A charging pile site selection multi-criteria decision method based on pythagorean fuzzy sets

Abstract

The application discloses a charging pile site selection multi-criteria decision method based on a Pythagorean fuzzy set, and comprises the following steps: obtaining an individual Pythagorean fuzzy decision matrix, then normalizing the matrix, and calculating an average Pythagorean fuzzy decision matrix; calculating the Hamming distance and Chebyshev distance between the normalized Pythagorean fuzzy decision matrix and the average Pythagorean fuzzy decision matrix, integrating the comprehensive distance to determine the expert weight; calculating the group Pythagorean fuzzy decision matrix based on the expert weight, and then calculating the knowledge measure matrix to determine the index weight; by comparing the size of the Pythagorean fuzzy number in the group matrix, the positive ideal solution and the negative ideal solution are determined, then the positive ideal deviation and the grey correlation degree are calculated according to the Pythagorean fuzzy distance measure satisfying the triangular inequality property, the comprehensive score of the scheme is obtained, the scheme is sorted, and the optimal new energy automobile charging pile site selection scheme is obtained.

Description

Technical Field

[0001] This invention relates to the field of planning technology for supporting facilities for new energy vehicles that integrate transportation and energy, specifically to a multi-criteria decision-making method for charging pile site selection based on Pythagorean fuzzy sets, which is specifically applied to the site selection planning and scheme decision-making process of new energy vehicle charging pile sites in scenarios such as cities, parks, and roads. Background Technology

[0002] The rationality of charging pile site selection directly affects the convenience of using new energy vehicles, the efficiency of charging services, the stability of power grid operation, and the economic benefits of construction and operation. The site selection decision-making level is influenced by multiple factors, including geographical distribution, power grid capacity, traffic conditions, land costs, and population density, and is characterized by multi-objective coupling, high uncertainty, and complex constraints. Scientifically formulating charging pile site selection decision-making schemes is of great significance for improving supporting facilities for new energy vehicles, promoting the integrated development of transportation and energy, and realizing the large-scale and refined construction of charging piles.

[0003] Currently, the following technical methods are mainly used for determining the location of charging stations:

[0004] 1. Site selection methods based on traditional mathematical models, such as the centroid method, coverage model, and integer programming model. These methods are simple in structure and easy to implement, but they usually only focus on deterministic indicators such as geographical distance and service coverage, making it difficult to accurately characterize the fuzzy and uncertain characteristics that are common in the site selection process, thus limiting the rationality of the decision.

[0005] 2. Site selection methods based on traditional multi-attribute decision-making, such as the analytic hierarchy process (AHP) and entropy weighting combined with comprehensive scoring. These methods consider multiple influencing factors to some extent, but the weight allocation relies heavily on expert subjective experience, lacks objective quantitative basis, and cannot effectively handle the dual characteristics of hesitation and ambiguity in indicator evaluation, resulting in insufficient decision-making accuracy.

[0006] 3. Multi-attribute decision-making and location selection methods based on fuzzy information fusion, such as fuzzy comprehensive evaluation and intuitionistic fuzzy TOPSIS, can handle some fuzzy information and improve the comprehensiveness of decision-making. However, in practical applications, the following problems still exist: insufficient accuracy in describing multi-dimensional fuzzy information, making it difficult to accurately reflect the true uncertainty state of location selection indicators; most methods only focus on the absolute superiority or inferiority comparison of indicators or single correlation analysis, failing to take into account the advantages of both; and the models do not fully consider the differences in needs of different application scenarios, resulting in deviations between the decision scheme and the actual application scenario.

[0007] Furthermore, most existing technologies do not deeply integrate fuzzy information processing with multi-attribute decision-making methods, and fail to effectively distinguish the impact characteristics of different types of uncertainty, making it difficult for models to simultaneously take into account the scientific nature, accuracy, and applicability of decision-making. Summary of the Invention

[0008] The purpose of this invention is to address the characteristics of multi-attribute, fuzzy, and uncertain evaluation index information involved in the site selection assessment of new energy vehicle charging piles. Pythagorean fuzzy sets can describe evaluation information from both membership and non-membership perspectives, improving the modeling effect of practical decision-making problems and effectively handling uncertain information. Therefore, a multi-criteria decision-making method for charging pile site selection based on Pythagorean fuzzy sets is proposed.

[0009] The technical solution adopted in this invention is as follows:

[0010] A multi-criteria decision-making method for charging pile site selection based on Pythagorean fuzzy sets includes the following steps:

[0011] S1: The evaluation information given by multiple experts using Pythagorean fuzzy numbers is organized to obtain the individual Pythagorean fuzzy decision matrix. Then, the matrix is ​​normalized and the average Pythagorean fuzzy decision matrix is ​​calculated.

[0012] S2: Calculate the Hamming distance and Chebyshev distance between the normalized Pythagorean fuzzy decision matrix and the average Pythagorean fuzzy decision matrix, integrate them to obtain the comprehensive distance, and determine the expert weights;

[0013] S3: Calculate the group Pythagorean fuzzy decision matrix based on expert weights, and then calculate the knowledge measurement matrix to determine the indicator weights;

[0014] S4: By comparing the magnitudes of the Pythagorean fuzzy numbers in the group matrix, the positive and negative ideal solutions are determined. Then, based on the Pythagorean fuzzy distance measure that satisfies the property of the triangle inequality, the positive and negative ideal deviations and grey relational degree are calculated to obtain the comprehensive score of the scheme. The schemes are then ranked to obtain the optimal new energy vehicle charging pile site selection scheme.

[0015] Furthermore, step S1 is implemented through the following steps:

[0016] Let the set of schemes be Experts gathered , Let be the expert weight vector, satisfying The indicator set is , Let be the indicator weight vector, satisfying Assume l experts rank and select the best option from m solutions based on n criteria; assume the experts... The given indicators Regarding the plan The evaluation value is calculated using Pythagorean fuzzy numbers. It is stated that experts have been consulted. Individual Pythagorean fuzzy decision matrix ;

[0017] in, Membership degree, representing the degree of membership. One solution In the Individual indicators Next An expert The degree to which it is judged as "excellent" ranges from [value range missing]. , The degree of non-membership indicates the degree of non-membership. One solution In the Individual indicators Next An expert The degree to which a score is judged as "not excellent" ranges from [value range missing]. and satisfy Pythagorean fuzzy number For experts The given indicators Regarding the plan The evaluation value, expert Individual Pythagorean fuzzy decision matrix; The total number of schemes corresponds to the number of rows in the matrix; This represents the total number of indicators and the corresponding number of columns in the matrix.

[0018] The individual Pythagorean fuzzy decision matrix will be obtained. The normalized decision matrix is ​​obtained through equation (1). ;

[0019]

[0020] Among them, benefit-type indicators are also known as positive indicators, and cost-type indicators are also known as negative indicators; Membership degree, representing the degree of membership. One solution In the Individual indicators Next An expert The degree to which it is judged as "excellent" ranges from [value range missing]. , The degree of non-membership indicates the degree of non-membership. One solution In the Individual indicators Next An expert The degree to which a score is judged as "not excellent" ranges from [value range missing]. and satisfy Pythagorean fuzzy number For experts The given indicators Regarding the plan Evaluation value; For standardized experts Individual Pythagorean fuzzy decision matrix; For the first One indicator; The total number of schemes corresponds to the number of rows in the matrix; This represents the total number of indicators and the corresponding number of columns in the matrix.

[0021] Furthermore, step S2 is implemented through the following steps:

[0022] Determining expert weights is a key issue in multi-criteria group decision-making. This method determines expert weights by combining Hamming distance and Chebyshev distance to determine the comprehensive distance. The evaluation information of the decision-making group can be measured by the average Pythagorean fuzzy decision matrix.

[0023] 1) Obtain the average Pythagorean fuzzy decision matrix through equation (2). ;

[0024]

[0025] in, Membership degree, representing the degree of membership. One solution In the Individual indicators Next An expert The degree to which it is judged as "excellent" ranges from [value range missing]. , The degree of non-membership indicates the degree of non-membership. One solution In the Individual indicators Next An expert The degree to which a score is judged as "not excellent" ranges from [value range missing]. and satisfy . Refers to the plan In terms of indicators Lower fusion The average Pythagorean fuzzy evaluation score of the experts, where the expert weights are: ; The average Pythagorean fuzzy decision matrix; The total number of schemes corresponds to the number of rows in the matrix; This represents the total number of indicators and the corresponding number of columns in the matrix.

[0026] 2) For and Two Pythagorean fuzzy matrices have and The Minkowski distance is defined as follows:

[0027]

[0028] in, Membership degree, representing the degree of membership. One solution In the Individual indicators Next An expert The degree to which it is judged as "excellent" ranges from [value range missing]. , The degree of non-membership indicates the degree of non-membership. One solution In the Individual indicators Next An expert The degree to which a score is judged as "not excellent" ranges from [value range missing]. and satisfy . Called the Pythagorean fuzzy number degree of hesitation Called the Pythagorean fuzzy number The degree of hesitation; for and Minkowski distance; It is a positive real number order parameter that determines the way distance is calculated and its properties; For standardized experts Individual Pythagorean fuzzy decision matrix; The average Pythagorean fuzzy decision matrix; For the total number of schemes, This represents the total number of indicators.

[0029] 3) When The corresponding Hamming distance and Chebyshev distance are as follows:

[0030]

[0031]

[0032]

[0033] in, for and Hamming distance, for and Chebyshev distance; Membership degree, representing the degree of membership. One solution In the Individual indicators Next An expert The degree to which it is judged as "excellent" ranges from [value range missing]. , The degree of non-membership indicates the degree of non-membership. One solution In the Individual indicators Next An expert The degree to which a score is judged as "not excellent" ranges from [value range missing]. and satisfy . Called the Pythagorean fuzzy number degree of hesitation Called the Pythagorean fuzzy number The degree of hesitation; for and Minkowski distance; For standardized experts Individual Pythagorean fuzzy decision matrix; The average Pythagorean fuzzy decision matrix; For the total number of schemes, The total number of indicators;

[0034] 4) By controlling parameters The combined distance, determined by combining Hamming distance and Chebyshev distance, is shown below:

[0035]

[0036] in, for and Hamming distance, for and Chebyshev distance; For standardized experts Individual Pythagorean fuzzy decision matrix; The average Pythagorean fuzzy decision matrix; , is a weight control parameter used to adjust the relative contributions of the two distances in the composite distance formula;

[0037] 5) Overall distance The smaller, the more experts are empowered. The greater the weight, the better; therefore, experts The weights can be obtained through equation (7);

[0038]

[0039] in, For the overall distance, For the first Experts The weights; This refers to the total number of experts.

[0040] Furthermore, step S3 is implemented through the following steps:

[0041] Knowledge measurement is used to characterize the information content of Pythagorean fuzzy numbers; this method determines the index weights through knowledge measurement.

[0042] 1) Obtain the group Pythagorean fuzzy decision matrix using equation (8) ;

[0043]

[0044]

[0045] in, Membership degree, representing the degree of membership. One solution In the Individual indicators Next An expert The degree to which it is judged as "excellent" ranges from [value range missing]. , The degree of non-membership indicates the degree of non-membership. One solution In the Individual indicators Next An expert The degree to which a score is judged as "not excellent" ranges from [value range missing]. and satisfy . Refers to the plan In terms of indicators Lower fusion A group of experts' Pythagorean fuzzy evaluation values. For the first Experts The weights; Total number of experts; For a group Pythagorean fuzzy decision matrix.

[0046] 2) For Pythagorean fuzzy numbers , Knowledge measurement Defined as follows:

[0047]

[0048] in, Membership degree, representing the degree of membership. One solution In the Individual indicators The degree to which something is judged as "excellent" ranges from [value range missing]. , The degree of non-membership indicates the degree of non-membership. One solution In the Individual indicators The degree to which something is judged as "not excellent" ranges from [value range missing]. and satisfy . Pythagorean fuzzy number degree of hesitation It is a preference parameter. From To the ideal point and negative ideal point The closest point distance, From To the ideal point and negative ideal point relatively distant points distance, From To the blur point The distance;

[0049] 3) Calculate the knowledge measurement matrix according to equation (10).

[0050]

[0051] in, Membership degree, representing the degree of membership. One solution In the Individual indicators The degree to which something is judged as "excellent" ranges from [value range missing]. , The degree of non-membership indicates the degree of non-membership. One solution In the Individual indicators The degree to which something is judged as "not excellent" ranges from [value range missing]. and satisfy ; Pythagorean fuzzy number The degree of hesitation; These are preference parameters; The larger the value, the greater the Pythagorean fuzziness number. The more information conveyed, the better;

[0052] 4) Determine the criterion weight vector by maximizing the overall knowledge measure of each alternative. Establish a multi-objective programming model as shown in equation (11);

[0053]

[0054] in, For the first Individual indicators The weight, It is the first One solution exist index Knowledge measurement; For the total number of schemes, The total number of indicators;

[0055] 5) Since there is no preference for any of the options, model (11) can be transformed into a single-objective mathematical programming model as shown in equation (12);

[0056]

[0057] in, For the first Individual indicators The weight, It is the first One solution exist index Knowledge measurement; For the total number of schemes, The total number of indicators;

[0058] 6) Construct the Lagrange function ; respectively about and The partial derivatives are zero, resulting in the following system of equations;

[0059]

[0060] in, For the first Individual indicators The weight, It is the first One solution exist index Knowledge measurement; They are Lagrange multipliers; For the total number of schemes, The total number of indicators;

[0061] 7) It can be obtained through calculation. and ;

[0062] Therefore, the criteria weight It can be written as equation (14).

[0063]

[0064] in, For the first Individual indicators The weight, It is the first One solution exist index Knowledge measurement; They are Lagrange multipliers; For the total number of schemes, The total number of indicators;

[0065] Furthermore, step S4 is implemented through the following steps:

[0066] 1) Calculate the Pythagorean fuzzy positive ideal solution of the scheme and negative ideal solution ;

[0067]

[0068]

[0069]

[0070]

[0071] in, It is a Pythagorean fuzzy number The scoring function; It is a Pythagorean fuzzy number The exact function; Membership degree, representing the degree of membership. One solution In the Individual indicators The degree to which something is judged as "excellent" ranges from [value range missing]. , The degree of non-membership indicates the degree of non-membership. One solution In the Individual indicators The degree to which something is judged as "not excellent" ranges from [value range missing]. and satisfy ; For the total number of schemes, The total number of indicators;

[0072] The rules for comparing the size of Pythagorean fuzzy numbers are as follows:

[0073] For any two Pythagorean fuzzy numbers ,have

[0074] (1) If ;

[0075] (2) If ;

[0076] (3) If but:

[0077] ①If ② ③

[0078] 2) Calculate the positive ideal deviation of the alternative schemes. and negative ideal deviation ;

[0079]

[0080]

[0081]

[0082]

[0083] Among them, let the positive ideal solution Negative ideal solution ; For the first One solution In the Individual indicators The deviation from the ideal solution. For the first One solution In the indivual The deviation from the negative ideal solution; For the first One solution Positive ideal deviation; No. One solution The value is a negative ideal deviation;

[0084] 3) Calculate the grey relational degree:

[0085]

[0086]

[0087]

[0088]

[0089] in, For the first One solution In the Individual indicators The correlation coefficient between the lower and positive ideal solutions. For the first One solution In the Individual indicators The correlation coefficient between the lower and negative ideal solutions; and Let these be the minimum and maximum values ​​of the deviation from the positive ideal solution under all schemes and indicators. and For all schemes and indicators, the corresponding negative theorem

[0090] We want to find the minimum and maximum values ​​of the deviation; The resolution coefficient is usually set to 0.5; For the first One criterion The weights; For the first One solution Grey relational degree with the positive ideal solution; For the first One solution Grey relational degree with negative ideal solution;

[0091] 4) To After performing dimensionless normalization, the comprehensive score of the alternative schemes is calculated.

[0092]

[0093]

[0094]

[0095] in, This is a compromise factor. The value is typically 0.5; For the first One solution Positive ideal deviation; No. One solution The value is a negative ideal deviation; For the first One solution Grey relational degree with the positive ideal solution; For the first One solution Grey relational degree with negative ideal solution; For the first One solution The ideal deviation after dimensionless normalization; For the first One solution Grey relational degree after dimensionless normalization; For the first One solution The overall score; The higher the value, the better the solution;

[0096] 5) Sort the solutions according to the overall score and select the best solution.

[0097] The beneficial effects of this invention are:

[0098] 1) Pythagorean fuzzy sets can describe evaluation information from both membership and non-membership perspectives, improving the modeling effect of practical decision-making problems and effectively handling uncertain information;

[0099] 2) Construct a comprehensive distance model between individuals and evaluation Pythagorean fuzzy decision matrices that minimizes the bias function, determine expert weights, and avoid bias caused by subjective assignment;

[0100] 3) Construct a multi-objective Pythagorean fuzzy programming model that maximizes the overall knowledge measurement of a single solution, and determine the weights of the indicators;

[0101] 4) A Pythagorean fuzzy distance measure that satisfies the properties of the triangle inequality is proposed, which enhances the mathematical scientism and accuracy of difference measurement in the decision-making process and improves the ability to distinguish between different options.

[0102] 5) The TOPSIS-GRA ensemble method, which combines distance and similarity metrics, was used to rank the site selection schemes for new energy vehicle charging piles. Attached Figure Description

[0103] Figure 1 This is a flowchart of the multi-criteria decision-making method for new energy charging pile site selection based on Pythagorean fuzzy sets, as presented in this invention.

[0104] Figure 2 For the purposes of this invention A diagram illustrating the sorting of schemes under different values;

[0105] Figure 3 For the purposes of this invention A diagram illustrating the weighted Spearman correlation coefficient of the values. Detailed Implementation

[0106] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0107] like Figure 1 As shown, a multi-criteria decision-making method for charging pile site selection based on Pythagorean fuzzy sets includes the following steps:

[0108] S1: The evaluation information given by multiple experts using Pythagorean fuzzy numbers is organized to obtain the individual Pythagorean fuzzy decision matrix. Then, the matrix is ​​normalized and the average Pythagorean fuzzy decision matrix is ​​calculated.

[0109] Let the set of schemes be Experts gathered , Let be the expert weight vector, satisfying The indicator set is , Let be the indicator weight vector, satisfying Suppose l experts rank and select the best option from m solutions based on n criteria. Assume the experts... The given indicators Regarding the plan The evaluation value is calculated using Pythagorean fuzzy numbers. It is stated that experts have been consulted. Individual Pythagorean fuzzy decision matrix .

[0110] in, Membership degree, representing the degree of membership. One solution In the Individual indicators Next An expert The degree to which it is judged as "excellent" ranges from [value range missing]. , The degree of non-membership indicates the degree of non-membership. One solution In the Individual indicators Next An expert The degree to which a score is judged as "not excellent" ranges from [value range missing]. and satisfy Pythagorean fuzzy number For experts The given indicators Regarding the plan The evaluation value, expert Individual Pythagorean fuzzy decision matrix; The total number of schemes corresponds to the number of rows in the matrix; This represents the total number of indicators and the corresponding number of columns in the matrix.

[0111] The individual Pythagorean fuzzy decision matrix will be obtained. The normalized decision matrix is ​​obtained through equation (1). ;

[0112]

[0113] Among them, benefit-type indicators are also known as positive indicators, and cost-type indicators are also known as negative indicators; Membership degree, representing the degree of membership. One solution In the Individual indicators Next An expert The degree to which it is judged as "excellent" ranges from [value range missing]. , The degree of non-membership indicates the degree of non-membership. One solution In the Individual indicators Next An expert The degree to which a score is judged as "not excellent" ranges from [value range missing]. and satisfy Pythagorean fuzzy number For experts The given indicators Regarding the plan Evaluation value; For standardized experts Individual Pythagorean fuzzy decision matrix; For the first One indicator; The total number of schemes corresponds to the number of rows in the matrix; This represents the total number of indicators and the corresponding number of columns in the matrix.

[0114] S2: Calculate the Hamming distance and Chebyshev distance between the normalized Pythagorean fuzzy decision matrix and the average Pythagorean fuzzy decision matrix, integrate them to obtain the comprehensive distance, and determine the expert weights;

[0115] Determining expert weights is a key issue in multi-criteria group decision-making. This method determines expert weights by combining Hamming distance and Chebyshev distance to determine the comprehensive distance. The evaluation information of the decision-making group can be measured by the average Pythagorean fuzzy decision matrix.

[0116] 1) Obtain the average Pythagorean fuzzy decision matrix through equation (2). ;

[0117]

[0118] in, Membership degree, representing the degree of membership. One solution In the Individual indicators Next An expert The degree to which it is judged as "excellent" ranges from [value range missing]. , The degree of non-membership indicates the degree of non-membership. One solution In the Individual indicators Next An expert The degree to which a score is judged as "not excellent" ranges from [value range missing]. and satisfy . Refers to the plan In terms of indicators Lower fusion The average Pythagorean fuzzy evaluation score of the experts, where the expert weights are: ; The average Pythagorean fuzzy decision matrix; The total number of schemes corresponds to the number of rows in the matrix; This represents the total number of indicators and the corresponding number of columns in the matrix.

[0119] 2) For and Two Pythagorean fuzzy matrices have and The Minkowski distance is defined as follows:

[0120]

[0121] in, Membership degree, representing the degree of membership. One solution In the Individual indicators Next An expert The degree to which it is judged as "excellent" ranges from [value range missing]. , The degree of non-membership indicates the degree of non-membership. One solution In the Individual indicators Next An expert The degree to which a score is judged as "not excellent" ranges from [value range missing]. and satisfy . Called the Pythagorean fuzzy number degree of hesitation Called the Pythagorean fuzzy number The degree of hesitation; for and Minkowski distance; It is a positive real number order parameter that determines the way distance is calculated and its properties; For standardized experts Individual Pythagorean fuzzy decision matrix; The average Pythagorean fuzzy decision matrix; For the total number of schemes, This represents the total number of indicators.

[0122] 3) When The corresponding Hamming distance and Chebyshev distance are as follows:

[0123]

[0124]

[0125]

[0126] in, for and Hamming distance, for and Chebyshev distance; Membership degree, representing the degree of membership. One solution In the Individual indicators Next An expert The degree to which it is judged as "excellent" ranges from [value range missing]. , The degree of non-membership indicates the degree of non-membership. One solution In the Individual indicators Next An expert The degree to which a score is judged as "not excellent" ranges from [value range missing]. and satisfy . Called the Pythagorean fuzzy number degree of hesitation Called the Pythagorean fuzzy number The degree of hesitation; for and Minkowski distance; For standardized experts Individual Pythagorean fuzzy decision matrix; The average Pythagorean fuzzy decision matrix; For the total number of schemes, The total number of indicators;

[0127] 4) By controlling parameters The combined distance, determined by combining Hamming distance and Chebyshev distance, is shown below:

[0128]

[0129] in, for and Hamming distance, for and Chebyshev distance; For standardized experts Individual Pythagorean fuzzy decision matrix; The average Pythagorean fuzzy decision matrix; , is a weight control parameter used to adjust the relative contributions of the two distances in the composite distance formula;

[0130] 5) Overall distance The smaller, the more experts are empowered. The greater the weight, the better; therefore, experts The weights can be obtained through equation (7);

[0131]

[0132] in, For the overall distance, For the first Experts The weights; This refers to the total number of experts.

[0133] S3: Calculate the group Pythagorean fuzzy decision matrix based on expert weights, and then calculate the knowledge measurement matrix to determine the indicator weights;

[0134] Knowledge measurement is used to characterize the information content of Pythagorean fuzzy numbers; this method determines the index weights through knowledge measurement.

[0135] 1) Obtain the group Pythagorean fuzzy decision matrix using equation (8) ;

[0136]

[0137]

[0138] in, Membership degree, representing the degree of membership. One solution In the Individual indicators Next An expert The degree to which it is judged as "excellent" ranges from [value range missing]. , The degree of non-membership indicates the degree of non-membership. One solution In the Individual indicators Next An expert The degree to which a score is judged as "not excellent" ranges from [value range missing]. and satisfy . Refers to the plan In terms of indicators Lower fusion A group of experts' Pythagorean fuzzy evaluation values. For the first Experts The weights; Total number of experts; For a group Pythagorean fuzzy decision matrix.

[0139] 2) For Pythagorean fuzzy numbers , Knowledge measurement Defined as follows:

[0140]

[0141] in, Membership degree, representing the degree of membership. One solution In the Individual indicators The degree to which something is judged as "excellent" ranges from [value range missing]. , The degree of non-membership indicates the degree of non-membership. One solution In the Individual indicators The degree to which something is judged as "not excellent" ranges from [value range missing]. and satisfy . Pythagorean fuzzy number degree of hesitation It is a preference parameter. From To the ideal point and negative ideal point The closest point distance, From To the ideal point and negative ideal point relatively distant points distance, From To the blur point The distance;

[0142] 3) Calculate the knowledge measurement matrix according to equation (10).

[0143]

[0144] in, Membership degree, representing the degree of membership. One solution In the Individual indicators The degree to which something is judged as "excellent" ranges from [value range missing]. , The degree of non-membership indicates the degree of non-membership. One solution In the Individual indicators The degree to which something is judged as "not excellent" ranges from [value range missing]. and satisfy ; Pythagorean fuzzy number The degree of hesitation; These are preference parameters; The larger the value, the greater the Pythagorean fuzziness number. The more information conveyed, the better;

[0145] 4) Determine the criterion weight vector by maximizing the overall knowledge measure of each alternative. Establish a multi-objective programming model as shown in equation (11);

[0146]

[0147] in, For the first Individual indicators The weight, It is the first One solution exist index Knowledge measurement; For the total number of schemes, The total number of indicators;

[0148] 5) Since there is no preference for any of the options, model (11) can be transformed into a single-objective mathematical programming model as shown in equation (12);

[0149]

[0150] in, For the first Individual indicators The weight, It is the first One solution exist index Knowledge measurement; For the total number of schemes, The total number of indicators;

[0151] 6) Construct the Lagrange function Separately about and The partial derivatives are zero, resulting in the following system of equations;

[0152]

[0153] in, For the first Individual indicators The weight, It is the first One solution exist index Knowledge measurement; They are Lagrange multipliers; For the total number of schemes, The total number of indicators;

[0154] 7) It can be obtained through calculation. and ;

[0155] Therefore, the criteria weight It can be written as equation (14).

[0156]

[0157] in, For the first Individual indicators The weight, It is the first One solution exist index Knowledge measurement; They are Lagrange multipliers; For the total number of schemes, The total number of indicators;

[0158] S4: By comparing the magnitudes of the Pythagorean fuzzy numbers in the group matrix, the positive and negative ideal solutions are determined. Then, based on the Pythagorean fuzzy distance measure that satisfies the property of the triangle inequality, the positive and negative ideal deviations and grey relational degree are calculated to obtain the comprehensive score of the scheme. The schemes are then ranked to obtain the optimal new energy vehicle charging pile site selection scheme.

[0159] 1) Calculate the Pythagorean fuzzy positive ideal solution of the scheme and negative ideal solution ;

[0160]

[0161]

[0162]

[0163]

[0164] in, It is a Pythagorean fuzzy number The scoring function; It is a Pythagorean fuzzy number The exact function; Membership degree, representing the degree of membership. One solution In the Individual indicators The degree to which something is judged as "excellent" ranges from [value range missing]. , The degree of non-membership indicates the degree of non-membership. One solution In the Individual indicators The degree to which something is judged as "not excellent" ranges from [value range missing]. and satisfy ; For the total number of schemes, The total number of indicators;

[0165] The rules for comparing the size of Pythagorean fuzzy numbers are as follows:

[0166] For any two Pythagorean fuzzy numbers ,have

[0167] (1) If ;

[0168] (2) If ;

[0169] (3) If but:

[0170] ①If ② ③

[0171] 2) Calculate the positive ideal deviation of the alternative schemes. and negative ideal deviation ;

[0172]

[0173]

[0174]

[0175]

[0176] Among them, let the positive ideal solution Negative ideal solution ; For the first One solution In the Individual indicators The deviation from the ideal solution. For the first One solution In the indivual The deviation from the negative ideal solution; For the first One solution Positive ideal deviation; No. One solution The value is a negative ideal deviation;

[0177] 3) Calculate the grey relational degree:

[0178]

[0179]

[0180]

[0181]

[0182] in, For the first One solution In the Individual indicators The correlation coefficient between the lower and positive ideal solutions. For the first One solution In the Individual indicators The correlation coefficient between the lower and negative ideal solutions; and Let these be the minimum and maximum values ​​of the deviation from the positive ideal solution under all schemes and indicators. and For all schemes and indicators, the corresponding negative theorem

[0183] We want to find the minimum and maximum values ​​of the deviation; The resolution coefficient is usually set to 0.5; For the first One criterion The weights; For the first One solution Grey relational degree with the positive ideal solution; For the first One solution Grey relational degree with negative ideal solution;

[0184] 4) To After performing dimensionless normalization, the comprehensive score of the alternative schemes is calculated.

[0185]

[0186]

[0187]

[0188] in, This is a compromise factor. The value is typically 0.5; For the first One solution Positive ideal deviation; No. One solution The value is a negative ideal deviation; For the first One solution Grey relational degree with the positive ideal solution; For the first One solution Grey relational degree with negative ideal solution; For the first One solution The ideal deviation after dimensionless normalization; For the first One solution Grey relational degree after dimensionless normalization; For the first One solution The overall score; The higher the value, the better the solution;

[0189] 5) Sort the solutions according to the overall score and select the best solution.

[0190] Table 1 lists the three experts. , , Charging compatibility of five alternative new energy vehicle solutions Charging efficiency With security Fuzzy evaluation matrix under three criteria.

[0191] Table 1 Individual Pythagorean Fuzzy Decision Matrix

[0192]

[0193] Using this decision-making method, as shown in Table 2, the positive ideal deviation of the alternative solutions was calculated. and negative ideal deviation ;plan Grey relational degree with the positive ideal solution ,plan Grey relational degree with negative ideal solution ; dimensionless normalized ideal deviation Grey relational degree after dimensionless normalization Overall score ;

[0194] Table 2. Grey Relational Degree, Ideal Deviation, and Overall Score of the Scheme

[0195]

[0196] The final solutions are ranked as follows: ,in This is the optimal solution.

[0197] To avoid errors caused by a single model, this invention combines TOPSIS and GRA to rank the alternative solutions. Considering the influence of subjective human factors, a trade-off coefficient is used. Changes in the coefficient of friction may affect the outcome. Therefore, by changing the trade-off coefficient... Sensitivity analysis was conducted to further investigate the robustness of the ensemble model.

[0198] First, the compromise coefficient Increment from 0 to 1 to simulate different scenarios. When When = 0, the model only uses grey relational analysis (GRA) to rank the alternatives. When =1, the model uses only the Top-Optimal Solution Ranking Method (TOPSIS) to rank the alternatives. Simulation results for different cases are as follows: Figure 2 As shown in Table 3. The results indicate that, Different values ​​of will produce different sorting results. When When ≥0.3, the optimal solution among the five alternatives is A2, which is consistent with the results of this study. When the value is less than 0.3, the optimal solution is A1. However, A2 is the optimal solution in a significant proportion of cases, indicating that the solution chosen in this study... A value of 0.5 is more reasonable. Therefore, combining models reduces the error caused by a single model. Of course, this also depends on the decision-maker's preferences.

[0199] Table 3 Differences The following is a comprehensive score and ranking of various new energy vehicle charging pile site selection schemes.

[0200]

[0201] To visually represent the different compromise coefficients This paper introduces a ranking similarity coefficient to analyze the differences in the ranking of charging pile site selection schemes. The similarity of the rankings obtained under the given values ​​is qualitatively measured. Figure 3 For different The weighted Spearman correlation coefficient heatmap of the ranking of charging pile site selection schemes is obtained by solving equation (30).

[0202] in, Weighted Spearman correlation coefficient, with a value range of [value missing]. The closer the result is to 1, the higher the consistency between the two sorting results; the closer it is to -1, the lower the consistency between the two sorting results. Both N and N represent the total number of schemes to be evaluated. For the first The weights of each option, No. The rank difference of the schemes in two different sorting results.

[0203] from Figure 3 It can be seen that, =0.5 and The weighted Spearman correlation coefficient corresponding to a value of 0.4 is 0.9, indicating that the rankings of the two new energy vehicle charging pile site selection schemes are highly similar, with only very minor differences, reflecting... When fine-tuning was performed in the range of 0.4 to 0.5, the priority ranking of the site selection schemes did not change significantly, demonstrating good stability. Furthermore, =0.5 ranking and For rankings with values ​​ranging from 0.6 to 1.0, the weighted Spearman correlation coefficient was 0.9, indicating a high degree of similarity. The ranking of site selection schemes with a value of 0.5 and high The ranking characteristics of the intervals are highly consistent. Meanwhile, the graph also shows low... The interval (0.0~0.3) and the height The correlation coefficient for the interval (0.6~1.0) is -0.9, indicating that the rankings of the site selection schemes under the two strategies are almost completely opposite, further highlighting the... The value of 0.5 as a balance point is that it avoids the conflict between the two extreme strategies and ensures the stability of the solution and the consistency of decision-making.

[0204] The above results fully validate the selection of charging pile site selection schemes for new energy vehicles. The scientific validity and rationality of a value of 0.5 demonstrate that rankings at this value exhibit both good stability and high accuracy. The core ranking logic of the intervals remains highly similar, which can provide a reliable reference for the actual decision-making of charging pile site selection.

[0205] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A multi-criteria decision-making method for charging pile site selection based on Pythagorean fuzzy sets, characterized in that: Includes the following steps: S1: The evaluation information given by multiple experts using Pythagorean fuzzy numbers is organized to obtain the individual Pythagorean fuzzy decision matrix. Then, the matrix is ​​normalized and the average Pythagorean fuzzy decision matrix is ​​calculated. S2: Calculate the Hamming distance and Chebyshev distance between the normalized Pythagorean fuzzy decision matrix and the average Pythagorean fuzzy decision matrix, integrate them to obtain the comprehensive distance, and determine the expert weights; S3: Calculate the group Pythagorean fuzzy decision matrix based on expert weights, and then calculate the knowledge measurement matrix to determine the indicator weights; S4: By comparing the magnitudes of the Pythagorean fuzzy numbers in the group matrix, the positive and negative ideal solutions are determined. Then, based on the Pythagorean fuzzy distance measure that satisfies the property of the triangle inequality, the positive and negative ideal deviations and grey relational degree are calculated to obtain the comprehensive score of the scheme. The schemes are then ranked to obtain the optimal new energy vehicle charging pile site selection scheme.

2. The multi-criteria decision-making method for charging pile site selection based on Pythagorean fuzzy sets according to claim 1, characterized in that: The process of step S1 is implemented through the following steps: Let the set of schemes be Experts gathered , Let be the expert weight vector, satisfying The indicator set is , Let be the indicator weight vector, satisfying Assume l experts rank and select the best option from m solutions based on n criteria; assume the experts... The given indicators Regarding the plan The evaluation value is calculated using Pythagorean fuzzy numbers. ; Get experts Individual Pythagorean fuzzy decision matrix ; ， in, Membership degree, representing the degree of membership. One solution In the Individual indicators Next An expert The degree to which it is judged as "excellent" ranges from [value range missing]. , The degree of non-membership indicates the degree of non-membership. One solution In the Individual indicators Next An expert The degree to which a score is judged as "not excellent" ranges from [value range missing]. and satisfy Pythagorean fuzzy number For experts The given indicators Regarding the plan The evaluation value, expert Individual Pythagorean fuzzy decision matrix; The total number of schemes corresponds to the number of rows in the matrix; This represents the total number of indicators and the corresponding number of columns in the matrix. The individual Pythagorean fuzzy decision matrix will be obtained. The normalized decision matrix is ​​obtained through equation (1). ; , Among them, benefit-type indicators are also known as positive indicators, and cost-type indicators are also known as negative indicators; Membership degree, representing the degree of membership. One solution In the Individual indicators Next An expert The degree to which it is judged as "excellent" ranges from [value range missing]. , The degree of non-membership indicates the degree of non-membership. One solution In the Individual indicators Next An expert The degree to which a score is judged as "not excellent" ranges from [value range missing]. and satisfy Pythagorean fuzzy number For experts The given indicators Regarding the plan Evaluation value; For standardized experts Individual Pythagorean fuzzy decision matrix; For the first One indicator; The total number of schemes corresponds to the number of rows in the matrix; This represents the total number of indicators and the corresponding number of columns in the matrix.

3. The multi-criteria decision-making method for charging pile site selection based on Pythagorean fuzzy sets according to claim 2, characterized in that: The process in step S2 is implemented through the following steps: 1) Obtain the average Pythagorean fuzzy decision matrix through equation (2). ; ， in, Membership degree, representing the degree of membership. One solution In the Individual indicators Next An expert The degree to which it is judged as "excellent" ranges from [value range missing]. , The degree of non-membership indicates the degree of non-membership. One solution In the Individual indicators Next An expert The degree to which a score is judged as "not excellent" ranges from [value range missing]. and satisfy . Refers to the plan In indicators Lower fusion The average Pythagorean fuzzy evaluation score of the experts, where the expert weights are: ; The average Pythagorean fuzzy decision matrix; The total number of schemes corresponds to the number of rows in the matrix; This represents the total number of indicators and the corresponding number of columns in the matrix. 2) For and Two Pythagorean fuzzy matrices have and The Minkowski distance is defined as follows: , in, Membership degree, representing the degree of membership. One solution In the Individual indicators Next An expert The degree to which it is judged as "excellent" ranges from [value range missing]. , The degree of non-membership indicates the degree of non-membership. One solution In the Individual indicators Next An expert The degree to which a score is judged as "not excellent" ranges from [value range missing]. and satisfy ; Called the Pythagorean fuzzy number degree of hesitation Called the Pythagorean fuzzy number The degree of hesitation; for and Minkowski distance; It is a positive real number order parameter that determines the way distance is calculated and its properties; For standardized experts Individual Pythagorean fuzzy decision matrix; The average Pythagorean fuzzy decision matrix; For the total number of schemes, The total number of indicators; 3) When The corresponding Hamming distance and Chebyshev distance are as follows: , ， ， in, for and Hamming distance, for and Chebyshev distance; Membership degree, representing the degree of membership. One solution In the Individual indicators Next An expert The degree to which it is judged as "excellent" ranges from [value range missing]. , The degree of non-membership indicates the degree of non-membership. One solution In the Individual indicators Next An expert The degree to which a score is judged as "not excellent" ranges from [value range missing]. and satisfy ; Called the Pythagorean fuzzy number degree of hesitation Called the Pythagorean fuzzy number The degree of hesitation; for and Minkowski distance; For standardized experts Individual Pythagorean fuzzy decision matrix; The average Pythagorean fuzzy decision matrix; For the total number of schemes, The total number of indicators; 4) By controlling parameters The combined distance, determined by combining Hamming distance and Chebyshev distance, is shown below: , in, for and Hamming distance, for and Chebyshev distance; For standardized experts Individual Pythagorean fuzzy decision matrix; The average Pythagorean fuzzy decision matrix; , is a weight control parameter used to adjust the relative contributions of the two distances in the composite distance formula; 5) Overall distance The smaller, the more experts are empowered. The greater the weight, the better; therefore, experts The weights are obtained through (7); , in, For the overall distance, For the first Experts The weights; This refers to the total number of experts.

4. The multi-criteria decision-making method for charging pile site selection based on Pythagorean fuzzy sets according to claim 3, characterized in that: The process of step S3 is implemented through the following steps: 1) Obtain the group Pythagorean fuzzy decision matrix using equation (8) ; ， ， in, Membership degree, representing the degree of membership. One solution In the Individual indicators Next An expert The degree to which it is judged as "excellent" ranges from [value range missing]. , The degree of non-membership indicates the degree of non-membership. One solution In the Individual indicators Next An expert The degree to which a score is judged as "not excellent" ranges from [value range missing]. and satisfy ; Refers to the plan In indicators Lower fusion A group of experts' Pythagorean fuzzy evaluation values. For the first Experts The weights; Total number of experts; For a group Pythagorean fuzzy decision matrix; 2) For Pythagorean fuzzy numbers , Knowledge measurement Defined as follows: , in, Membership degree, representing the degree of membership. One solution In the Individual indicators The degree to which something is judged as "excellent" ranges from [value range missing]. , The degree of non-membership indicates the degree of non-membership. One solution In the Individual indicators The degree to which something is judged as "not excellent" ranges from [value range missing]. and satisfy ; Pythagorean fuzzy number degree of hesitation It is a preference parameter. From To the ideal point and negative ideal point The closest point distance, From To the ideal point and negative ideal point relatively distant points distance, From To the blur point The distance; 3) Calculate the knowledge measurement matrix according to equation (10). , ， in, Membership degree, representing the degree of membership. One solution In the Individual indicators The degree to which something is judged as "excellent" ranges from [value range missing]. , The degree of non-membership indicates the degree of non-membership. One solution In the Individual indicators The degree to which something is judged as "not excellent" ranges from [value range missing]. and satisfy ; Pythagorean fuzzy number The degree of hesitation; These are preference parameters; The larger the value, the greater the Pythagorean fuzziness number. The more information conveyed, the better; 4) Determine the criterion weight vector by maximizing the overall knowledge measure of each alternative. Establish a multi-objective programming model as shown in equation (11); , in, For the first Individual indicators The weight, It is the first One solution exist index Knowledge measurement; For the total number of schemes, The total number of indicators; 5) Since there is no preference for any of the options, model (11) is transformed into a single-objective mathematical programming model as shown in equation (12); ， in, For the first Individual indicators The weight, It is the first One solution exist index Knowledge measurement; For the total number of schemes, The total number of indicators; 6) Construct the Lagrange function ; respectively about and With partial derivatives of zero, j=1,2,⋯,n, we obtain the following system of equations; ， in, For the first Individual indicators The weight, It is the first One solution exist index Knowledge measurement; They are Lagrange multipliers; For the total number of schemes, The total number of indicators; 7) It can be obtained through calculation. and j=1,2,⋯,n; Therefore, the criteria weight It is denoted as equation (14). , in, For the first Individual indicators The weight, It is the first One solution exist index Knowledge measurement; They are Lagrange multipliers; For the total number of schemes, This represents the total number of indicators.

5. The multi-criteria decision-making method for charging pile site selection based on Pythagorean fuzzy sets according to claim 4, characterized in that: The process in step S4 is implemented through the following steps: 1) Calculate the Pythagorean fuzzy positive ideal solution of the scheme and negative ideal solution ; , ， ， ， in, It is a Pythagorean fuzzy number The scoring function; It is a Pythagorean fuzzy number The exact function; Membership degree, representing the degree of membership. One solution In the Individual indicators The degree to which something is judged as "excellent" ranges from [value range missing]. , The degree of non-membership indicates the degree of non-membership. One solution In the Individual indicators The degree to which something is judged as "not excellent" ranges from [value range missing]. and satisfy ; For the total number of schemes, The total number of indicators; The rules for comparing the size of Pythagorean fuzzy numbers are as follows: For any two Pythagorean fuzzy numbers ,have (1) If ; (2) If ; (3) If but: ①If ② ③ , 2) Calculate the positive ideal deviation of the alternative schemes. and negative ideal deviation ; , ， ， ， Among them, let the positive ideal solution Negative ideal solution ; For the first One solution In the Individual indicators The deviation from the ideal solution. For the first One solution In the indivual The deviation from the negative ideal solution; For the first One solution Positive ideal deviation; No. One solution The value is a negative ideal deviation; 3) Calculate the grey relational degree: , ， ， ， in, For the first One solution In the Individual indicators The correlation coefficient between the lower and positive ideal solutions. For the first One solution In the Individual indicators The correlation coefficient between the lower and negative ideal solutions; and Let these be the minimum and maximum values ​​of the deviation from the positive ideal solution under all schemes and indicators. and These represent the minimum and maximum values ​​of the negative ideal solution deviation for all schemes and indicators. The resolution coefficient is set to 0.

5. For the first One criterion The weights; For the first One solution Grey relational degree with the positive ideal solution; For the first One solution Grey relational degree with negative ideal solution; 4) To After performing dimensionless normalization, the comprehensive score of the alternative schemes is calculated. , ， ， in, This is a compromise factor. The value is 0.5; For the first One solution Positive ideal deviation; No. One solution The value is a negative ideal deviation; For the first One solution Grey relational degree with the positive ideal solution; For the first One solution Grey relational degree with negative ideal solution; For the first One solution The ideal deviation after dimensionless normalization; For the first One solution Grey relational degree after dimensionless normalization; For the first One solution The overall score; The higher the value, the better the solution; 5) Sort the solutions according to the overall score and select the best solution.

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