Intelligent fishery operation effect evaluation method based on fuzzy multi-objective decision

Abstract

The invention relates to a smart fishery operation effect evaluation method based on fuzzy multi-objective decision. The method comprises the following steps: step 1, establishing a smart fishery operation effect index system; 2, standardizing a decision target; step 3, determining a decision target weight; 4, carrying out group decision making; and step 5, performing fuzzy multi-target decision. The method is based on the fuzzy multi-objective decision, is mainly used for evaluating utilization and management of fishery resources and evaluating changes of fishery ecological environment, can reflect the operation condition and effect of the fishery more reasonably and accurately, provides more scientific decision support, and is of great significance to sustainable development of the fishery. The method can also be applied to other related fields, and the application range is wide.

Description

Technical Field

[0001] The present invention relates to the field of utilization and management of fishery resources, and in particular to a method for evaluating a fishery operation effect and ranking schemes. Background Art

[0002] In today's society, with the continuous increase in population and rapid economic development, the capture and utilization of fishery resources have become increasingly important. As one of the representatives of fishery modernization, smart fishery can not only improve fishery production efficiency and ensure the sustainable development of fishery resources, but also achieve better economic, social and ecological benefits. In order to maximize the operation effect of smart fisheries, it is necessary to conduct a comprehensive evaluation of the operation of fisheries and comprehensively analyze the performance of fisheries in terms of economic benefits, social benefits and ecological benefits.

[0003] In terms of data processing and analysis, domestic fishery evaluation methods mainly rely on traditional statistical analysis methods, such as mean, variance, correlation analysis, regression analysis, etc., to process and analyze data. However, these methods can only handle some simple data types and cannot cope with the various variables and relationships involved in complex fishery ecosystems. For example, traditional data processing methods cannot handle multi-index problems and are difficult to comprehensively evaluate the operating effects of fisheries; they cannot handle fuzzy information and are difficult to accurately evaluate the operating effects of fisheries; they cannot handle uncertainty and are difficult to improve the robustness and reliability of evaluation; they cannot provide reasonable decision support for evaluators and are difficult to help them make reasonable decisions. Summary of the invention

[0004] The present invention establishes an evaluation index system to comprehensively evaluate various aspects of the fishery, and uses fuzzy mathematics and multi-objective optimization algorithms to fuzzify the scores of each index, thereby solving the problems of mutual contradictions and mutual constraints between indicators, and finally comprehensively evaluating the scores of each index. At the same time, the present invention fully considers the sustainability of social, economic and ecological development, avoids destroying the ecological environment and resources in pursuit of short-term economic benefits, helps smart fisheries make business decisions, optimizes production processes, improves management models, and increases fishery output value and social benefits, thereby achieving sustainable development of smart fisheries and maximizing operational effects.

[0005] In order to achieve the above object, the present invention provides the following technical solutions:

[0006] A method for evaluating the operation effect of a smart fishery based on fuzzy multi-objective decision-making includes the following steps:

[0007] Step 1: Establish an evaluation index system for the operation effect of smart fisheries based on the principle of hierarchical analysis method

[0008] Establish a two-level three-layer structure of smart fishery operation effect evaluation index system, which includes three first-level indicators: technical factors, economic factors, environmental factors and social factors; technical factors include three second-level indicators: technical applicability, technical feasibility and technical maturity; economic factors include two second-level indicators: technical cost and technical benefit; environmental factors include one second-level indicator: environmental protection benefit; social factors include two second-level indicators: resource utilization and social value;

[0009] Step 2: Normalize quantitative and qualitative goals

[0010] The qualitative objectives in the decision-making objectives are converted into fuzzy numbers, and the quantitative objectives are processed by linear transformation method;

[0011] Step 3: Determine the weight of the decision goal

[0012] The entropy method is used to determine the weight of decision-making objectives, which include benefit indicators and economic indicators;

[0013] Step 4: Make group decisions

[0014] Construct a group decision model and solve it through the relevant fuzzy decision model to obtain the group judgment vector of each plan;

[0015] Step 5: Make fuzzy multi-objective decision

[0016] The TOPSIS method and grey correlation analysis method are combined to make fuzzy multi-objective decision-making, and the various plans are ranked according to the indicators.

[0017] Moreover, the specific steps of normalizing the quantitative and qualitative targets in step 2 are:

[0018] (1) Distinguish between qualitative and quantitative goals.

[0019] Qualitative goals are technical applicability, technical feasibility, technical maturity, resource utilization and social value. Among them, technical applicability refers to the difficulty of implementation and debugging of a smart fishery, environmental adaptability, matching with related technologies and energy efficiency ratio, technical feasibility refers to the safety index and equipment life of a smart fishery, technical maturity refers to the degree of automation and extensive application of a smart fishery, resource utilization refers to the sustainable development of a smart fishery, and social value refers to the social impact of a fishery, the degree of commercial operation and the driving force for other industries; quantitative goals are technical costs, technical benefits and environmental benefits. Among them, technical costs refer to the costs incurred by a smart fishery in terms of investment, energy consumption, daily operation and equipment maintenance, technical benefits refer to the sum of the internal income, net annual value and annual replacement electricity of a smart fishery, and environmental benefits refer to the ability of a smart fishery to reduce the emission of harmful gases, dust and other particulate matter.

[0020] (2) The specific steps for standardizing qualitative objectives are:

[0021] Ⅰ. The language evaluation level is expressed as five levels: poor, poor, medium, good, and very good;

[0022] Ⅱ. Determine the language evaluation level to which the qualitative objective belongs;

[0023] III. The language evaluation level of the qualitative target is converted into a triangular fuzzy number. The evaluation level of the i-th evaluator on the j-th target is expressed as The conversion relationship between triangular fuzzy numbers and different evaluation levels is: when the language evaluation level is poor, the corresponding triangular fuzzy number is (0, 0, 0.25); when the language evaluation level is poor, the corresponding triangular fuzzy number is (0, 0.25, 0.5); when the language evaluation level is medium, the corresponding triangular fuzzy number is (0.25, 0.5, 0.75); when the language evaluation level is good, the corresponding triangular fuzzy number is (0.5, 0.75, 1); when the language evaluation level is very good, the corresponding triangular fuzzy number is (0.75, 1, 1).

[0024] (3) The specific steps for normalizing quantitative targets are:

[0025] Ⅰ. Differentiate the quantitative target into benefit-oriented index and economic-oriented index;

[0026] II. Construct a decision matrix X for the target ij}

[0027] Among them, x ij is the evaluation value of the jth evaluation target of the i-th candidate object.

[0028] III. For benefit-based indicators, the normalization parameters are

[0029]

[0030] IV. For economic indicators, the normalization parameters are

[0031]

[0032] Moreover, the specific steps of determining the weight of the decision target in step 3 are:

[0033] (1) Let the normalized decision matrix be R = (r ij ) m×n , for the jth indicator, the deviation D between the i-th solution and all other solutions ij for: Among them, d(r ij ,rkj ) represents r ij With r kj For the jth attribute, the deviation D between all solutions and other solutions j for

[0034]

[0035] (2) Calculate the decision information E of each indicator j

[0036]

[0037] (3) Calculate the difference G of the jth index j

[0038] G j =1-E j

[0039] (4) Calculate the entropy weight μ j

[0040]

[0041] Moreover, the specific steps of performing group decision making in step 4 are as follows:

[0042] (1) Determine the decision maker’s weight

[0043] Suppose in the group decision problem, the group consisting of p decision makers is P = {P1, P2, ..., P P}, the kth decision maker P k The weight is μ k , forming a weight vector μ={μ1,μ2,…,μ p}, and satisfy in That is, each decision maker has equal importance.

[0044] (2) Constructing a group decision-making model

[0045] The information gathering method of first integration and then dictatorship is adopted. Suppose there are p decision makers P k (k=1,2,…,p) form a decision-making group P={P1,P2,…,P p}, the decision maker expert weight is: μ={μ1,μ2,…,μ p},μ1+μ2+…+μ p =1, let decision maker P k The evaluation matrix given is

[0046]

[0047] The judgment matrix of each decision maker is weighted and aggregated to obtain the group judgment matrix R = (r ij ) m×n ,in

[0048]

[0049] (3) Solve according to the relevant fuzzy decision model and obtain the group judgment vector u = {u1,u2,…,u p},in

[0050]

[0051] Furthermore, in step 5

[0052] The specific steps of fuzzy multi-objective decision making are as follows:

[0053] (1) Constructing a decision matrix

[0054] The decision maker has m candidates A1, A2, ..., A m The judgment values ​​x1, x2, …, x given by the n targets n , we get an m×n decision matrix X m×n

[0055]

[0056] Among them, x ij is the evaluation value of the jth evaluation target of the i-th candidate object.

[0057] (2) First, normalize the decision matrix to R m×n =(r ij ) mn

[0058] Then the weighted normalized decision matrix is ​​obtained according to the following formula:

[0059]

[0060] (3) Determine positive and negative ideal solutions

[0061] Positive ideal solution: G = {g1, g2, ..., g n}、Negative ideal solution: B={b1,b2,…,b n}

[0062] When the target value is an exact number:

[0063]

[0064] When the target value is a triangular fuzzy number:

[0065]

[0066]

[0067] (4) Calculate the distance between each solution and the positive and negative ideal solutions and

[0068] The distance between the i-th solution and the positive ideal solution and the negative ideal solution is:

[0069]

[0070]

[0071] (5) Calculate the grey correlation degree of each solution for the positive and negative ideal solutions

[0072] The grey correlation coefficient of the positive ideal solution and the negative ideal solution of the i-th scheme under the j-th index is:

[0073]

[0074] in, ξ is the resolution coefficient, which is generally taken as 0.5.

[0075] The grey correlation coefficient matrix of each scheme for positive ideal solution and negative ideal solution is:

[0076]

[0077] The grey correlation degree between the ith solution and the positive and negative ideal solutions is:

[0078]

[0079]

[0080] (6) Standardize distance and grey correlation

[0081] The measurement methods and magnitudes of grey relational degree and distance are different. It is necessary to normalize them to obtain standard grey relational degree and distance. The normalization formula is:

[0082]

[0083]

[0084] (7) Calculate overall closeness

[0085] The greater the distance from the positive ideal solution, the smaller the distance from the negative ideal solution, the better the solution; the greater the correlation with the positive ideal solution, the smaller the correlation with the negative ideal solution, the better the solution. Therefore, the following formula is constructed:

[0086]

[0087]

[0088] Among them, α+β=1, the size of α and β reflects the decision maker's preference for the grey relational analysis method and TOPSIS method, and the overall proximity C is defined as i

[0089]

[0090] (8) C determined according to (7) i The solutions are ranked by size. BRIEF DESCRIPTION OF THE DRAWINGS

[0091] Figure 1 is a flow chart of the method of the present invention;

[0092] Figure 2 The smart fishery operation effect evaluation index system constructed by the present invention; DETAILED DESCRIPTION

[0093] The following is a further description of the embodiments of the present invention in conjunction with the accompanying drawings:

[0094] like Figure 1 As shown, a smart fishery operation effect evaluation method based on fuzzy multi-objective decision-making includes the following steps:

[0095] Step 1: Establish an evaluation index system for the operation effect of smart fisheries based on the principle of hierarchical analysis method

[0096] like Figure 2 As shown in the figure, a two-level three-layer structured smart fishery operation effect evaluation index system is established, which includes three first-level indicators: technical factors, economic factors, environmental factors and social factors; technical factors include three second-level indicators: technical applicability, technical feasibility and technical maturity; economic factors include two second-level indicators: technical cost and technical benefit; environmental factors include one second-level indicator: environmental protection benefit; social factors include two second-level indicators: resource utilization and social value;

[0097] Step 2: Normalize quantitative and qualitative goals

[0098] The qualitative objectives in the decision-making objectives are converted into fuzzy numbers, and the quantitative objectives are processed by linear transformation method;

[0099] Step 3: Determine the weight of the decision goal

[0100] The entropy method is used to determine the weight of decision-making objectives, which include benefit indicators and economic indicators;

[0101] Step 4: Make group decisions

[0102] Construct a group decision model and solve it through the relevant fuzzy decision model to obtain the group judgment vector of each plan;

[0103] Step 5: Make fuzzy multi-objective decision

[0104] The TOPSIS method and grey correlation analysis method are combined to make fuzzy multi-objective decision-making, and the various plans are ranked according to the indicators.

[0105] Moreover, the specific steps of normalizing the quantitative and qualitative targets in step 2 are:

[0106] (1) Distinguish between qualitative and quantitative goals.

[0107] Qualitative goals are technical applicability, technical feasibility, technical maturity, resource utilization and social value. Among them, technical applicability refers to the difficulty of implementation and debugging of a smart fishery, environmental adaptability, matching with related technologies and energy efficiency ratio, technical feasibility refers to the safety index and equipment life of a smart fishery, technical maturity refers to the degree of automation and extensive application of a smart fishery, resource utilization refers to the sustainable development of a smart fishery, and social value refers to the social impact of a fishery, the degree of commercial operation and the driving force for other industries; quantitative goals are technical costs, technical benefits and environmental benefits. Among them, technical costs refer to the costs incurred by a smart fishery in terms of investment, energy consumption, daily operation and equipment maintenance, technical benefits refer to the sum of the internal income, net annual value and annual replacement electricity of a smart fishery, and environmental benefits refer to the ability of a smart fishery to reduce the emission of harmful gases, dust and other particulate matter.

[0108] (2) The specific steps for standardizing qualitative objectives are:

[0109] Ⅰ. The language evaluation level is expressed as five levels: poor, poor, medium, good, and very good;

[0110] Ⅱ. Determine the language evaluation level to which the qualitative objective belongs;

[0111] III. The language evaluation level of the qualitative target is converted into a triangular fuzzy number. The evaluation level of the i-th evaluator on the j-th target is expressed as The conversion relationship between triangular fuzzy numbers and different evaluation levels is: when the language evaluation level is poor, the corresponding triangular fuzzy number is (0, 0, 0.25); when the language evaluation level is poor, the corresponding triangular fuzzy number is (0, 0.25, 0.5); when the language evaluation level is medium, the corresponding triangular fuzzy number is (0.25, 0.5, 0.75); when the language evaluation level is good, the corresponding triangular fuzzy number is (0.5, 0.75, 1); when the language evaluation level is very good, the corresponding triangular fuzzy number is (0.75, 1, 1).

[0112] (3) The specific steps for normalizing quantitative targets are:

[0113] Ⅰ. Differentiate the quantitative target into benefit-oriented index and economic-oriented index;

[0114] II. Construct a decision matrix X for the target ij}

[0115] Among them, x ij is the evaluation value of the jth evaluation target of the i-th candidate object.

[0116] III. For benefit-based indicators, the normalization parameters are

[0117]

[0118] IV. For economic indicators, the normalization parameters are

[0119]

[0120] Moreover, the specific steps of determining the weight of the decision target in step 3 are:

[0121] (1) Let the normalized decision matrix be R = (r ij ) m×n , for the jth indicator, the deviation D between the i-th solution and all other solutions ij for: Among them, d(r ij ,r kj ) represents r ij With r kj For the jth attribute, the deviation D between all solutions and other solutions j for

[0122]

[0123] (2) Calculate the decision information E of each indicator j

[0124]

[0125] (3) Calculate the difference G of the jth index j

[0126] G j =1-E j

[0127] (4) Calculate the entropy weight μ j

[0128]

[0129] Moreover, the specific steps of performing group decision making in step 4 are as follows:

[0130] (1) Determine the decision maker’s weight

[0131] Suppose in the group decision problem, the group consisting of p decision makers is P = {P1, P2, ..., P P}, the kth decision maker P k The weight is μ k , forming a weight vector μ={μ1,μ2,…,μ p}, and satisfy in That is, each decision maker has equal importance.

[0132] (2) Constructing a group decision-making model

[0133] The information gathering method of first integration and then dictatorship is adopted. Suppose there are p decision makers P k (k=1,2,…,p) form a decision-making group P={P1,P2,…,P p}, the decision maker expert weight is: μ={μ1,μ2,…,μ p},μ1+μ2+…+μ p =1, let decision maker P k The evaluation matrix given is

[0134]

[0135] The judgment matrix of each decision maker is weighted and aggregated to obtain the group judgment matrix R = (r ij ) m×n ,in

[0136]

[0137] (3) Solve according to the relevant fuzzy decision model and obtain the group judgment vector u = {u1,u2,…,u p},in

[0138]

[0139] Furthermore, in step 5

[0140] The specific steps of fuzzy multi-objective decision making are as follows:

[0141] (1) Constructing a decision matrix

[0142] The decision maker has m candidates A1, A2, ..., A m The judgment values ​​x1, x2, ..., given by the n targets, we get an m×n decision matrix X m×n

[0143]

[0144] Among them, x ij is the evaluation value of the jth evaluation target of the i-th candidate object.

[0145] (2) First, normalize the decision matrix to R m×n =(r ij ) mn

[0146] Then the weighted normalized decision matrix is ​​obtained according to the following formula:

[0147]

[0148] (3) Determine positive and negative ideal solutions

[0149] Positive ideal solution: G = {g1, g2, ..., g n}、Negative ideal solution: B={b1,b2,…,b n}

[0150] When the target value is an exact number:

[0151]

[0152] When the target value is a triangular fuzzy number:

[0153]

[0154]

[0155] (4) Calculate the distance between each solution and the positive and negative ideal solutions and

[0156] The distance between the i-th solution and the positive ideal solution and the negative ideal solution is:

[0157]

[0158]

[0159] (5) Calculate the grey correlation degree of each solution for the positive and negative ideal solutions

[0160] The grey correlation coefficient of the positive ideal solution and the negative ideal solution of the i-th scheme under the j-th index is:

[0161]

[0162] in, ξ is the resolution coefficient, which is generally taken as 0.5.

[0163] The grey correlation coefficient matrix of each scheme for positive ideal solution and negative ideal solution is:

[0164]

[0165] The grey correlation degree between the ith solution and the positive and negative ideal solutions is:

[0166]

[0167]

[0168] (6) Standardize distance and grey correlation

[0169] The measurement methods and magnitudes of grey relational degree and distance are different. It is necessary to normalize them to obtain standard grey relational degree and distance. The normalization formula is:

[0170]

[0171]

[0172] (7) Calculate overall closeness

[0173] The greater the distance from the positive ideal solution, the smaller the distance from the negative ideal solution, the better the solution; the greater the correlation with the positive ideal solution, the smaller the correlation with the negative ideal solution, the better the solution. Therefore, the following formula is constructed:

[0174]

[0175]

[0176] Among them, α+β=1, the size of α and β reflects the decision maker's preference for the grey relational analysis method and TOPSIS method, and the overall proximity C is defined as i

[0177]

[0178] (8) C determined according to (7) iThe solutions are ranked by size.

[0179] The above description is only by way of illustration of certain exemplary embodiments of the present invention. It is undoubted that those skilled in the art can modify the described embodiments in various ways without departing from the spirit and scope of the present invention. Therefore, the above drawings and descriptions are illustrative in nature and should not be construed as limiting the scope of protection of the claims of the present invention.

Claims

1. A method for evaluating the operation effect of a smart fishery based on fuzzy multi-objective decision making, characterized in that: This method implements the following steps: Step 1: Establish an evaluation index system for the operation effect of smart fisheries based on the principle of hierarchical analysis method Establish a two-level three-layer structure of smart fishery operation effect evaluation index system, which includes three first-level indicators: technical factors, economic factors, environmental factors and social factors; technical factors include three second-level indicators: technical applicability, technical feasibility and technical maturity; economic factors include two second-level indicators: technical cost and technical benefit; environmental factors include one second-level indicator: environmental protection benefit; social factors include two second-level indicators: resource utilization and social value; Step 2: Normalize quantitative and qualitative goals The qualitative objectives in the decision-making objectives are converted into fuzzy numbers, and the quantitative objectives are processed by linear transformation method; Step 3: Determine the weight of the decision goal The entropy method is used to determine the weight of decision-making objectives, which include benefit indicators and economic indicators; Step 4: Make group decisions Construct a group decision model and solve it through the relevant fuzzy decision model to obtain the group judgment vector of each plan; Step 5: Make fuzzy multi-objective decision The TOPSIS method and grey correlation analysis method are combined to make fuzzy multi-objective decision-making, and the various plans are ranked according to the indicators.

2. According to claim 1, a smart fishery operation effect evaluation method based on fuzzy multi-objective decision-making is characterized in that: The qualitative objectives described in step 2 are as follows: technical applicability indicates the difficulty of implementation and debugging of a smart fishery, environmental adaptability, matching with relevant technologies and energy efficiency ratio; technical feasibility indicates the safety index and equipment life of a smart fishery; technical maturity indicates the degree of automation and extensive application of a smart fishery; resource utilization indicates the sustainable development of a smart fishery; social value indicates the social impact of a fishery, the degree of commercial operation and the driving force for other industries.

3. According to the qualitative target described in claim 2, the specific steps of performing fuzzy number processing on it are as follows: (1) The language evaluation level is expressed as five levels: poor, poor, medium, good, and very good; (2) Determine the language evaluation level to which the qualitative objective belongs; (3) The language evaluation level of the qualitative target is converted into a triangular fuzzy number. The evaluation level of the i-th evaluator on the j-th target is expressed as The conversion relationship between triangular fuzzy numbers and different evaluation levels is: when the language evaluation level is poor, the corresponding triangular fuzzy number is (0, 0, 0.25); when the language evaluation level is poor, the corresponding triangular fuzzy number is (0, 0.25, 0.5); when the language evaluation level is medium, the corresponding triangular fuzzy number is (0.25, 0.5, 0.75); when the language evaluation level is good, the corresponding triangular fuzzy number is (0.5, 0.75, 1); when the language evaluation level is very good, the corresponding triangular fuzzy number is (0.75, 1, 1).

4. According to the method for evaluating the operation effect of a smart fishery based on fuzzy multi-objective decision making in claim 1, it is characterized in that: The quantitative objectives described in step 2 are as follows: technical cost represents the cost of investment, energy consumption, daily operation and equipment maintenance of a smart fishery; technical benefit represents the sum of the internal benefit, net annual value and annual electricity replacement of a smart fishery; environmental benefit represents the ability of a smart fishery to reduce emissions of harmful gases, dust and other particulate matter.

5. According to the quantitative target of claim 4, the specific steps of performing linear transformation processing on it are as follows: (1) Differentiate between the quantitative target as a benefit-based indicator and an economic indicator; (2) Construct a decision matrix X for the target = {x ij } Among them, x ij is the evaluation value of the jth evaluation target of the i-th candidate object. (3) For benefit-based indicators, the normalization parameters are: (4) For economic indicators, the normalization parameters are:

6. According to the method for evaluating the operation effect of a smart fishery based on fuzzy multi-objective decision making in claim 1, it is characterized in that: In step 3, the specific steps for determining the weight of the decision target are: (1) Let the normalized decision matrix be R = (r ij ) m×n , for the jth indicator, the deviation D between the i-th solution and all other solutions ij for: Among them, d(r ij ,r kj ) represents r ij With r kj For the jth attribute, the deviation D between all solutions and other solutions j for (2) Calculate the decision information E of each indicator j (3) Calculate the difference G of the jth index j G j =1-E j (4) Calculate the entropy weight μ j 7. According to claim 1, a smart fishery operation effect evaluation method based on fuzzy multi-objective decision-making is characterized in that: The specific steps of group decision making in step 4 are as follows: (1) Determine the decision maker’s weight Suppose in the group decision problem, the group consisting of p decision makers is P = {P1, P2, ..., P P }, the kth decision maker P k The weight is μ k , forming a weight vector μ={μ1,μ2,…,μ p }, and satisfy in That is, each decision maker has equal importance. (2) Constructing a group decision-making model The information gathering method of first integration and then dictatorship is adopted. Suppose there are p decision makers P k (k=1,2,…,p) form a decision-making group P={P1,P2,…,P p }, the decision maker expert weight is: μ={μ1,μ2,…,μ p },μ1+μ2+…+μ p =1, let decision maker P k The evaluation matrix given is The judgment matrix of each decision maker is weighted and aggregated to obtain the group judgment matrix R = (r ij ) m×n ,in (3) Solve according to the relevant fuzzy decision model and obtain the group judgment vector u = {u1,u2,…,μ p },in 8. According to claim 1, a smart fishery operation effect evaluation method based on fuzzy multi-objective decision-making is characterized in that: The specific steps of performing fuzzy multi-objective decision making in step 5 are as follows: (1) Constructing a decision matrix The decision maker has m candidates A1, A2, ..., A m The judgment values ​​x1, x2, …, x given by the n targets n , we get an m×n decision matrix X m×n Among them, x ij is the evaluation value of the jth evaluation target of the i-th candidate object. (2) First, normalize the decision matrix to R m×n =(r ij ) mn Then the weighted normalized decision matrix is ​​obtained according to the following formula: (3) Determine positive and negative ideal solutions Positive ideal solution: G = {g1, g2, ..., g n }、Negative ideal solution: B={b1,b2,…,b n } When the target value is an exact number: When the target value is a triangular fuzzy number: (4) Calculate the distance between each solution and the positive and negative ideal solutions and The distance between the i-th solution and the positive ideal solution and the negative ideal solution is: (5) Calculate the grey correlation degree of each solution for the positive and negative ideal solutions The grey correlation coefficient of the positive ideal solution and the negative ideal solution of the i-th scheme under the j-th index is: in, ξ is the resolution coefficient, which is generally taken as 0.

5. The grey correlation coefficient matrix of each scheme for positive ideal solution and negative ideal solution is: The grey correlation degree between the ith solution and the positive and negative ideal solutions is: (6) Standardize distance and grey correlation The measurement methods and magnitudes of grey relational degree and distance are different. It is necessary to normalize them to obtain standard grey relational degree and distance. The normalization formula is: (7) Calculate overall closeness The greater the distance from the positive ideal solution, the smaller the distance from the negative ideal solution, the better the solution; the greater the correlation with the positive ideal solution, the smaller the correlation with the negative ideal solution, the better the solution. Therefore, the following formula is constructed: Among them, α+β=1, the size of α and β reflects the decision maker's preference for the grey relational analysis method and TOPSIS method, and the overall proximity C is defined as i (8) C determined according to (7) i The solutions are ranked by size.

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