Qualitative and quantitative multi-type index comprehensive fuzzy static evaluation method and related product

Abstract

The invention relates to the technical field of engineering suitability evaluation, in particular to a qualitative and quantitative multi-type index comprehensive fuzzy static evaluation method and related products, and the method comprises the steps: constructing an evaluation factor influence degree matrix, carrying out the standardization processing of the matrix, and comprehensively considering the influence degree, affected degree, centrality and reason degree of evaluation factors; performing interval assignment on the evaluation indexes according to the comprehensive influence degree, and constructing a comprehensive evaluation coefficient matrix so as to simultaneously describe interval characteristics and uncertainty of qualitative and quantitative indexes; in combination with a trapezoidal fuzzy number model, uniformly processing different types of indexes, and obtaining a comprehensive attribute index vector through defuzzification calculation; and according to the comprehensive attribute index vector and a preset weight, calculating a weighted comprehensive attribute value of each scheme, carrying out sorting based on a fuzzy membership model, and finally optimizing an optimal scheme.

Description

Technical Field

[0001] The present invention relates to the field of evaluation technologies, and particularly to a qualitative and quantitative multi-type index comprehensive fuzzy static evaluation method and related products. Background Art

[0002] Existing technologies usually only perform fuzzy evaluation or calculation for a single index, such as the stability analysis of geological bodies or the safety assessment of engineering structures. Such evaluation methods for single indexes are difficult to comprehensively reflect the complex interrelationships of multiple factors in a more comprehensive site suitability analysis. For the overall evaluation of engineering construction suitability, the industry generally uses the expert method for demonstration. However, due to the strong dependence on subjective experience, the objectivity and reliability of the evaluation results are often insufficient.

[0003] Currently existing interval assignment evaluation methods are mainly applied to fields with monitoring data. These methods usually construct intervals for clear monitoring deviation values and perform index analysis based on the data. However, for scenarios with little or no monitoring data, the applicability of such methods is poor. At the same time, existing interval assignment methods mostly focus on the interval attributes of indexes and fail to systematically introduce and process the influence degree attributes of indexes theoretically. In addition, for the interval fuzzy scale comprehensive evaluation of multi-type indexes (including qualitative and quantitative indexes), there is still no relevant technical report currently.

[0004] In the field of multi-index evaluation of qualitative and quantitative mixtures, existing fuzzy evaluation methods are more applied to fields such as business decision-making and military strategies. These methods usually assume that multiple factors are independent or orthogonal to each other during design. However, this assumption is difficult to reflect the complex coupling relationships of multiple factors in engineering suitability evaluation. For example, when evaluating indexes such as geological conditions and project costs, the mutual influence between each index is significant in actual scenarios, and this mutual influence is often ignored in existing technologies. In addition, existing technologies do not fully consider the overall influence of the mutual influence degree of multiple factors on the evaluation results, resulting in limitations in the scientificity and applicability of the comprehensive evaluation results. Summary of the Invention

[0005] In order to solve the above technical problems, the present invention provides a qualitative and quantitative multi-type index comprehensive fuzzy static evaluation method and related products, realizing a comprehensive fuzzy static evaluation of a complex site based on interval assignment of influence evaluation factors, and being able to accurately and objectively determine the optimal solution under insufficient data, improving the scientificity and reliability of engineering decision-making.

[0006] The present invention is realized through the following technical solutions:

[0007] A qualitative and quantitative multi-type index comprehensive fuzzy static evaluation method, applicable to complex scenarios with little or no monitoring data, includes:

[0008] Obtain multiple evaluation schemes to be evaluated and their influencing factors, determine the influence scale of each influencing factor, construct an evaluation scheme coefficient matrix, and normalize the evaluation scheme coefficient matrix;

[0009] Based on the influence scale, the weight coefficients of the influencing factors in each evaluation scheme are determined, and trapezoidal fuzzy number assignment is performed;

[0010] The weight coefficients after the trapezoidal fuzzy number assignment are subjected to attribute processing and defuzzification to obtain the attribute indicators of the influencing factors in each evaluation scheme;

[0011] Calculate the membership degree of each evaluation scheme based on the attribute index;

[0012] According to the membership degree and the preset performance evaluation function, the comprehensive evaluation function of each evaluation scheme is determined, and the evaluation schemes are ranked.

[0013] Specifically, the method of obtaining the impact scale includes:

[0014] According to the mutual influence relationship between the evaluation factors, the initial influence matrix X is constructed;

[0015] Normalize the initial influence matrix X to obtain the normalized influence matrix Y;

[0016] According to the normalized influence matrix Y, calculate the comprehensive influence matrix T, T = Y (IY) -1 , where is the identity matrix;

[0017] The sum of each row of the comprehensive influence matrix T is used as the influence scale of each evaluation factor, and the sum of each column is used as the affected scale of each evaluation factor;

[0018] According to the influence scale and the affected scale, calculate the centrality and causality of each evaluation factor. The centrality is the sum of the influence scale and the affected scale, and the causality is the difference between the influence scale and the affected scale.

[0019] If there is an evaluation factor whose cause degree is less than the preset threshold, it will be eliminated and recalculated until the final impact scale that meets the evaluation requirements is formed.

[0020] Specifically, the method of obtaining the normalized coefficient matrix includes:

[0021] Multiple options to be evaluated A i For the line, evaluate the factor D j As columns, construct the initial coefficient matrix Where i = 1, 2, ..., m, j = 1, 2, ..., n, m is the number of solutions, n is the number of evaluation factors that have not been eliminated, is the initial value of the jth evaluation factor of the i-th solution;

[0022] For each element of the initial coefficient matrix perform assignment: If it is a qualitative index, use the scale value given by the expert method and normalize it; if it is a quantitative index, use the monitoring data or calculation result as the initial assignment and normalize it; Separate the initial coefficient matrix into multiple sub-matrices according to the different attributes of qualitative and quantitative indexes, including a qualitative sub-matrix and one or more quantitative sub-matrices;

[0023] Normalize the qualitative sub-matrix and multiple quantitative sub-matrices;

[0024] Merge the processed qualitative sub-matrix and quantitative sub-matrices to form a comprehensive evaluation coefficient matrix G, which is used to characterize uncertainty and multi-type attributes simultaneously.

[0025] Specifically, if it is the initial assignment in the qualitative sub-matrix, the processing formula is

[0026] If it is the initial assignment in the quantitative sub-matrix, the processing formula is If it is the initial assignment in the quantitative sub-matrix, the processing formula is K ij is the reasonable target value of this evaluation factor;

[0027] When there is a reasonable target standard value X, K ij takes the reasonable target standard value; when the deviation degree needs to be evaluated,

[0028] Specifically, the method of assigning trapezoidal fuzzy numbers includes:

[0029] For the decision index set ij in the comprehensive evaluation coefficient matrix G = {G classify it according to the qualitative index set and the quantitative index set where: represents a qualitative index, and use the expert method or Delphi method to construct a trapezoidal fuzzy number represents a quantitative index, and construct a trapezoidal fuzzy number according to the monitoring data or calculation result, combined with the reasonable target value range

[0030] Normalize the constructed trapezoidal fuzzy numbers and respectively to obtain the normalized fuzzy numbers and Among them, for qualitative indexes: For quantitative indexes:

[0031] Specifically, the methods for obtaining the attribute indicators of the influencing factors in each evaluation scheme include:

[0032] For the normalized fuzzy numbers and calculate the exact values of the evaluation indicators for each scheme A i

[0033] For each scheme A i , process all the defuzzified indicator values of it.

[0034] When When Among them,

[0035] Obtain the comprehensive attribute index vector Ψ(A i )

[0036] Specifically, the methods for calculating the membership degrees of each evaluation scheme include:

[0037] Determine the weight vector w = {w i |j = 1, 2,..., n} of each index in the comprehensive attribute index vector Ψ(A j ), calculate the influence degree index coefficient w ij , being the decision weight of the j-th index;

[0038] Calculate the membership degree value of scheme A i

[0039] Specifically, the methods for ranking the evaluation schemes according to the comprehensive evaluation function include:

[0040] Construct the comprehensive performance evaluation function J({μ j (A i )}), Among them: represents the weighted distance between the vector Ψ(A i ) and the prototype vector ;

[0041] Determine the optimization objective of the comprehensive performance evaluation function Optimize to obtain the optimal membership degree μ j (A i ), j = 1, 2,..., n, υ is the number of reference samples;

[0042] Obtain the optimized membership degree value

[0043] Sort all the solutions in descending order according to the membership value μ(S(A i )) and finally select the solution with the largest membership value as the optimal solution A best ,

[0044] A computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the above-mentioned method is implemented.

[0045] A computer program product includes a computer program / instructions, and when the computer program / instructions are executed by a processor, the above-mentioned method is implemented.

[0046] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0047] The present invention constructs an evaluation factor influence degree matrix, normalizes it, and comprehensively considers the influence degree, influenced degree, centrality, and reason degree of evaluation factors; assigns interval values to evaluation indicators according to the comprehensive influence degree, and constructs a comprehensive evaluation coefficient matrix to simultaneously characterize the interval characteristics and uncertainties of qualitative and quantitative indicators; combines the trapezoidal fuzzy number model to uniformly process different types of indicators, and obtains a comprehensive attribute index vector through defuzzification calculation; calculates the weighted comprehensive attribute values of each solution according to the comprehensive attribute index vector and the preset weight, and performs sorting based on the fuzzy membership model, and finally selects the optimal solution.

[0048] By constructing an evaluation factor influence degree matrix and introducing the calculation of centrality and reason degree, the present invention can comprehensively reflect the mutual relationship between evaluation factors. By assigning interval values to each evaluation indicator and constructing a comprehensive evaluation coefficient matrix, it simultaneously characterizes the uncertainties and multi-type attributes of qualitative and quantitative indicators, overcomes the limitation of inconsistent processing of different indicators in the existing methods, and uses the trapezoidal fuzzy number model and defuzzification method to effectively unify the index evaluation criteria with less monitoring data, thereby enhancing the accuracy and objectivity of the evaluation results. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] The drawings illustrate exemplary embodiments of the present invention and are used together with the description to explain the principles of the present invention. These drawings are included to provide a further understanding of the present invention, and the drawings are included in this specification and form a part of this specification, and do not constitute a limitation to the embodiments of the present invention.

[0050] Figure 1 is a schematic flowchart of a qualitative and quantitative multi-type index comprehensive fuzzy static evaluation method according to the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0051] To make the objectives, technical solutions, and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It can be understood that the specific embodiments described herein are only used to explain the relevant content and do not limit the present invention.

[0052] In addition, it should be noted that for the convenience of description, only the parts related to the present invention are shown in the drawings.

[0053] Without conflict, the embodiments in the present invention and the features in the embodiments can be combined with each other. The present invention will be described in detail below with reference to the drawings and embodiments.

[0054] Embodiment 1

[0055] As Figure 1 shown, a qualitative and quantitative comprehensive fuzzy static evaluation method for multiple types of indicators is provided, which is applicable to complex scenarios with no or few monitoring data, including:

[0056] S1. Obtain multiple evaluation schemes to be evaluated and their influencing factors, determine the influence scales of each influencing factor, construct an evaluation scheme coefficient matrix, and perform normalization processing on the evaluation scheme coefficient matrix;

[0057] The evaluation scheme refers to the options that need to be compared and evaluated, such as engineering design schemes, site selection schemes, etc. The influencing factors refer to various factors that affect the quality of the scheme, which can be qualitative (such as aesthetics, safety) or quantitative (such as cost, construction period).

[0058] Determine the mutual influence degree between each influencing factor and represent it numerically, usually determined through expert experience or specific algorithms (such as the improved DEMATEL algorithm). Represent the performance of each scheme on each influencing factor numerically to form a matrix. The rows of the matrix represent different schemes, and the columns represent different influencing factors. The elements in the matrix represent the scores or values of a specific scheme on a specific factor. Process the evaluation scheme coefficient matrix to eliminate the differences in dimensions and value ranges between different factors, making the data between different factors comparable.

[0059] S2. Determine the weight coefficients of the influencing factors in each evaluation scheme based on the influence scale and perform trapezoidal fuzzy number assignment;

[0060] The weight coefficient represents the numerical value of the importance of a certain factor in the overall evaluation. Due to the uncertainty and fuzziness in the evaluation process, using trapezoidal fuzzy numbers can better express this uncertainty.

[0061] S3. Perform attribute processing and defuzzification on the weighted coefficients after assigning values to trapezoidal fuzzy numbers to obtain the attribute indicators of the influencing factors in each evaluation scheme; further process the weighted coefficients represented by trapezoidal fuzzy numbers, and through defuzzification, convert the fuzzy weighted coefficients into a definite numerical value, that is, the "attribute indicator".

[0062] S4. Calculate the membership degrees of each evaluation scheme based on the attribute indicators; according to the attribute indicators, calculate the degrees to which each scheme belongs to different levels such as "excellent", "good", "medium", and "poor". The higher the membership degree, the better the scheme.

[0063] S5. According to the membership degrees and the preset performance evaluation function, determine the comprehensive evaluation function of each evaluation scheme and rank the evaluation schemes. Comprehensively consider the membership degrees and weights of each factor, optimize the membership degrees of each scheme according to the comprehensive evaluation function, and rank according to the optimized membership degrees. The higher the score, the better the scheme.

[0064] Example Two

[0065] The method for obtaining the comprehensive influence scale will be described in detail below. The method for obtaining the comprehensive influence scale is based on an improved DEMATEL (Decision Making Trial and Evaluation Laboratory) algorithm, aiming to construct a mutual influence matrix between evaluation factors and, through a series of mathematical processes, obtain a comprehensive influence scale matrix and indicators such as the centrality, reason degree, and influence of each factor. This method takes matrix operations as the core, converts the index relationship of fuzzy evaluation into a real-number relationship, and the methods for performing influence scale analysis include:

[0066] S11. Construct an initial influence matrix X according to the mutual influence relationship between evaluation factors;

[0067] Construct a self-evaluation matrix based on the direct influence scale between each pair of evaluation factors; according to each evaluation factor D i and D j Construct a self-evaluation matrix X = (x ij ) n×n to express the influence of the jth index on the ith index.

[0068] For Plan A i the evaluation factors are D i , D i = (D1, D2, D3 … D n ), D i ∈R, which is a set of real numbers. Mainly by evaluating the correlation between each pair of these factors, select the factors that have a greater impact on the evaluation system and the factors with little impact. The scale x i of the mutual influence degree between the involved index D j and D ijTo construct the self-evaluation matrix X of the n-order index correlation, X = (x ij ) n×n , which is used to express the influence of the j-th index on the i-th index.

[0069] Where: x ij is the scale of the direct influence of index D i on index D j . For calculation, it is necessary to assign values to the influence of the indexes. Generally, the influence degree can be classified and assigned values. For example, for {very large influence, relatively large influence, medium influence, general influence, relatively small influence, no influence}, they are forcibly assigned values {5, 4, 3, 2, 1, 0} respectively, or the Delphi method is used to take the average value for assignment, and then a comprehensive influence matrix is constructed for calculation. When i = j, x ij = 5; when x ij = 0, it means that index D i has no direct influence on index D j .

[0070] For example, assume there is a set of 4 evaluation factors, the order of influence on the other 3 factors is (5, 3, 2), the order of influence on the other 3 factors is (1, 4, 4), the order of influence on the other 3 factors is (0, 0, 3), the order of influence on the other 3 factors is (5, 1, 5), then the constructed 4-order index evaluation matrix,

[0071] S12. Normalize the initial influence matrix X to obtain the normalized influence matrix Y;

[0072] To make the matrix operation converge, it is necessary to normalize the X matrix to form the Y matrix. Currently, generally, the sum of each row of the matrix is calculated and the maximum value is recorded as max. The normalized matrix is processed by Y = x ij / max.

[0073] Matrix (case ), after calculation, the normalized matrix,

[0074] S13. According to the normalized influence matrix Y, calculate the comprehensive influence matrix T, T = Y·(I - Y) -1 , where I is the identity matrix;

[0075] Construct a comprehensive influence matrix And apply the T matrix to solve the centrality, reasonability, and factor D i The basic influence in the system, form the influence scale matrix of the influencing factors, as the basis for subsequent evaluation.

[0076] Construct a comprehensive influence matrix T,

[0077] where: I is the identity matrix, t ij Can reflect factor D i On D j The comprehensive influence degree of.

[0078] Still using the above case D4, the calculated T matrix is:

[0079]

[0080] S13. Take the sum of each row of the comprehensive influence matrix T as the influence scale of each evaluation factor, and the sum of each column as the influenced scale of each evaluation factor;

[0081] Apply the T matrix to solve the centrality and reasonability. The sum of each row f of matrix T i (The sum of the influences of factor D i On other factors) is D i The influence scale of, and the sum of each column e i (The sum of the influences received by factor D i From other factors) is D i The influenced scale of. For example, in case D4, the calculated results are:

[0082] f4 = (0.3776, 0.3490, 0.1917, 0.3999) T ………… Equation 6-6

[0083] e4 = (0.2714, 0.2648, 0.4299, 0.3520) ………… Equation 6-7

[0084] S14. According to the influence scale and the influenced scale, calculate the centrality and reasonability of each evaluation factor. The centrality is the sum of the influence scale and the influenced scale, and the reasonability is the difference between the influence scale and the influenced scale;

[0085] If you want to compare the importance of each factor, you need to set parameters for sorting. Set the following parameters:

[0086] Let:

[0087] γ i = f i + ei (Equation 6-8), D i 's centrality, indicating D i 's relative importance;

[0088] δ i = f i - e i (Equation 6-9), D i 's causality, δ i > 0 indicates that D i is a causal (active) factor;

[0089] ω i = f i / γ i (Equation 6-10), which expresses the ratio of the influence scale to the centrality, reflecting the basic influence of factor D i in the system;

[0090] Z i = γ i / 1 - e i , indicating D i 's effective centrality... Equation 6-11;

[0091] K i = min{(ω i / 1 - f i ), 1}, indicating D i 's maximum estimated value of the influence scale... Equation 6-12;

[0092] H i = f i / 1 - e i , indicating D i 's minimum estimated value of the influence scale... Equation 6-13.

[0093] For example, in case D4, the calculated results are: γ4 = (0.6490, 0.6138, 0.6216, 0.7520), δ4 = (0.1062, 0.0841, -0.2382, 0.0479), ω4 = (0.5818, 0.5685, 0.3083, 0.5319), Z4 = (0.4728, 0.4511, 0.3544, 0.4872), K4 = (0.9346, 0.8730, 0.3815, 0.8864), H4 = (0.2751, 0.2565, 0.1093, 0.2592).

[0094] Sorting ω i from largest to smallest reflects the importance ranking. For example, in the case The importance ranking of the 4 factors is D1 > D2 > D4 > D3, which is basically consistent with the influence judgment of each factor during assignment.

[0095] S15. If there are evaluation factors with negative cause degrees, they shall be excluded and recalculated iteratively until the final influence scale that meets the evaluation requirements is formed, and the basic influence factor vector of the evaluation scheme and the basic influence force vector of the influence factors in the evaluation scheme are determined.

[0096] If there are evaluation factors with negative cause degrees, they shall be excluded and recalculated iteratively until the final influence scale matrix that meets the evaluation requirements is formed, where the final influence scale includes the influence scale, the influenced scale, the centrality, and the cause degree of each evaluation factor.

[0097] During the evaluation process, the factors of the system may be selected to exclude interference factors.

[0098] For δ i Factors with δ < 0 are generally excluded. For example, in case D4, the cause degree δ3 of D3 = -0.2382 < 0 and should be excluded.

[0099] To make the evaluation factors of multiple schemes uniform, only the factors that do not meet the evaluation conditions for all schemes can be excluded. If an influencing factor is excluded, the influence scale should be recalculated until the evaluation conditions are met.

[0100] Embodiment III

[0101] The method for constructing the evaluation coefficient matrix takes multiple schemes to be evaluated as rows and evaluation factors as columns, and constructs an initial coefficient matrix by subjectively assigning values or obtaining data for the indicators; subsequently, the method for normalizing the matrix according to the attributes of qualitative and quantitative indicators includes:

[0102] S21. Taking multiple schemes A to be evaluated i as rows and evaluation factors D j as columns to construct an initial coefficient matrix where i = 1, 2,..., m, j = 1, 2,..., n, m is the number of schemes, and n is the number of evaluation factors that have not been excluded, is the initial assignment of the jth evaluation factor of the ith scheme;

[0103] Taking the comparison evaluation scheme A i as rows and the influence factor assignments of scheme A i as columns to construct an evaluation scheme coefficient matrix

[0104]

[0105] S22. For the initial coefficient matrix For each element Assignment is carried out as follows: If it is a qualitative index, the scale value given by the expert method is used and normalized. The scale interval is divided according to actual needs, generally [1, 9].

[0106] If it is a quantitative index, the monitoring data or calculation results are used as the initial assignment and normalized;

[0107] Taking Example 1 as an illustration, assuming they are all qualitative indexes, on the basis of the above case, three more cases are added. Assuming each case has 4 influencing factors. If the comparison assignment results are x i1 = {3, 6, 7, 5}, x i2 = {4, 6, 8, 7}, x i3 = {1, 2, 5, 7}, x i4 = {7, 6, 9, 3}, then the coefficient matrix (qualitative matrix) is:

[0108]

[0109] Taking Example 2 as an illustration, assuming x i1 and x i3 are qualitative indexes, x i2 and x i4 are quantitative indexes. Taking as four cases, if the comparison assignment results of the scheme are x i1 = {3, 6, 7}, x i3 = {1, 2, 5}, and the monitoring and calculation results are x i2 = {0.98, 1.13, 1.07}, x i4 = {1900, 2010, 1985}, then the constructed coefficient matrix (mixed matrix) is:

[0110]

[0111] If is a qualitative matrix, normalization processing is carried out;

[0112] If it is the initial assignment in the qualitative sub-matrix, the processing formula is

[0113] That is, in the above Example 1, the new matrix after normalization processing is:

[0114]

[0115] But generally, is a mixing matrix, so execute S23.

[0116] S23, according to different attributes of the qualitative indicators and the quantitative indicators, separating the initial coefficient matrix into a plurality of sub-matrices, including a qualitative sub-matrix and one or more quantitative sub-matrices;

[0117] Right now It is a mixed matrix. First, the matrix is separated according to the qualitative and quantitative indicator categories (assuming there are v, such as dependent variable growth type, dependent variable decreasing type, and fluctuation type), and organized into sub-matrices G1, G2...G v The qualitative submatrix is processed as follows; when processing the quantitative submatrix, the reasonable target value of the evaluation factor is set to K ij , then process as follows:

[0118]

[0119] K ij Determination method: When there is a reasonable target standard value X, it is directly adopted; if the deviation needs to be evaluated, it is determined according to the following formula: Let: the target value is X, there is

[0120] As in Example 1 above, the new matrix after normalization is:

[0121]

[0122] S24, normalizing the qualitative sub-matrix and the multiple quantitative sub-matrices;

[0123] S25. The processed qualitative sub-matrix and quantitative sub-matrix are merged to form a comprehensive evaluation coefficient matrix G. The comprehensive evaluation coefficient matrix is used to simultaneously characterize uncertainty and multi-type attributes.

[0124] Embodiment 4

[0125] By classifying the indicators in the comprehensive evaluation coefficient matrix and assigning trapezoidal fuzzy numbers to each indicator, the uncertainty and interval characteristics of the evaluation indicators can be accurately described. By constructing trapezoidal fuzzy numbers for qualitative and quantitative indicators respectively, and combining with normalization processing, a unified quantitative basis is finally provided for subsequent fuzzy calculations.

[0126] Theoretical basis of fuzzy numbers:

[0127] It is a trapezoidal function, such as using excellent or large or good feasibility (δ), good or large or good feasibility (γ), medium or general or acceptable (β), poor or small or poor feasibility (α) to describe the fuzzy set, and the site suitability evaluation just meets the characteristics of the trapezoidal function.

[0128] The basic definition is as follows: Fuzzy number on the domain R Membership function Satisfies the relational expression of Equation 6-19, and the fuzzy number Is a trapezoidal fuzzy number, denoted as

[0129]

[0130] Where: α ≤ β ≤ γ ≤ δ ∈ ψ,

[0131] When α = β = γ = δ, Represents a non-fuzzy number, and the exact numerical value can also be used To represent.

[0132] The membership degree μ of G in the evaluation scheme coefficient matrix G after normalization processing ij : R → [0, 1], for the same influencing factor X G , Obviously, the scheme set A i ={(X1, G1), (X2, G2), …, (X i , G i , G i )} satisfies the trapezoidal function model, and can be scaled by (α, β, γ, δ) for the levels of poor, medium, good, and excellent.

[0133] Define a method for defuzzifying a fuzzy number:

[0134] Let: S be a bounded convex fuzzy number set λ (0 < λ ≤ 1), and its level cut set Is a real closed interval. When λ j = j / n (j = 1, 2…n), denote If R is the set of real numbers, the function D: S → R, for All have:

[0135]

[0136] And Then D is called a defuzzification function on S. From the definition of the trapezoidal fuzzy number in the previous text,

[0137] The methods for determining fuzzy numbers include:

[0138] S31. For the decision index set ij In the comprehensive evaluation coefficient matrix G = {G Classify it according to the qualitative index set And the quantitative index set , Where: Indicates qualitative indicators, applicable to subjective evaluation indicators that cannot obtain numerical values through precise measurement. Trapezoidal fuzzy numbers are constructed using the expert method or Delphi method. Indicates quantitative indicators, applicable to objective evaluation indicators with clear dimensions and target values. Trapezoidal fuzzy numbers are constructed based on monitoring data or calculation results, combined with a reasonable target value range.

[0139] S32. For the constructed trapezoidal fuzzy numbers and Normalize them respectively to obtain the normalized fuzzy numbers and

[0140] First, perform assignment. The assignment method is as follows:

[0141] For each decision-making indicator Perform evaluation assignment

[0142] ① Expert assignment method.

[0143] Experts assign values based on experience, which can be used for big data training.

[0144] ② Calculation assignment method.

[0145] Process according to the results obtained from the preprocessing.

[0146] Indicator set The evaluation values are all:

[0147] After obtaining the assignment, classify according to quantitative and qualitative indicators. Taking the previous D, A, B, C cases as examples, after calculation, the value matrices of each plan are respectively:

[0148]

[0149]

[0150] Then, perform attribute processing on the decision-making indicators:

[0151]

[0152] S33. For the normalized fuzzy numbers and Calculate the exact values i of each evaluation indicator for each plan A

[0153] For each plan A i , process all the defuzzified indicator values of it,

[0154] When When When When Among them

[0155] That is: after solving equations 6-23 and 6-24 with equation 6-22, solve the ambiguity with equation 6-20 to obtain the attribute indexes of each influencing factor in the solution, and process the attribute indexes

[0156]

[0157] Obtain the comprehensive attribute index vector Ψ(A i )

[0158] For example, after calculation, the attribute index matrix of the aforementioned case is as follows

[0159]

[0160] The attribute index matrix of the case is as follows

[0161]

[0162] S34. Determine the weight vector ω = {ω i |j = 1, 2,..., n} of each index in the comprehensive attribute index vector Ψ(A j ), where the element ω j of the weight vector ω satisfies the normalization condition: solve the influence degree index coefficient with equation 6-40

[0163]

[0164] D(ω j ) is the decision weight of the jth index

[0165] Case and case The normalized vector matrices are respectively

[0166]

[0167] S35. Calculate the weighted comprehensive attribute value S(A i ) of each solution A i through the weight vector ω and the comprehensive attribute index vector Ψ(A i ),

[0168] Example 5

[0169] S41. In actual work, the feasibility of a solution is expressed as "good" or "bad". At this time, v = 2, and the Euclidean distance in the n-dimensional real number space can be used to represent the inner product of n-dimensional vectors (Equation 6-26). Finally, by comparing the membership degrees of each solution belonging to "good", it is used as a function for comprehensive evaluation of the solutions (Equation 6-27).

[0170] For example, for case and case After calculation, the comprehensive evaluation value of its factors is:

[0171]

[0172] S42. Construct a comprehensive performance evaluation function J({μ j (A i )}):

[0173]

[0174] Among them, represents the weighted distance between the vector Ψ(A i ) and the prototype vector ; ‖·‖ is the inner product operation of two vectors.

[0175] S43. When the following formula is satisfied, μ j (A i ) obtains the optimal solution:

[0176]

[0177] Optimize to obtain the optimal membership degree μ j (A i ), j = 1, 2,..., n, υ is the number of reference samples;

[0178] S44. Obtain the optimized membership degree value

[0179] Sort all solutions in descending order according to the membership degree value μ(S(A i ))), and finally select the solution with the largest membership degree value as the optimal solution A best ,

[0180] Example 6

[0181] A computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the above-mentioned method is implemented.

[0182] Without loss of generality, computer-readable media can include computer storage media and communication media. Computer storage media includes volatile and non-volatile, removable and non-removable media implemented by any method or technology for storing information such as computer-readable instructions, data structures, program modules, or other data. Computer storage media includes RAM, ROM, EPROM, EEPROM, flash memory or other solid-state storage technologies, CD-ROM, DVD or other optical storage, magnetic tape cartridges, magnetic tapes, disk storage or other magnetic storage devices. Of course, those skilled in the art will know that computer storage media is not limited to the above several types. The above-mentioned system memory and mass storage devices can be collectively referred to as memory.

[0183] A computer program product includes computer programs / instructions that, when executed by a processor, implement the steps of the method described in any one of the above.

[0184] A computer program product includes a computer program or set of instructions for performing a specific task or implementing a specific function. These programs or instructions are designed to be executable by a processor to achieve a series of predefined steps or operations. The program product may be stored in various forms of computer storage media, such as memory, hard disk, solid-state drive, optical disc, or other forms of digital storage devices. It may exist in the form of compiled binary code or in the form of scripts or bytecodes executable by an interpreter. Through carefully designed algorithms and logical instructions, the program product enables the processor to process data in a specific order and manner to complete various functions such as data analysis, user interaction, and device control.

[0185] In the description of this specification, the description with reference to terms such as "one embodiment / way", "some embodiments / ways", "example", "specific example", or "some examples" means that the specific features, structures, materials, or characteristics described in connection with the embodiment / way or example are included in at least one embodiment / way or example of this application. In this specification, the schematic expressions of the above terms do not necessarily refer to the same embodiment / way or example. Moreover, the specific features, structures, materials, or characteristics described can be combined in a suitable manner in any one or more embodiments / ways or examples. In addition, without contradiction, those skilled in the art can combine and combine the different embodiments / ways or examples described in this specification and the features of different embodiments / ways or examples.

[0186] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the quantity of the indicated technical features. Thus, features defined with "first" and "second" may explicitly or implicitly include at least one such feature. In the description of the present application, the meaning of "a plurality" is at least two, such as two, three, etc., unless otherwise specifically defined.

[0187] Those skilled in the art should understand that the above embodiments are merely for clearly illustrating the present invention and are not intended to limit the scope of the present invention. For those skilled in the art, other changes or modifications can be made based on the above invention, and these changes or modifications are still within the scope of the present invention.

Claims

1. A qualitative and quantitative comprehensive fuzzy static evaluation method for multiple types of indicators, applicable to complex scenarios with no or few monitoring data, characterized in that include: Obtain multiple evaluation schemes to be evaluated and their influencing factors, determine the influence scale of each influencing factor, construct an evaluation scheme coefficient matrix, and normalize the evaluation scheme coefficient matrix; Based on the influence scale, the weight coefficients of the influencing factors in each evaluation scheme are determined, and trapezoidal fuzzy number assignment is performed; The weight coefficients after the trapezoidal fuzzy number assignment are subjected to attribute processing and defuzzification to obtain the attribute indicators of the influencing factors in each evaluation scheme; Calculate the membership degree of each evaluation scheme based on the attribute index; According to the membership degree and the preset performance evaluation function, the comprehensive evaluation function of each evaluation scheme is determined, and the evaluation schemes are ranked.

2. The qualitative and quantitative comprehensive fuzzy static evaluation method for multiple types of indicators according to claim 1, wherein Methods for obtaining influence scales include: According to the mutual influence relationship between the evaluation factors, the initial influence matrix X is constructed; Normalize the initial influence matrix X to obtain the normalized influence matrix Y; Calculate the comprehensive influence matrix T according to the standardized influence matrix Y, where T = Y·(I - Y) -1 , where I is the identity matrix; The sum of each row of the comprehensive influence matrix T is used as the influence scale of each evaluation factor, and the sum of each column is used as the affected scale of each evaluation factor; According to the influence scale and the affected scale, calculate the centrality and causality of each evaluation factor. The centrality is the sum of the influence scale and the affected scale, and the causality is the difference between the influence scale and the affected scale. If there is an evaluation factor whose cause degree is less than the preset threshold, it will be eliminated and recalculated until the final impact scale that meets the evaluation requirements is formed.

3. A qualitative and quantitative comprehensive fuzzy static evaluation method for multiple types of indicators according to claim 2, characterized in that Methods for obtaining a normalized coefficient matrix include: Multiple solutions A to be evaluated i Take the rows as the multiple solutions A to be evaluated, and the evaluation factor D j Take the columns to construct an initial coefficient matrix where \(i = 1, 2, \cdots, m\), \(j = 1, 2, \cdots, n\), \(m\) is the number of solutions, and \(n\) is the number of evaluation factors not excluded is the initial assignment of the \(j\)-th evaluation factor of the \(i\)-th solution For each element of the initial coefficient matrix assign a value: if it is a qualitative index, use the scale value given by the expert method and normalize it; if it is a quantitative index, use the monitoring data or calculation result as the initial assignment and normalize it; ​ According to different attributes of qualitative indicators and quantitative indicators, the initial coefficient matrix is separated into multiple sub-matrices, including a qualitative sub-matrix and one or more quantitative sub-matrices; Normalizing the qualitative sub-matrix and multiple quantitative sub-matrices; The qualitative sub-matrix and the quantitative sub-matrix after merging are formed to form a comprehensive evaluation coefficient matrix G, which is used to simultaneously characterize uncertainty and multi-type attributes.

4. A qualitative and quantitative comprehensive fuzzy static evaluation method for multiple types of indicators according to claim 3, characterized in that If it is the initial assignment in the qualitative sub-matrix, the processing formula is If it is the initial assignment in the quantitative sub-matrix, the processing formula is K ij is the reasonable target value of this evaluation factor; When there is a reasonable target standard value X, K ij Take the reasonable target standard value; when the degree of deviation needs to be evaluated, 5. The qualitative and quantitative comprehensive fuzzy static evaluation method for multiple types of indicators according to claim 3, characterized in that, The methods for assigning trapezoidal fuzzy numbers include: For the decision-making index set in the comprehensive evaluation coefficient matrix G = {G ij}, classify it according to the qualitative index set and the quantitative index set , where: represents qualitative indicators, and trapezoidal fuzzy numbers are constructed using the expert method or the Delphi method represents quantitative indicators, and trapezoidal fuzzy numbers are constructed based on monitoring data or calculation results in combination with a reasonable target value range The constructed trapezoidal fuzzy numbers and are respectively normalized to obtain the normalized fuzzy numbers and Among them, for qualitative indicators: For quantitative indicators:

6. A qualitative and quantitative comprehensive fuzzy static evaluation method for multiple types of indicators according to claim 5, characterized in that, Methods for obtaining attribute indicators of influencing factors in each evaluation scheme include: For the normalized fuzzy numbers and calculate the exact values of each evaluation index for each solution A i ​ For each solution A i , process the index values after defuzzifying all of its solutions When then When then wherein Obtain the comprehensive attribute index vector Ψ(A i ), 7. A qualitative and quantitative comprehensive fuzzy static evaluation method for multiple types of indicators according to claim 6, characterized in that, The methods for calculating the membership degree of each evaluation scheme include: Determine the weight vector ω = {ω i | j = 1, 2,..., n} of each index in the comprehensive attribute index vector Ψ(A j ), calculate the influence degree index coefficient ω ij , D(ω j ) is the decision weight of the j-th index; Calculation scheme A i of the membership degree value 8. A qualitative and quantitative comprehensive fuzzy static evaluation method for multiple types of indicators according to claim 7, characterized in that Methods for ranking evaluation schemes according to comprehensive evaluation functions include: Construct a comprehensive performance evaluation function J({μ j (A i )}) where: denotes the weighted distance between the vector Ψ(A i ) and the prototype vector ; Determine the optimization objective of the comprehensive performance evaluation function Obtain the optimal membership degree μ of each evaluation factor j (A i ), j = 1, 2,..., n, and v is the number of reference samples; Obtain the optimized membership degree value According to the membership value μ(S(A i )) sort all the solutions in descending order, and finally select the solution with the largest membership value as the optimal solution A best , 9. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, the method according to any one of claims 1 to 8 is implemented.

10. A computer program product, comprising a computer program / instructions, characterized in that, When the computer program / instructions are executed by a processor, the method according to any one of claims 1 to 8 is implemented.

Images