regret perception utility value of the sample points of each attribute at each stage Given the probability of each stage occurring The comprehensive regret perception utility value of each scheme , and establish a perception value matrix according to the calculation results , and the calculation formula is as follows: (1) At stage t, the satisfaction-regret perception utility of each scheme is calculated as follows: In the formula Represents the regret value of scheme At stage t Under the attribute, Represents the regret avoidance coefficient, generally taking a value of 0.3

[0034] (2) The probability of all stages occurring in the scheme during the decision-making process: (3) The comprehensive utility of the decision-making scheme is calculated as follows: Among them, ; Considering a certain earthquake disaster, emergency rescue There are Rescue stages, and its set is ; the probability set corresponding to the rescue stage is There are Rescue plans, and the set is , There are Attributes, and its set is , and the weight set corresponding to its attributes is .

[0035] Weight determination module Function: Determine the weights of each attribute. The combined weighting method is adopted, which combines the subjective weighting method and the objective weighting method. The subjective weighting method determines the subjective weight based on the preference ratio method, and determines the weight by comparing the preference degrees of decision-makers for different attributes; the objective weighting method calculates the objective weight based on the maximum deviation method, and directly calculates the weight according to the internal relationship between the index data. Finally, the subjective and objective weights are combined by the multiplication normalization method to obtain the combined weights of each attribute.

[0036] Implementation method: Calculate and process according to the corresponding algorithms and formulas to obtain accurate weight values.

[0037] Step 2 Determine the weight attributes The subjective weighting method and the objective weighting method are commonly used methods for determining index weights in multi-attribute decision-making. The subjective weighting method is a method of assigning weights to each index based on the knowledge, experience or preference of decision-makers through a certain method. The objective weighting method is a method of directly calculating the index weight through mathematical methods according to the internal relationship between the index data. The subjective weighting method mainly relies on the experience of experts in research, which will lead to the research results being too subjective; the objective weighting method mainly relies on research data and experimental conclusions for judgment, and when the data is distorted, this method will fail. In this paper, both the subjective judgment of experts and the support of objective data are required in the decision-making process. The subjective weighting method and the objective weighting method are combined, and weights are added so that the final result contains both subjective experience and objective basis.

[0038] Step 2.1 Determine the subjective weight based on the preference ratio method The preference ratio method is a subjective weighting method, which determines the subjective weight of an attribute by comparing the preference degrees of decision-makers for different attributes. First, establish a preference ratio scale table. Secondly, in the research process, compare according to the influence degree of each attribute on the entire decision-making object. When the influence degree of one attribute is greater than that of another attribute, the preference ratio of this attribute is greater than that of the other attribute, and they are arranged in descending order from large to small, as follows: . Let represent the ratio preference value of attribute to attribute . Establish the following matrix to solve the weight values of each attribute: Among them, ; Solve the model , and the subjective weight vector of the attribute is: .

[0039] Step 2.2 Calculate the objective weight of the matrix based on the maximum deviation method The formula for the maximum deviation calculation method is as follows: wherein represents the objective weight of the attribute .

[0040] Step 2.3 Determine the subjective and objective fusion weight of the attribute based on the multiplicative normalization method Here, it is considered that the importance degrees of the subjective and objective weights assigned by the preference ratio method and the maximum deviation method are the same. The multiplicative normalization method is used to fuse the subjective and objective weights, and its calculation formula is as follows: wherein represents the fusion weight of the attribute ; is the number of methods for assigning weights; represents the product of the subjective and objective weights; represents the cumulative sum of the products of the subjective and objective weights.

[0041] Scheme ranking module Function: Rank the evaluation and decision results based on the improved VIKOR method according to the regret theory. First, calculate the positive ideal solution (PIS) and negative ideal solution (NIS) of each alternative scheme, then calculate the minimum individual regret degree and maximum group benefit of each scheme using the positive ideal solution and negative ideal solution, and obtain the compromise ranking value of each scheme according to the minimum individual regret degree and maximum group benefit of each scheme. Finally, arrange the schemes in descending order according to the compromise ranking value to obtain the optimal scheme to the worst scheme.

[0042] Implementation method: Use the improved VIKOR algorithm for calculation and ranking operations.

[0043] Step 3 Solve the optimal scheme using the VIKOR method Step 3.1 Solve the positive ideal solution (PIS) and negative ideal solution (NIS) , the positive ideal solution (PIS) and negative ideal solution (NIS) The solution formulas are as follows: Step 3.2 Calculate the individual regret degree of the scheme and the maximum value of the group benefit .

[0044] Step 3.3 Calculate the compromise ranking value of each scheme , the formula is as follows: In the formula, represents the risk coefficient, and the value of the risk coefficient is . When the risk coefficient is close to 1, it means that the decision result approaches the maximum utility value. When it is close to 0, it means that the decision result approaches the minimum utility value. Here, it takes 0.5. is the maximum value, is the minimum value; is the maximum value, is the minimum value.

[0045] Result output module Function: Output the final decision result, including the ranking of different rescue plans in each rescue stage and the selection of the optimal rescue plan.

[0046] Implementation method: Present the calculated result to the user in an intuitive way, such as through a chart interface display or generating a report.

[0047] Table 1 Compromise ranking values of expert evaluation results The comprehensive rankings of its three plans are respectively: Table 2 Plan ranking To sum up, when five experts considered rescue in the first week (0 - 168h) after the earthquake, when using drones, manned aircraft, and unmanned / manned aircraft as rescue plans, three experts believed that the manned aircraft ( ) was the best rescue plan. Because drones cannot provide good treatment for the injured during rescue and can only be engaged in related material transportation. The other two experts respectively believed that the drone ( ) and the cooperation of unmanned / manned aircraft ( ) were the best rescue plans.

[0048] As Figure 2 shown in the overall architecture diagram of the system, it shows the connection relationship and data flow between the data acquisition module, decision matrix construction module, weight determination module, plan ranking module, and result output module.

[0049] Design a user - friendly interface for the expert scoring system. The interface should clearly list options such as rescue stages (pre - search and rescue stage (0 - 24h), mid - treatment and rescue stage (24 - 72h), late - material transportation stage (72 - 168h)), rescue plans (drone rescue, manned aircraft rescue, unmanned, combined manned and unmanned aircraft rescue), and attributes (tightness of the number of aircraft, complexity of the geographical environment, resource utilization rate, material transportation efficiency).

[0050] Set corresponding scoring input boxes for each attribute. The scoring range can be set from 0 - 6 points (0 points being the worst and 6 points being the best). At the same time, set membership degree and non - membership degree input boxes, allowing experts to input values between 0.2 - 0.9.

[0051] Based on their professional knowledge and experience, experts score each rescue plan for different rescue stages under each attribute and input the corresponding membership degree and non - membership degree values. The system should have a data verification function to ensure that the input data meets the requirements.

[0052] Decision matrix construction Obtain the collected data from the expert scoring system. For the scoring data of each expert, process it according to the following steps: Expand the Pythagorean fuzzy linguistic vector into a two - dimensional form. For example, if an expert's score for a certain rescue plan under a certain attribute is 5 points, the membership degree is 0.8, and the non - membership degree is 0.3, then convert it into a two - dimensional form, which may be expressed as ([4, 5], [0.8, 0.3]), where [4, 5] represents the upper and lower limits of the score, and [0.8, 0.3] represents the membership degree and non - membership degree.

[0053] Construct a complete two - dimensional Pythagorean fuzzy uncertain linguistic evaluation decision matrix (2DPUFL - PT - VIKOR) based on all experts' data. The rows of the matrix correspond to the combinations of rescue stages and rescue plans, and the columns correspond to the attributes.

[0054] Weight determination Subjective weight determination Establish a preference ratio scale table according to experts' preference degrees for different attributes. For example, if an expert believes that the resource utilization rate is more important than the complexity of the geographical environment, then the relative preference ratio of the resource utilization rate to the complexity of the geographical environment in the preference ratio scale table may be set to 3.0 (stronger).

[0055] The subjective weight vector is calculated by comparing the relative preferences of each attribute in the preference ratio scale table. For example, if there are four attributes, the subjective weight vector may be (0.3, 0.25, 0.2, 0.25) after comparison and calculation.

[0056] Objective weight determination The maximum deviation method is used to calculate the objective weight. The deviation between each attribute data is calculated, and the objective weight is determined according to the deviation size. For example, if the objective weight of a certain attribute is 0.28 after calculation.

[0057] Integration of subjective and objective weights The subjective and objective weights are integrated by the multiplication normalization method. Suppose the subjective weight vector is (0.3, 0.25, 0.2, 0.25), and the objective weights are (0.28, 0.22, 0.2, 0.3) respectively, then the integrated weights are calculated as follows: Calculate the product of the subjective and objective weights: For the first attribute, the product is 0.3×0.28 = 0.084; for the second attribute, the product is 0.25×0.22 = 0.055; for the third attribute, the product is calculated by the same method to be 0.04; for the fourth attribute, the product is 0.25×0.3 = 0.075.

[0058] Calculate the cumulative sum of the products of the subjective and objective weights: 0.084 + 0.055 + 0.04 + 0.075 = 0.254.

[0059] Calculate the integrated weights: For the first attribute, the integrated weight is 0.084÷0.254 ≈ 0.331; for the second attribute, the integrated weight is 0.055÷0.254≈ 0.217; for the third attribute, the integrated weight is 0.04÷0.254≈ 0.157; for the fourth attribute, the integrated weight is 0.075÷0.254≈ 0.295.

[0060] Scheme ranking The VIKOR method improved based on regret theory is used to rank the evaluation and decision results.

[0061] Calculate the positive ideal solution (PIS) and negative ideal solution (NIS) of each alternative scheme. For example, for a certain attribute, the positive ideal solution may be the case with the highest score and the highest membership degree, and the negative ideal solution may be the case with the lowest score and the lowest membership degree.

[0062] Calculate the minimum individual regret degree and the maximum group benefit of each solution using the positive ideal solution and the negative ideal solution. For example, the minimum individual regret degree of a certain solution may be calculated by comparing the differences between this solution and the positive ideal solution in each attribute, and the maximum group benefit may be calculated by comprehensively considering the performance of each solution in each attribute.

[0063] Obtain the compromise ranking value of each solution based on the minimum individual regret degree and the maximum group benefit of each solution. For example, if the minimum individual regret degree of a certain solution is 0.2, the maximum group benefit is 0.8, and the risk coefficient is 0.5, then the compromise ranking value is (0.2×0.5)+(0.8×(1 - 0.5)) = 0.5.

[0064] Arrange the solutions in descending order according to the compromise ranking value to obtain the optimal solution to the worst solution.

[0065] Result output Present the final decision result to the user in an intuitive way.

[0066] The ranking of different rescue solutions at each rescue stage and the selection of the optimal rescue solution can be displayed through a graphical interface. For example, use a bar chart to show the ranking of each solution at different stages, and use different colors to distinguish different solutions.

[0067] A report can also be generated to elaborate on the decision-making process and results. The content of the report may include the situation of raw data collection, the construction process of the decision matrix, the method and results of weight determination, the process of solution ranking, and the final results.

Claims

1. A decision-making method for unmanned / manned aircraft earthquake rescue plans based on VIKOR, characterized in that It includes the following steps: Step 1: Calculate the advantage evaluation value and disadvantage evaluation value of the selected solutions in the expert evaluation decision matrix, aggregate the expert decision-making information using the PFULPWAA operator to form an aggregated evaluation decision matrix, perform normalization processing on the aggregated evaluation decision matrix, compare the sample reference point values of each attribute at each stage according to the normalized evaluation decision matrix, calculate the regret perception utility value of each attribute at each stage, calculate the comprehensive regret perception utility value of each solution according to the regret perception utility value and the probability of each stage occurring, and form a perceived value matrix; Step 2: Use the fusion weighting method, combine the subjective weighting method and the objective weighting method to determine the weights of each attribute, and use the multiplication normalization method to fuse the subjective and objective weights to obtain the fusion weights of each attribute; Step 3: Use the improved VIKOR method to calculate the positive ideal solution and negative ideal solution of each alternative solution; According to the positive ideal solution and negative ideal solution, calculate the minimum individual regret degree and maximum group benefit of each solution; according to the minimum individual regret degree and maximum group benefit, obtain the compromise ranking value of each solution; arrange the solutions in descending order according to the compromise ranking value to obtain the optimal solution to the worst solution; Step 4: Output the final decision result, and the decision result includes the ranking of different rescue solutions at each rescue stage and the optimal rescue solution.

2. The VIKOR-based decision-making method for unmanned / manned aircraft earthquake rescue plans according to claim 1, wherein, The calculation of the advantage evaluation value and disadvantage evaluation value of the selected solutions in the expert evaluation decision matrix, and the aggregation of expert decision-making information using the PFULPWAA operator to form an aggregated evaluation decision matrix includes: Calculate the advantages of the selected solutions in the expert evaluation decision matrix Evaluation value: Indicates that in the stage, the evaluation decision value of the scoring expert for the i-th solution under the j-th attribute; It means that at the stage, the membership degree of the evaluation and decision scoring value of the scoring expert for the i-th solution under the j-th attribute It represents the non-membership degree of the evaluation and decision scoring value of the scoring expert for the i-th solution under the j-th attribute at the is an element of the linguistic variable and its value is the number of dimensions selected for the evaluation decision matrix in the case of alternative selection; and represent the upper and lower bounds of the entire evaluation decision matrix; Calculate the evaluation value of the disadvantage matrix of the alternative in the expert evaluation decision matrix : Aggregate the expert decision-making information using the PFULPWAA operator: Among them ; represents the disadvantage matrix at each stage, represents the cumulative sum of the disadvantage matrix at each stage.

3. The decision-making method for the unmanned / manned aircraft earthquake rescue plan based on VIKOR according to claim 2, characterized in that, The normalization processing of the aggregated evaluation decision matrix includes: Represents a set of solutions, : Represents a set of index attributes, where is a subscript parameter; represents a set of evaluation dimensions.

4. The decision-making method for the unmanned / manned aircraft earthquake rescue plan based on VIKOR according to claim 3, wherein, According to the normalized evaluation decision matrix, compare the sample reference point values of each attribute at each stage, calculate the regret perception utility value of each attribute at each stage, calculate the comprehensive regret perception utility value of each solution according to the regret perception utility value and the probability of each stage occurring, and form a perceived value matrix, including: According to the normalized evaluation and decision matrix Compare the sample reference point values of each attribute at each stage, and then determine the sample reference points of each attribute at each stage according to the sample reference values , using the following formula: : represents the maximum perceived value; Calculate the regret perception utility value of the sample points of each attribute at each stage Given the probability of occurrence at each stage The comprehensive regret perception utility value of each solution , and construct a perception value matrix based on the calculation results , and the calculation formula is as follows: At the t stage, the satisfaction-regret perception utility of each solution is calculated as follows: In the formula represents the solution under the stage the regret value under the attribute, and represents the regret aversion coefficient; The probability of all stages occurring in the decision-making process in the solution: The comprehensive utility of the decision-making solution is calculated as follows: where represents the result of solution i under criterion j; represents the probability of the occurrence of an event; and are parameters used to adjust the shape of the function and are positive real numbers.

5. The decision-making method for the unmanned / manned aircraft earthquake rescue plan based on VIKOR according to claim 4, wherein The use of the fusion weighting method, combining the subjective weighting method and the objective weighting method to determine the weights of each attribute, and using the multiplication normalization method to fuse the subjective and objective weights to obtain the fusion weights of each attribute includes: Determine the subjective weight based on the preference ratio method: Let represent attributes For the attributes of ratio preference values, establish the following matrix to solve the weight values of each attribute: Among them ; Solving model , the subjective weight vector of attributes is obtained as follows: ； Calculate the objective weight of the matrix based on the maximum deviation method: The formula for the maximum deviation calculation method is as follows: Among them represents the objective weight of the attribute ; Use the multiplication normalization method to fuse the subjective and objective weights, and its calculation formula is as follows: Among them represents the fusion weight of the attribute ; is the number of methods for assigning weights; represents the product of the subjective and objective weights; represents the cumulative sum of the product of the subjective and objective weights.

6. The decision-making method for the unmanned / manned aircraft earthquake rescue plan based on VIKOR according to claim 5, characterized in that, The use of the improved VIKOR method to calculate the positive ideal solution and negative ideal solution of each alternative solution; according to the positive ideal solution and negative ideal solution, calculate the minimum individual regret degree and maximum group benefit of each solution; according to the minimum individual regret degree and maximum group benefit, obtain the compromise ranking value of each solution; Arrange the solutions in descending order according to the compromise ranking value to obtain the optimal solution to the worst solution, including: Positive ideal solution and negative ideal solution The solution formula is as follows: Calculation scheme Individual regret degree and maximum group benefit : Calculate each solution of the compromise sorting value , the formula is as follows: wherein, represents the risk coefficient, and the value of the risk coefficient is . When the risk coefficient approaches 1, it means that the decision result approaches the maximum utility value; when it approaches 0, it means that the decision result approaches the minimum utility value. is the maximum value, is the minimum value; is the maximum value, is the minimum value.

7. The decision-making system for the unmanned / manned aircraft earthquake rescue plan based on VIKOR, characterized in that, Applying the VIKOR-based decision-making method for unmanned / manned aircraft earthquake rescue plans described in any one of claims 1-6, including: A data acquisition module, which is used to collect the evaluation data of unmanned / manned aircraft rescue plans by civil aviation domain experts under different attributes, including the scores of different rescue plans under attributes in each rescue stage, as well as the membership degree and non-membership degree information corresponding to the scores; A decision matrix construction module, which is used to construct a two-dimensional Pythagorean fuzzy uncertain linguistic evaluation decision matrix based on the collected data, process and transform the collected data through mathematical algorithms and formulas, perceive decision-making information from multiple dimensions, and optimize the PT decision matrix; A weight determination module, which is used to determine the weights of each attribute, combines the subjective weighting method and the objective weighting method by using the fusion weighting method, and calculates and processes through corresponding algorithms and formulas to obtain the fusion weights of each attribute; A plan ranking module, which improves the VIKOR method based on regret theory, calculates the positive ideal plan and negative ideal plan of each alternative plan, calculates the minimum individual regret degree and maximum group benefit of each plan by using the positive ideal plan and negative ideal plan, and ranks the plans according to the compromise ranking value; A result output module, which is used to output the final decision result, including the ranking of different rescue plans in each rescue stage and the selection of the optimal rescue plan.

Images