A method for evaluating maritime decision-making schemes based on subjective and objective weighting of directed graph models

Abstract

The present invention provides a method for evaluating marine decision-making schemes based on subjective and objective weighting of directed graph models, which belongs to the field of data analysis and evaluation of decision-making schemes. The present invention adopts a fuzzy random method to calculate the subjective weight of each evaluation index, and better characterizes the subjectivity and uncertainty of decision-making problems through random simulation and fuzzy set theory; the objective weight of each evaluation index is determined by using a fuzzy entropy value method, and the objective relationship between each marine decision-making scheme and each dimensional information of each indicator is fully reflected in the weight by introducing fuzzy mapping function and information entropy into weight calculation, thereby improving the rationality and reliability of objective weights and reducing the influence of subjective judgment; a directed graph model is used to allocate combined weight indicators combining subjective and objective factors, and the comprehensive score of each marine decision-making scheme is calculated according to the combined weight, which overcomes the deficiency of heavy subjective factors in the evaluation index, and takes into account the influence of objective reality, so as to achieve the purpose of scientific and comprehensive evaluation of marine decision-making schemes.

Description

Technical Field

[0001] The invention belongs to the field of data analysis and evaluation of decision-making schemes and management, supervision and prediction of combat schemes, and relates to a method for evaluating maritime decision-making schemes based on subjective and objective weighting of a directed graph model. Background Art

[0002] Maritime decision-making scheme evaluation is the specific application of decision-making evaluation problems in the fields of management, supervision and prediction of maritime decision-making schemes. The evaluation content covers various elements and corresponding data of maritime confrontation and decision-making schemes, involving relevant theories of maritime confrontation, marine environment and geographic information systems, intelligence surveillance and reconnaissance, confrontation scenario simulation, risk assessment management and decision support systems. These elements together constitute a complex maritime decision-making scheme evaluation framework, which is used to evaluate, analyze and predict the effectiveness and feasibility of maritime decision-making schemes.

[0003] The importance of maritime decision-making scheme evaluation lies in its ability to assist commanders in predicting possible confrontation outcomes, adjusting response strategies, and developing optimal confrontation plans. Due to the complexity of maritime decision-making scheme evaluation, there are inevitably many difficulties in the process, such as too many influencing factors leading to strong overall uncertainty in the system, many judgments relying on expert knowledge leading to strong subjectivity in empowerment, and extreme evaluation results caused by idealized evaluation modeling. In order to solve the negative impact of the above problems on the evaluation results and reduce the unreliability of decision-making scheme evaluation, with the rapid development of computing technology and computer hardware, decision-making scheme evaluation technology and methods are constantly being improved.

[0004] At present, the mainstream decision-making scheme evaluation adopts the form of combining confrontation simulation and mathematical analysis. Through mathematical methods such as scenario analysis, evidence reasoning and Lanchester equation, combined with real confrontation data and simulation data, the decision-making scheme evaluation of maritime confrontation is realized. Although the above methods have played a certain role in the evaluation of decision-making schemes, with the extension of the concept of maritime confrontation and the development of actual equipment, many general technologies and decision-making scheme evaluation methods still face the following challenges in reducing subjective bias and providing reliable decision-making basis, especially under the trend of massive scale of maritime confrontation data, large-scale simulation and real-time scheme evaluation:

[0005] 1) The uncertainty of assessment data is high. Due to factors such as incomplete or inaccurate maritime confrontation intelligence, difficulty in accurately predicting the confrontation effect, and difficulty in quantifying the degree of damage, it is necessary to evaluate maritime decision-making plans based on uncertain information to a large extent;

[0006] 2) The evaluation process is too subjective. Since many issues in the evaluation of maritime decision-making options need to rely on expert knowledge and subjective decisions, the personal experience, preferences or prejudices of decision-makers have a great influence on the evaluation results, which seriously reduces the objectivity and accuracy of the evaluation of maritime decision-making options.

[0007] 3) The evaluation results are extreme. Due to the idealized assumptions of constraints in the existing mathematical models for evaluating offshore decision-making options, the evaluation results of offshore decision-making options are extreme. The evaluation results either harden the scores for decision-making options with no obvious actual differences, or it is difficult to distinguish decision-making options with obvious differences from the evaluation results due to mathematical quantification, which affects the reliability of the decision. Summary of the invention

[0008] In view of the problems of uncertainty information, strong subjectivity and low differentiation of evaluation results in the evaluation of maritime decision-making schemes, the present invention proposes a maritime decision-making scheme evaluation method based on subjective and objective weighting of a directed graph model, including:

[0009] Construct an evaluation index system for maritime decision-making options;

[0010] Constructing an evaluation matrix for each maritime decision-making scheme according to the evaluation index system; wherein the rows of the evaluation matrix represent each maritime decision-making scheme, and the columns represent each evaluation index;

[0011] The subjective weight of each evaluation index in the evaluation matrix is ​​calculated by using a fuzzy random method;

[0012] The objective weight of each evaluation index in the evaluation matrix is ​​calculated by using the fuzzy entropy method;

[0013] Based on the subjective weight and the objective weight, a directed graph model is used to allocate a combined weight index combining subjective and objective factors;

[0014] The comprehensive scores of various maritime decision-making options are calculated and ranked according to the combined weights to obtain the evaluation results of each maritime decision-making option.

[0015] Furthermore, the indicators in the maritime decision-making plan evaluation index system include maritime early warning and detection capability, maritime mission planning capability, maritime confrontation and monitoring capability, maritime command capability, coordinated attack capability, coordinated defense capability, interconnection capability and equipment support capability, etc.

[0016] Furthermore, the method for constructing the evaluation matrix includes:

[0017] For each maritime decision-making plan, data related to each evaluation indicator in the evaluation indicator system is collected, and these data come from actual data, expert evaluation, experimental training, simulation or intelligence analysis;

[0018] The evaluation index data of all the marine decision-making schemes are combined into an evaluation matrix in the form of a two-dimensional array, wherein the rows represent different marine decision-making schemes and the columns represent different evaluation indexes; the value of each element in the evaluation matrix represents the performance of a marine decision-making scheme on a certain evaluation index;

[0019] The different evaluation indicators in the evaluation matrix are standardized using the minimum-maximum standardization method; wherein, for indicators with larger evaluation indicator values ​​and higher comprehensive evaluation values, the standardization formula is:

[0020]

[0021] For indicators with smaller evaluation index values ​​and higher comprehensive evaluation values, the standardized formula is:

[0022]

[0023] Among them, x is the original data, X is the standardized data, and They are the minimum and maximum values ​​of all the data of the evaluation indicator.

[0024] Furthermore, the calculation method of the subjective weight of each evaluation indicator in the evaluation matrix includes:

[0025] By fuzzy mapping in a fuzzy random method, the deterministic data in the evaluation matrix is ​​converted into fuzzy numerical values ​​to generate a fuzzy evaluation matrix; the fuzzy numerical values ​​in the fuzzy evaluation matrix are used to characterize the subjectivity of the evaluation indicators of the marine decision-making scheme;

[0026] For each fuzzy value in the fuzzy evaluation matrix, a set of random numbers is generated using a random simulation method of a fuzzy random method to characterize the uncertainty of the evaluation index of the marine decision-making scheme, and a random number matrix is ​​constructed;

[0027] A random fuzzy matrix is ​​constructed by using the fuzzy evaluation matrix and the random number matrix; relative proximity is calculated based on the random fuzzy matrix, and a subjective weight is generated.

[0028] Furthermore, the construction process of the fuzzy evaluation matrix is ​​as follows:

[0029] The fuzzy mapping that converts the deterministic data in the evaluation matrix into fuzzy values ​​is expressed as follows:

[0030]

[0031] in, It is The maritime decision-making program is Fuzzy numerical values ​​on evaluation indicators; is the original deterministic data in the evaluation matrix; It is The fuzzy mapping function of the evaluation index can be expressed by the following formula:

[0032]

[0033] in, Indicates The minimum value of all data of the evaluation index, Indicates The maximum value of all data of the evaluation index;

[0034] The obtained fuzzy values ​​are normalized, and the fuzzy evaluation matrix is ​​generated from the normalized fuzzy values; the normalization formula is:

[0035]

[0036] in, is the first in the normalized evaluation matrix The maritime decision-making program is Fuzzy numerical values ​​on evaluation indicators, is the number of decision options at sea.

[0037] Furthermore, the specific process of using the random simulation method to generate a set of random numbers and construct a random number matrix is ​​as follows:

[0038] The random simulation method generates random numbers by inverse transformation according to the fuzzy mapping function; assuming that U is a random number uniformly distributed in the interval [0,1], then the corresponding random value is It can be obtained by the following inverse transformation formula:

[0039]

[0040] in, is the fuzzy mapping function The cumulative distribution function is used to convert the distribution of fuzzy values, that is, uncertainty, into a probability value with statistical significance. It can be expressed by the following formula:

[0041]

[0042] The above inverse transformation process uses a new random number U each time, and can be used for each Generate a random value , by repeating Select a random number each time A set of random values ​​can be obtained, that is, a set of The corresponding dimension is , which can generate a matrix with dimension Three-dimensional random number matrix .in, is the number of decision options at sea, is the number of evaluation metrics; Each value in reflects the randomness of the corresponding indicators of different schemes under different random conditions, laying the foundation for describing data uncertainty in subsequent steps. At the same time, multiple random samplings are used to take into account the effectiveness and extensiveness of fitting uncertainty to prevent falling into local optimality.

[0043] Furthermore, the calculation process of the subjective weight is:

[0044] According to the fuzzy evaluation matrix and the random number matrix ,based on The third dimension uses element-by-element multiplication to construct a random fuzzy matrix :

[0045] =

[0046] Among them, the matrix By transforming the fuzzy evaluation matrix The first two dimensions are replicated along the third dimension times obtained;

[0047] The fuzzy distance formula is used to calculate the distance between each indicator and other indicators. The fuzzy distance formula is as follows:

[0048]

[0049] Among them, A and B are any two evaluation indicators, and are the random fuzzy values ​​of the corresponding indexes of indicators A and B in the three-dimensional matrix, that is, and Random fuzzy matrix Elements in

[0050] According to the above fuzzy distance formula, the fuzzy distance of the jth index is: ;

[0051] Based on the fuzzy distance formula, the fuzzy distance between the jth evaluation index and the ideal solution O at different indexes in the third dimension is calculated and sorted to obtain the minimum distance between the jth evaluation index and the ideal solution. ; The fuzzy distance calculation formula of different indexes in the third dimension is as follows:

[0052]

[0053] Calculate the average distance between the jth evaluation index and the ideal solution O in the third dimension , No. The average distance between the evaluation index and the worst solution in the third dimension ;

[0054] According to the distance between each offshore decision-making plan and the ideal solution and the distance between each offshore decision-making plan and the worst solution, the relative closeness is calculated as follows:

[0055]

[0056] in, It is The relative closeness of the evaluation indicators, It is The average distance between the evaluation index and the ideal solution in the third dimension, It is The average distance between the evaluation index and the worst solution in the third dimension, It is An evaluation index and the minimum distance to the ideal solution;

[0057] The subjective weight of the jth evaluation indicator is calculated based on the relative proximity, and the formula is:

[0058]

[0059] Finally, construct a set of subjective weights for each evaluation indicator .

[0060] Furthermore, the methods for determining the ideal solution and the worst solution include: determining the ideal solution and the worst solution according to the theoretical optimal and worst quantized values ​​of the evaluation index set, determining the ideal solution and the worst solution according to pre-set rules, and outputting the ideal solution and the worst solution according to the random fuzzy matrix by a heuristic algorithm or a deep learning model, etc.; wherein, the heuristic or deep learning method needs to design a reasonable optimization target and train the parameters of the relevant model through labeled positive and negative samples to support the output of the ideal solution or the worst solution. Based on the above random fuzzy algorithm, if the computing power allows, this method has the ability to analyze high-dimensional evaluation indicators based on a deep model.

[0061] Furthermore, the fuzzy entropy method is used to determine the objective weights, reduce the influence of subjective judgment, and better describe the uncertainty and ambiguity in the evaluation of maritime decision-making schemes by introducing fuzzy mapping functions and information entropy into weight calculation. The specific process is as follows:

[0062] The information entropy of each indicator is calculated based on the normalized fuzzy value. The information entropy reflects the degree of discreteness of the indicator. If the data points are evenly distributed within a certain range, the degree of discreteness of the distribution is high and the information entropy is also large; on the contrary, if most of the data points are concentrated in a small range, the degree of discreteness is lower and the information entropy is smaller. The calculation formula of information entropy is:

[0063]

[0064] in, It is The information entropy of the evaluation index is After normalization, The maritime decision-making program is Fuzzy numerical values ​​on evaluation indicators;

[0065] Calculate the weight of each evaluation indicator. The weight is inversely proportional to the information entropy, that is, the smaller the information entropy, the greater the weight. The weight calculation formula is:

[0066]

[0067] in, It is The weight of each evaluation indicator;

[0068] Using the calculated weights and the original deterministic data, the comprehensive score of each evaluation indicator is calculated as follows:

[0069]

[0070] in, For the The comprehensive score of the evaluation indicators is is the raw deterministic data of the evaluation matrix;

[0071] The objective weight of each evaluation indicator is calculated based on the comprehensive score. The formula is:

[0072]

[0073] Finally, determine the objective weight set of each evaluation indicator .

[0074] Furthermore, a directed graph model is used to allocate combined weight indicators that combine subjective and objective factors to overcome the shortcomings of relying solely on subjective or objective factors when evaluating maritime decision-making options. At the same time, the actual impact is taken into account to ensure the interpretability of the weight indicator allocation method and enhance the distinction between the evaluation results of different maritime decision-making options, thereby improving the practicality and rationality of the evaluation of maritime decision-making options. The specific process is as follows:

[0075] The topological structure of the directed graph model is determined according to the evaluation matrix, including nodes and directed edges, where nodes represent indicators and directed edges represent dependencies or influences between indicators; wherein the dependencies or influences are determined according to the evaluation indicator system, which is equivalent to generating an adjacency list according to preset rules or manual designation when constructing the evaluation matrix, which can be directly used to guide the construction of directed edges in the directed graph. In different indicator systems, the dependencies or influences are generally reflected as vertical associations or horizontal associations. Vertical associations refer to the fact that the evaluation indicator system has a three-dimensional hierarchical structure, such as the indicator value of the first-level indicator needs to be comprehensively calculated based on the indicator value of the second-level indicator; horizontal associations refer to the existence of related influences in the evaluation indicator system, such as the indicator values ​​of some evaluation indicators need to be comprehensively calculated based on the indicator values ​​of related evaluation indicators at the same level;

[0076] Determine the conditional probability of nodes in the graph structure; when the directed graph model is a Bayesian network, define a conditional probability table (CPT) for each node in the Bayesian network, which contains the conditional probability (weight) of the indicator under different associations; each entry of the CPT Indicated in the indicator As an indicator Under the condition of the associated index, the index The conditional probability of

[0077] The evaluation matrix is ​​used to estimate the parameters of the conditional probability in the Bayesian network. The parameters in CPT are:

[0078]

[0079] in, is the estimated conditional probability; in Bayesian networks, It is in the indicator Related indicators The number of connections;

[0080] The subjective weight of each evaluation index As prior knowledge, the objective weight As new knowledge, it is integrated, combining subjective weights and objective weights, using Bayesian network for reasoning, and calculating the combined weights of subjective and objective combinations of each evaluation indicator based on the conditional probability table and known indicator information. , the formula is as follows:

[0081]

[0082] in, is the combined weight; It is the coefficient for adjusting the influence of subjective and objective weights.

[0083] Furthermore, the comprehensive scores of the various marine decision-making schemes are calculated based on the combined weights and sorted to obtain evaluation results of multiple marine decision-making schemes. The specific process is as follows:

[0084] For each maritime decision option, its composite score is calculated using the following formula:

[0085]

[0086] in, It is The comprehensive score of the maritime decision-making options;

[0087] All maritime decision-making plans are sorted from high to low according to the comprehensive scores to obtain the evaluation results of each maritime decision-making plan.

[0088] Beneficial effects of the present invention:

[0089] The fuzzy random method is used to calculate the subjective weights of the evaluation matrix of multiple decision-making schemes at sea. Through fuzzy set theory and random simulation, the subjectivity and uncertainty of maritime decision-making problems can be better characterized, and an objective formal description of the subjective factors in the evaluation of maritime decision-making schemes can be achieved.

[0090] The objective weights of the evaluation indicators of multiple decision-making schemes at sea are determined by using the fuzzy entropy method. By combining the fuzzy concept with the information entropy technology, the objective relationship between each marine decision-making scheme and each indicator in each dimension is fully reflected in the weight, which improves the rationality and reliability of the objective weights and reduces the influence of subjective judgment.

[0091] 3) A directed graph model is used to allocate combined weight indicators that combine subjective and objective factors. The subjective weight and objective weight are combined through the directed graph model to generate a comprehensive weight. This not only takes into account the subjective factors in the evaluation of maritime decision-making options, but also covers the inherent objective relationship reflected by the data. At the same time, based on the combination principle of subjective and objective weighting and reasonable judgment criteria, the interpretability of the weight indicator allocation method is guaranteed, the distinction between the evaluation results of different maritime decision-making options is enhanced, and the practicality and rationality of the evaluation of maritime decision-making options are improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0092] Figure 1 is a flow chart of an embodiment of the present invention.

[0093] Figure 2 The flowchart of using Bayesian network to fuse subjective weight and objective weight in an embodiment of the present invention. DETAILED DESCRIPTION

[0094] The following is a detailed description of the embodiments of the present invention in conjunction with the accompanying drawings and technical solutions.

[0095] like Figure 1As shown, this embodiment provides a method for evaluating marine decision-making schemes based on subjective and objective weighting of a directed graph model, comprising the following steps:

[0096] Step S1: In accordance with the principles of constructing a maritime decision-making solution evaluation indicator system, establish a systematic, complete, independent and quantifiable set of maritime decision-making solution evaluation indicators, which includes maritime early warning and detection capabilities, maritime mission planning capabilities, maritime confrontation monitoring capabilities, maritime command capabilities, coordinated attack capabilities, coordinated defense capabilities, interconnection capabilities and equipment support capabilities, etc., to ensure that each indicator is directly related to the maritime confrontation target and the purpose of decision-making solution evaluation, and to reasonably control the scale of the indicator set.

[0097] Assume that offshore decision options to be evaluated and evaluation index, let The evaluation index set of the marine decision-making scheme is ,in Indicates The first of the maritime decision-making programs evaluation index value.

[0098] Step S2: Based on the set of evaluation indicators established in step S1, an evaluation matrix C is constructed for each marine decision-making scheme.

[0099] The evaluation matrix is ​​a two-dimensional array, in which rows represent different maritime decision-making schemes and columns represent different evaluation indicators; data related to each evaluation indicator are collected, and these data come from actual data, expert evaluation, experimental training, simulation deduction or intelligence analysis; the data related to each evaluation indicator are converted into numerical data through quantitative methods, and the numerical data are filled into the evaluation matrix. The value of each element in the evaluation matrix represents the performance of a maritime decision-making scheme on a certain evaluation indicator.

[0100] Then, the different evaluation indicators in the evaluation matrix are standardized using the minimum-maximum standardization method; wherein, for indicators with larger evaluation indicator values ​​and higher comprehensive evaluation values, the standardization formula is:

[0101]

[0102] For indicators with smaller evaluation index values ​​and higher comprehensive evaluation values, the standardized formula is:

[0103]

[0104] Among them, x is the original data, X is the standardized data, and They are the minimum and maximum values ​​of all the data of the evaluation indicator.

[0105] The standardized evaluation matrix C is shown as follows:

[0106] .

[0107] Step S3: using the standardized evaluation matrix C in step S2, the deterministic data in the evaluation matrix is ​​converted into fuzzy numerical values ​​through the designed fuzzy random method, and a random number matrix is ​​generated. Finally, a random fuzzy matrix is ​​constructed according to the fuzzy numerical values ​​and random numbers to generate subjective weights, so as to realize the formal description of subjective evaluation and its uncertainty in the evaluation of marine decision-making schemes. The steps include:

[0108] Firstly, the deterministic data in the evaluation matrix are converted into fuzzy numerical values ​​through fuzzy mapping in the fuzzy random method to generate a fuzzy evaluation matrix; these fuzzy numerical values ​​in the fuzzy evaluation matrix are used to characterize the subjectivity of the evaluation indicators of the maritime decision-making scheme; then, for each fuzzy numerical value in the fuzzy evaluation matrix, a set of random numbers are generated using the random simulation method of the fuzzy random method to characterize the uncertainty of the evaluation indicators of the maritime decision-making scheme, and a random number matrix is ​​constructed; finally, a random fuzzy matrix is ​​constructed using the fuzzy evaluation matrix and the random number matrix to generate subjective weights, so as to more accurately capture and express the subjectivity and uncertainty in the decision-making process, and solve the uncertainty and subjective representation of weights in the evaluation of maritime decision-making schemes.

[0109] Specifically, the fuzzy mapping that converts the deterministic data in the evaluation matrix into fuzzy values ​​is expressed as follows:

[0110]

[0111] in, It is The maritime decision-making program is Fuzzy numerical values ​​on evaluation indicators; is the original deterministic data in the evaluation matrix; It is The fuzzy mapping function of the evaluation index needs to be explained. It can be a mapping function with unknown parameters or a manually designed or parameter-free mapping function. The mapping function with unknown parameters can adopt Gaussian function, bell-shaped function, step function, etc., or a single-layer or multi-layer neural network, extreme learning machine and other latent variable models. The former can simplify the function parameter estimation problem into a linear transformation function after manual setting. A common parameter-free form of can be expressed as:

[0112]

[0113] in, Indicates The minimum value of all data of the evaluation index, Indicates The maximum value of all the data of the evaluation indicator.

[0114] The obtained fuzzy values ​​are normalized so that the fuzzy values ​​of each evaluation index can be compared on the same scale. The normalization formula is:

[0115]

[0116] in, is the first in the normalized evaluation matrix The maritime decision-making program is The fuzzy numerical value of the evaluation index.

[0117] The fuzzy evaluation matrix is ​​generated by the normalized fuzzy numerical values, which are used to describe the subjectivity of each scheme in each indicator.

[0118] For each fuzzy value in the fuzzy evaluation matrix, a set of random numbers is generated using the random simulation method of the fuzzy random method. The random numbers can describe the uncertainty of the data by combining random simulation and fuzzy logic. In actual decision-making problems, uncertainty generally stems from the randomness and unknown nature of variables. This randomness is essentially a manifestation of cognitive subjectivity and incomplete information. The random numbers generated based on fuzzy values ​​can unify these two characteristics under one framework for analysis. Therefore, the fuzzy random method can better characterize the subjectivity and uncertainty of decision-making problems. The specific steps are as follows:

[0119] The random simulation method generates random numbers by inverse transformation according to the fuzzy mapping function; assuming that U is a random number uniformly distributed in the interval [0,1], then the corresponding random fuzzy value It can be obtained by the following inverse transformation formula:

[0120]

[0121] in, is the fuzzy mapping function The cumulative distribution function of It is used to convert the distribution of fuzzy values, i.e. uncertainty, into probability values ​​with statistical significance. It can be expressed by the following formula:

[0122]

[0123] The above inverse transformation process uses a new random number U each time, and can be used for each Generate a random value , by repeating Select a random number each time A set of random values ​​can be obtained, that is, a set of The corresponding dimension is , which can generate a matrix with dimension Three-dimensional random number matrix . Each value in reflects the randomness of the corresponding indicators of different schemes under different random conditions, laying the foundation for describing data uncertainty in subsequent steps. At the same time, multiple random samplings are used to take into account the effectiveness and extensiveness of fitting uncertainty to prevent falling into local optimality.

[0124] According to the fuzzy evaluation matrix and the random number matrix ,based on The third dimension uses element-by-element multiplication to construct a random fuzzy matrix :

[0125]

[0126] Among them, the matrix By transforming the fuzzy evaluation matrix The first two dimensions are replicated along the third dimension times obtained.

[0127] In the random fuzzy matrix On the basis of the ideal solution and the worst solution, the fuzzy distance formula is used to calculate the distance between each offshore decision-making scheme and the ideal solution and the worst solution. The fuzzy distance formula is as follows:

[0128] d(A,B)=

[0129] Among them, A and B are any two evaluation indicators; and are the random fuzzy values ​​of the corresponding indexes of indicators A and B in the three-dimensional matrix, that is, and Random fuzzy matrix According to the above formula, we can get the elements in The fuzzy distance of the evaluation index is .

[0130] Based on the fuzzy distance formula, the The fuzzy distances of the evaluation indicators with different indexes in the third dimension and the ideal solution O are sorted and the first The minimum distance between the evaluation index and the ideal solution ;

[0131] Calculate the The average distance between the evaluation index and the ideal solution in the third dimension , No. The average distance between the evaluation index and the worst solution in the third dimension ;

[0132] Then, the relative closeness is calculated based on the distance between each marine decision-making scheme and the ideal solution and the distance between each marine decision-making scheme and the worst solution. The calculation formula of the relative closeness is:

[0133]

[0134] in, It is The relative closeness of the evaluation indicators, It is The average distance between the evaluation index and the ideal solution in the third dimension, It is The average distance between the evaluation index and the worst solution in the third dimension, It is The minimum distance between an evaluation indicator and the ideal solution.

[0135] It should be noted that the method of determining the ideal solution and the worst solution includes but is not limited to determining the ideal solution and the worst solution based on the theoretical optimal and worst quantitative values ​​of the evaluation index system, determining the ideal solution and the worst solution based on pre-set rules, and outputting the ideal solution and the worst solution based on the random fuzzy matrix by a heuristic algorithm or a deep learning model, etc.; among them, the heuristic or deep learning method needs to design a reasonable optimization goal and train the parameters of the relevant model through labeled positive and negative samples to support the output of the ideal solution or the worst solution. Based on the above random fuzzy algorithm, if the computing power allows, this method has the ability to analyze high-dimensional evaluation indicators based on a deep model.

[0136] Calculate the first The subjective weight of the evaluation index is calculated as follows:

[0137]

[0138] Finally, construct a set of subjective weights for each evaluation indicator .

[0139] Step S4: Use the fuzzy entropy method to determine the objective weights, reduce the influence of subjective judgment, and better describe the uncertainty and ambiguity in the evaluation of maritime decision-making options by introducing fuzzy mapping functions and information entropy into weight calculations. The specific process is:

[0140] The information entropy of each indicator is calculated based on the normalized fuzzy value. The information entropy reflects the degree of discreteness of the indicator. If the data points are evenly distributed within a certain range, the degree of discreteness of the distribution is high and the information entropy is also large; on the contrary, if most of the data points are concentrated in a small range, the degree of discreteness is lower and the information entropy is smaller. The calculation formula of information entropy is:

[0141]

[0142] in, It is The information entropy of the evaluation index is After normalization, The maritime decision-making program is The fuzzy numerical value of the evaluation index.

[0143] Calculate the weight of each evaluation indicator. The weight is inversely proportional to the information entropy, that is, the smaller the information entropy, the greater the weight. The weight calculation formula is:

[0144]

[0145] in, It is The weight of the evaluation indicator.

[0146] Using the calculated weights and the original deterministic data, the comprehensive score of each evaluation indicator is calculated as follows:

[0147]

[0148] in, For the The comprehensive score of the evaluation indicators is is the raw deterministic data of the evaluation matrix.

[0149] The objective weight of each evaluation indicator is calculated according to the comprehensive score. The formula is:

[0150]

[0151] Finally, determine the objective weight of each evaluation indicator .

[0152] Step S5: A Bayesian network is used to perform a combined weight index allocation method combining subjective and objective factors to overcome the deficiency of relying solely on subjective or objective factors when evaluating maritime decision-making schemes. At the same time, the actual impact is taken into account to ensure the interpretability of the weight index allocation method, enhance the differentiation of evaluation results of different maritime decision-making schemes, and thus improve the practicality and rationality of maritime decision-making scheme evaluation;

[0153] The topological structure of the Bayesian network is determined according to the evaluation matrix C, including nodes and directed edges, where nodes represent indicators, and directed edges represent dependencies or influences between indicators; wherein the dependencies or influences are determined according to the evaluation indicator system, which is equivalent to generating an adjacency list according to preset rules or manual designation when constructing the evaluation matrix, which can be directly used to guide the construction of directed edges in the directed graph. In different indicator systems, the dependencies or influences are generally reflected as vertical associations or horizontal associations. Vertical associations refer to the fact that the evaluation indicator system has a three-dimensional hierarchical structure, such as the indicator value of the first-level indicator needs to be comprehensively calculated based on the indicator value of the second-level indicator; horizontal associations refer to the existence of related influences in the evaluation indicator system, such as the indicator values ​​of some evaluation indicators need to be comprehensively calculated based on the indicator values ​​of related evaluation indicators at the same level;

[0154] Define a conditional probability table (CPT) for each node in the Bayesian network, which contains the conditional probability (weight) of the indicator under different associations; each entry of the CPT Indicated in the indicator As an indicator Under the condition of the associated index, the index The conditional probability of

[0155] The evaluation matrix C is used to estimate the parameters of the conditional probability in the Bayesian network. The parameters in CPT are:

[0156]

[0157] in, is the estimated conditional probability. In the Bayesian network, It is in the indicator Related indicators The number of connections;

[0158] The subjective weight of each evaluation index As prior knowledge, the objective weight As new knowledge, it is integrated, combining subjective weights and objective weights, using Bayesian network for reasoning, and calculating the combined weights of subjective and objective combinations of each evaluation indicator based on the conditional probability table and known indicator information. ; The fusion method can be obtained by the following formula, which adjusts and updates the weights according to the conditional probability CPT in the Bayesian network:

[0159]

[0160] in, is the combination weight, It is the coefficient for adjusting the influence of subjective and objective weights.

[0161] Step S6: Calculate the comprehensive scores of each marine decision-making scheme based on the combined weights and sort them to obtain the evaluation results of multiple marine decision-making schemes; the specific process is:

[0162] For each maritime decision option, its composite score is calculated using the following formula:

[0163]

[0164] in, It is The comprehensive score of the maritime decision-making options, It is The maritime decision-making program is The standardized value of the evaluation indicator.

[0165] Finally, all maritime decision-making options are sorted from high to low according to the comprehensive scores to obtain the evaluation results of each maritime decision-making option.

[0166] 1) The opinions of 5 experts were sorted out and 8 evaluation indicators of maritime decision-making solutions were summarized and designed. The data are shown in Table 1. For the convenience of presentation, Table 1 uses the transposition of the aforementioned evaluation indicators, where rows represent evaluation indicators and columns represent maritime decision-making solutions;

[0167] Table 1 Evaluation index matrix for offshore decision-making options

[0168]

[0169] 2) Standardize the evaluation matrix through the standardization method to obtain the standardized evaluation matrix C;

[0170] C=

[0171] 3) Taking the offshore decision-making scheme 1 as an example, adopt The evaluation matrix is ​​fuzzy mapped and stochastically simulated, where The random fuzzy matrix R1 of dimension is:

[0172] R1=

[0173] 4) Similarly, we can get the offshore decision plan 2 to the offshore decision plan 4 in Dimensional random fuzzy matrices R2~R4;

[0174] R2=

[0175] R3=

[0176] R4=

[0177] 5) According to steps S3, S4 and S5, the subjective weight, objective weight and combined weight are calculated respectively, and the data are shown in Table 2;

[0178] Table 2

[0179]

[0180] 6) Calculate the final score of each marine decision-making scheme, as shown in Table 3;

[0181] Table 3

[0182]

[0183] 7) Use fuzzy comprehensive evaluation results for sorting.

[0184]

[0185] It should be noted that the above embodiments are intended to illustrate the technical solutions of the present invention and do not constitute any form of limitation on the present invention. Those skilled in the art should fully understand that it is completely feasible to modify the technical solutions described in the above embodiments or to perform equivalent replacements on any part or all of the technical features. These modifications or replacements, as long as they do not deviate from the scope of protection determined by the claims of the present invention, should be regarded as reasonable extensions of the present invention.

Claims

1. A method for evaluating marine decision-making schemes based on subjective and objective weighting of directed graph models, characterized in that: include: Construct an evaluation index system for maritime decision-making solutions, with dependencies or influence relationships between the evaluation indicators; The dependency or influence relationship is reflected in vertical association or horizontal association. Vertical association means that the evaluation index system has a three-dimensional hierarchical structure, and horizontal association means that the evaluation index system has related influences. The indicators in the evaluation index system for maritime decision-making solutions include maritime early warning and detection capability, maritime mission planning capability, maritime confrontation and monitoring capability, maritime command capability, coordinated attack capability, coordinated defense capability, interconnection capability and equipment support capability. Constructing an evaluation matrix for each maritime decision-making scheme according to the evaluation index system; wherein the rows of the evaluation matrix represent each maritime decision-making scheme, and the columns represent each evaluation index; The subjective weight of each evaluation index in the evaluation matrix is ​​calculated using a fuzzy random method; specifically, the following steps are included: Through the fuzzy mapping in the fuzzy random method, the deterministic data in the evaluation matrix is ​​converted into fuzzy values ​​to generate a fuzzy evaluation matrix; the construction process of the fuzzy evaluation matrix is ​​as follows: The fuzzy mapping that converts the deterministic data in the evaluation matrix into fuzzy values ​​is expressed as follows: in, It is The maritime decision-making program is Fuzzy numerical values ​​on evaluation indicators; is the original deterministic data in the evaluation matrix; It is The fuzzy mapping function of the evaluation index is expressed by the following formula: in, Indicates The minimum value of all data of the evaluation index, Indicates The maximum value of all data of the evaluation index; The obtained fuzzy value Normalization is performed, and the normalized fuzzy value Generate fuzzy evaluation matrix; For each fuzzy value in the fuzzy evaluation matrix, a set of random numbers is generated using the random simulation method of the fuzzy random method, and a random number matrix is ​​constructed; the specific process is: Let U be a random number uniformly distributed in the interval [0,1], then the corresponding random value Obtained by the following inverse transformation formula: in, is the fuzzy mapping function The cumulative distribution function is used to convert the distribution of fuzzy values, that is, uncertainty, into a probability value with statistical significance. It is expressed by the following formula: The above inverse transformation process uses a new random number U each time, which can be used for each fuzzy value in the fuzzy evaluation matrix Generate a random value , by repeating Select random numbers, each fuzzy value Get a set of random values, that is, get a set of dimensions corresponding to the fuzzy value , thus generating a matrix with dimension Three-dimensional random number matrix ;in, is the number of decision options at sea, is the number of evaluation metrics; The fuzzy evaluation matrix and the random number matrix are used to construct a random fuzzy matrix; the relative proximity is calculated based on the random fuzzy matrix, and a subjective weight is generated; the calculation process of the subjective weight is: According to the fuzzy evaluation matrix and the random number matrix ,based on The third dimension uses element-by-element multiplication to construct a random fuzzy matrix : Among them, the matrix By transforming the fuzzy evaluation matrix The first two dimensions are replicated along the third dimension times obtained; The fuzzy distance formula is used to calculate the distance between each indicator and other indicators. The fuzzy distance formula is as follows: Among them, A and B are any two evaluation indicators, and are the random fuzzy values ​​of the corresponding indexes of indicators A and B in the three-dimensional matrix, that is, and Belongs to random fuzzy matrix Elements in According to the above fuzzy distance formula, we can get The fuzzy distance of the indicator is ; Based on the fuzzy distance formula, the The fuzzy distances of the evaluation indicators with different indexes in the third dimension and the ideal solution O are sorted and the first The minimum distance between the evaluation index and the ideal solution ; The fuzzy distance calculation formula of different indexes in the third dimension is as follows: Calculate the The average distance between the evaluation index and the ideal solution in the third dimension , No. The average distance between the evaluation index and the worst solution in the third dimension ; Calculate the The relative closeness of the evaluation indicators , the formula is: Calculate the first The subjective weight of the evaluation index is as follows: Finally, construct a set of subjective weights for each evaluation indicator ; The objective weight of each evaluation index in the evaluation matrix is ​​calculated using the fuzzy entropy method; the specific process is as follows: Calculate the information entropy of each indicator based on the normalized fuzzy value , the formula is: in, After normalization, The maritime decision-making program is Fuzzy numerical values ​​on evaluation indicators; Calculate the weight of each evaluation metric , the formula is: Using the calculated weights and the original deterministic data, the comprehensive score of each evaluation indicator is calculated as follows: in, For the The comprehensive score of the evaluation indicators is is the raw deterministic data of the evaluation matrix; The objective weight of each evaluation indicator is calculated based on the comprehensive score. The formula is: Finally, determine the objective weight set of each evaluation indicator ; Based on the subjective weight and the objective weight, a directed graph model is used to allocate a combined weight index combining subjective and objective factors. The specific process is as follows: Determine the topological structure of the directed graph model according to the evaluation matrix, including nodes and directed edges, where the nodes represent indicators and the directed edges represent the association relationship between indicators; When the directed graph model is a Bayesian network, a conditional probability table CPT is defined for each node in the Bayesian network. The table contains the conditional probabilities of indicators under different associations. Each entry in the CPT Indicated in the indicator As an indicator Under the condition of the associated index, the index The conditional probability of The evaluation matrix is ​​used to estimate the parameters of the conditional probability in the Bayesian network. The parameters in CPT are: in, is the estimated conditional probability; in Bayesian networks, It is in the indicator Related indicators The number of connections; The subjective weight of each evaluation index As prior knowledge, the objective weight As new knowledge, it is integrated, combining subjective weights and objective weights, using Bayesian network for reasoning, and calculating the combined weights of subjective and objective combinations of each evaluation indicator based on the conditional probability table and known indicator information. , the formula is as follows: in, is the combined weight; It is the coefficient to adjust the influence of subjective and objective weights; The comprehensive scores of each maritime decision-making scheme are calculated and ranked according to the combined weights to obtain the evaluation results of each maritime decision-making scheme; the specific process is as follows: The comprehensive score of each maritime decision-making option is calculated as follows: in, It is The comprehensive score of the maritime decision-making options; All maritime decision-making plans are sorted from high to low according to the comprehensive scores to obtain the evaluation results of each maritime decision-making plan.

2. According to claim 1, a method for evaluating marine decision-making schemes based on subjective and objective weighting of directed graph models is characterized in that: The method for constructing the evaluation matrix includes: Collect the evaluation index data of all maritime decision-making schemes and form an evaluation matrix in the form of a two-dimensional array, where the rows represent different maritime decision-making schemes and the columns represent different evaluation indicators; The different evaluation indicators in the evaluation matrix are standardized using the minimum-maximum standardization method.

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