Fuzzy evaluation method based on evaluation index interval assignment and related product

Abstract

The invention relates to the field of fuzzy evaluation, in particular to a fuzzy evaluation method based on evaluation index interval assignment and a related product, and aims to realize objective screening and importance sorting of evaluation factors through an improved DEMATEL algorithm to analyze a mutual influence relationship among the evaluation factors; by constructing and normalizing an evaluation scheme coefficient matrix, unified processing of different types of evaluation indexes is realized; the interval number is adopted to carry out assignment on the influence degree of the evaluation factors, and the uncertainty in the evaluation process is effectively described; through combination of influence degree analysis, a coefficient matrix, interval assignment, weight determination, attribute aggregation and sorting analysis, a set of complete fuzzy comprehensive evaluation system is constructed. And the comprehensive attribute values of the schemes are compared and sorted by using the possibility degree matrix and the sorting vector, so that the evaluation results with uncertainty are effectively sorted.

Description

Technical Field

[0001] The present invention relates to the field of fuzzy evaluation, and specifically relates to a fuzzy evaluation method based on interval assignment of evaluation indicators and related products. Background Art

[0002] Existing technologies usually only conduct fuzzy evaluation or measurement for a single indicator, and such evaluation methods for single indicators are difficult to comprehensively reflect the complex mutual relationships of multiple factors. Generally, the expert method is adopted in the industry for demonstration, but due to the strong dependence on subjective experience of this method, the objectivity and reliability of its evaluation results are often insufficient.

[0003] The existing interval assignment evaluation methods are mainly applied to fields with monitoring data. These methods usually construct intervals for clear monitoring deviation values and conduct indicator 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, the existing interval assignment methods mostly focus on the interval attributes of indicators and fail to systematically introduce and process the influence degree attributes of indicators theoretically. In addition, there is still no relevant technical report on the comprehensive interval fuzzy scaling evaluation of multiple types of indicators (including qualitative and quantitative indicators).

[0004] In the field of multi-index evaluation with a mixture of qualitative and quantitative indicators, the existing fuzzy evaluation methods are more applied to fields such as business decision-making and military strategy. These methods usually assume that multiple factors are independent or orthogonal to each other during design, but this assumption is difficult to reflect the complex coupling relationships of multiple factors in engineering suitability evaluation. For example, when evaluating indicators such as geological conditions and project cost, the mutual influence between each indicator is significant in the actual scenario, but this mutual influence is often ignored in the existing technologies. In addition, the existing technologies do not fully consider the overall impact 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] The technical problem to be solved by the present invention is to achieve fuzzy evaluation in complex scenarios with little or no monitoring data. The purpose is to provide a fuzzy evaluation method based on interval assignment of evaluation indicators and related products, which realizes comprehensive fuzzy static evaluation based on interval assignment of influencing evaluation factors, and can accurately and objectively determine the optimal solution in the case of insufficient data.

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

[0007] A fuzzy evaluation method based on interval assignment of evaluation indicators, comprising:

[0008] Construct an evaluation system, determine multiple evaluation schemes and multiple evaluation factors, and the evaluation factors include qualitative indicators and quantitative indicators;

[0009] Analyze and evaluate the influence scales between factors, determine the influence scales of each evaluation factor, and screen the evaluation factors according to the influence scales to obtain the final influence scale;

[0010] Construct and normalize the coefficient matrix of the evaluation scheme to obtain the normalized coefficient matrix;

[0011] According to the analysis results of the influence scales of each evaluation scheme, assign interval values to the influence scales of each evaluation factor of each evaluation scheme to obtain the influence degree coefficient matrix;

[0012] Determine the weight vector of each evaluation factor;

[0013] Calculate the comprehensive attribute values of each evaluation scheme through the normalized coefficient matrix, the influence degree coefficient matrix and the weight vector;

[0014] Based on the comprehensive attribute values, construct a possibility complementary judgment matrix, calculate the sorting vector, and sort each evaluation scheme according to the sorting vector.

[0015] Specifically, the methods for conducting influence scale analysis include:

[0016] Construct an initial influence matrix X according to the mutual influence relationship between evaluation factors;

[0017] Normalize the initial influence matrix X to obtain the normalized influence matrix Y;

[0018] According to the normalized influence matrix Y, calculate the comprehensive influence matrix T, T = Y·(I - Y) -1 , where I is the identity matrix;

[0019] 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;

[0020] 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;

[0021] If there are evaluation factors with negative reasonability, eliminate them and recalculate iteratively until the final influence scale that meets the evaluation requirements is formed, and determine the basic influence factor vector of the evaluation scheme and the basic influence force vector of the influence factors in the evaluation scheme.

[0022] Specifically, the methods for obtaining the normalized coefficient matrix include:

[0023] With multiple schemes A to be evaluated i as rows and evaluation factors D j as columns, construct the 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;

[0024] For each element of the initial coefficient matrix make an 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;

[0025] 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;

[0026] Normalize the qualitative sub-matrix and multiple quantitative sub-matrices;

[0027] Combine 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.

[0028] Optionally, 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;

[0029] 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,

[0030] Optionally, the methods for obtaining the influence degree coefficient matrix include:

[0031] Determine the interval assignment method, including interval assignment using centrality and causality; or interval assignment using influence scale and effective centrality;

[0032] If interval assignment is performed using centrality and causality, let \(\omega\) ij \(=[\gamma\) ij \(-|\delta\) ij |, \(\gamma\) ij \(+|\delta\) ij |]\), \(i\in m\), \(j\in n\), where \(\omega\) ij is the influence degree, \(\gamma\) ij is the centrality of the \(j\)-th evaluation factor of the \(i\)-th solution, and \(\delta\) ij is the causality of the \(j\)-th evaluation factor of the \(i\)-th solution;

[0033] If the interval assignment is carried out by using the influence scale and effective centrality, then let ω ij ={f ij , Z ij , where f ij is the influence scale of the j-th evaluation factor of the i-th scheme, and Z ij is the effective centrality of the j-th evaluation factor of the i-th scheme;

[0034] Taking all ω ij as elements, construct the influence degree coefficient matrix W.

[0035] Specifically, the methods for determining the weight vector of each evaluation factor include:

[0036] Judge whether there is mutual influence between each evaluation factor;

[0037] If the evaluation factors are independent of each other, the weight vector of the j-th evaluation factor of the i-th scheme

[0038] If there is mutual influence between the evaluation factors, then the weight is assigned through the basic influence, and the de-fuzzified basic influence is used as the weight.

[0039] Optionally, the methods for calculating the comprehensive attribute value include: where G ij is the element of the normalization coefficient matrix, α ij is the weight, and ω ij is the element of the influence degree coefficient matrix;

[0040] If it is necessary to adjust the importance degree of a certain influence factor alone, then its comprehensive attribute value where ρ i is the adjustment coefficient.

[0041] Specifically, the methods for sorting each evaluation scheme include:

[0042] According to the comprehensive attribute values of each evaluation scheme, calculate the possibility p ij =p(ε i ≥ε k ), and construct the possibility complementary judgment matrix P=(p ij ) n×n ;

[0043] Calculate the sorting vector τ i =(τ1, τ2…τ n ) T ,

[0044] Sort each evaluation scheme according to the magnitude of each component value in the sorting vector.

[0045] A computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the above-described method is implemented.

[0046] A computer program product includes a computer program / instructions, and when the computer program / instructions are executed by a processor, the above-described method is implemented.

[0047] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0048] The method provided by the present invention analyzes the mutual influence relationship between evaluation factors through an improved DEMATEL algorithm, realizes the objective screening and importance ranking of evaluation factors; realizes the unified processing of different types of evaluation indicators (qualitative and quantitative) by constructing and normalizing the evaluation scheme coefficient matrix; uses interval numbers to assign values to the influence degrees of evaluation factors, effectively characterizing the uncertainty in the evaluation process; constructs a complete fuzzy comprehensive evaluation system by combining influence degree analysis, coefficient matrix, interval assignment, weight determination, attribute aggregation and ranking analysis; compares and ranks the comprehensive attribute values (interval numbers) of each scheme by using the possibility matrix and the ranking vector, realizing the effective ranking of the evaluation results with uncertainty; realizes the flexible adjustment of the weights of specific evaluation factors by introducing a adjustment coefficient in attribute aggregation. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] The drawings illustrate exemplary embodiments of the present invention and, together with the description, are used 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 on the embodiments of the present invention.

[0050] Figure 1 is a schematic flowchart of a fuzzy evaluation method based on interval assignment of evaluation indicators according to the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0051] To make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below with reference to the 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] It should be further noted that, for the sake of convenience of description, only 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] Example 1

[0055] As Figure 1 shown, a fuzzy evaluation method based on interval assignment of evaluation indicators is provided to handle the uncertainty in the evaluation process and rank multiple evaluation schemes. The method includes:

[0056] Construct an evaluation system, determine multiple evaluation schemes and multiple evaluation factors. The evaluation factors include qualitative indicators and quantitative indicators; the evaluation schemes are the objects that need to be compared and ranked. The evaluation factors are the indicators used to evaluate the schemes, divided into qualitative indicators (such as "user experience", "design aesthetics") and quantitative indicators (such as "cost", "efficiency").

[0057] Analyze the influence scale between evaluation factors, determine the influence scale of each evaluation factor, and screen the evaluation factors according to the influence scale to obtain the final influence scale; the influence scale is used to measure the influence degree of one evaluation factor on another evaluation factor, and through screening, those evaluation factors that have little influence on the evaluation result or are mainly affected by other factors can be eliminated.

[0058] Construct and normalize the coefficient matrix of the evaluation scheme to obtain the normalized coefficient matrix; each row represents an evaluation scheme, each column represents an evaluation factor, and each element in the table represents the performance of the corresponding scheme on this factor.

[0059] According to the analysis results of the influence scale of each evaluation scheme, perform interval assignment on the influence scale of each evaluation factor of each evaluation scheme to obtain the influence degree coefficient matrix; instead of using a single value to represent the influence degree of the evaluation factor, an interval is used to represent it to reflect the uncertainty of the evaluation.

[0060] Determine the weight vector of each evaluation factor, indicating the importance of each evaluation factor in the comprehensive evaluation.

[0061] Calculate the comprehensive attribute value of each evaluation scheme through the normalized coefficient matrix, the influence degree coefficient matrix and the weight vector;

[0062] Since the comprehensive attribute value is an interval number and cannot be directly compared in size, it is necessary to construct a matrix by calculating the "possibility" (the probability that one interval number is greater than another interval number), that is, construct a possibility complementary judgment matrix based on the comprehensive attribute value and calculate the sorting vector, and rank each evaluation scheme according to the sorting vector.

[0063] Example 2

[0064] The method for obtaining the comprehensive impact scale will be described in detail below. The method for obtaining the comprehensive impact scale is based on an improved DEMATEL (Decision Making Trial and Evaluation Laboratory) algorithm, aiming to construct a mutual influence matrix among evaluation factors and obtain a comprehensive impact scale matrix and indicators such as the centrality, reasonability, and influence of each factor through a series of mathematical processes. This method takes matrix operation as the core, transforms the index relationship of fuzzy evaluation into a real-number relationship, and the methods for impact scale analysis include:

[0065] S11. Construct an initial impact matrix X according to the mutual influence relationship among evaluation factors;

[0066] Construct a self-evaluation matrix based on the direct impact scale between each pair of evaluation factors; according to the direct influence degree between each pair of evaluation factors D i and D j construct a self-evaluation matrix X = (x ij ) n×n to express the influence of the j-th index on the i-th index.

[0067] For the evaluation factors of Plan A i are D i , D i = (D1, D2, D3 … D n ), D i ∈R, which is a real number set. It is mainly to select the factors with greater influence and those with little influence on the evaluation system by evaluating the correlation between these factors pairwise. The scale x i of the mutual influence degree between the involved index D j and D ij can be used to construct an n-order self-evaluation matrix X = (x ij ) n×n to express the influence of the j-th index on the i-th index, and its general expression is shown in Equation 6-1.

[0068]

[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 index. Generally, the influence degree can be classified and assigned values. For example, {very large influence, relatively large influence, medium influence, general influence, relatively small influence, no influence} are forcibly assigned values {5, 4, 3, 2, 1, 0} respectively, or the Delphi method can be 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 influence on index Dj There is no direct impact.

[0070] For example, assume there is a set of 4 evaluation factors, and the order of the impact degrees on the other 3 factors is (5, 3, 2), the order of the impact degrees on the other 3 factors is (1, 4, 4), the order of the impact degrees on the other 3 factors is (0, 0, 3), the order of the impact degrees on the other 3 factors is (5, 1, 5), then the constructed 4-order index evaluation matrix is as shown in Equation 6-3.

[0071]

[0072] S12. Normalize the initial impact matrix X to obtain the normalized impact matrix Y;

[0073] To make the matrix operations 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 taken, denoted as max. The normalized matrix is processed by Y = x ij / max, and this paper uses Equation 6-3 for processing.

[0074]

[0075] For the matrix shown in Equation 6-2 (case ), after calculation, the normalized matrix is as shown in Equation 6-4.

[0076]

[0077] S13. According to the normalized impact matrix Y, calculate the comprehensive impact matrix T, T = Y·(I - Y) -1 , where I is the identity matrix;

[0078] Construct the comprehensive impact matrix and apply the T matrix to solve the centrality and reasonability, as well as the basic influence of factor D i in the system, forming the impact scale matrix of the influencing factors as the basis for subsequent evaluation.

[0079] Construct a comprehensive impact matrix T, and the calculation formula is as shown in Equation 6-5.

[0080]

[0081] Among them: I is the identity matrix, and t ij can reflect factor D i on D jThe comprehensive influence degree.

[0082] Still using the above case D4, the calculated T matrix is:

[0083]

[0084] 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;

[0085] Solve the centrality and reasonability using the T matrix. The sum of each row f i (The sum of the influences of factor D i on other factors) is the influence scale of D i , and the sum of each column e i (The sum of the influences received by factor D i from other factors) is the influenced scale of D i . For example, in case D4, the calculated results are:

[0086] f4 = (0.3776, 0.3490, 0.1917, 0.3999) T ………… Equation 6-6

[0087] e4 = (0.2714, 0.2648, 0.4299, 0.3520) ………… Equation 6-7

[0088] S14. Calculate the centrality and reasonability of each evaluation factor according to the influence scale and the influenced scale. 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;

[0089] If you want to compare the importance of each factor, you need to set parameters for sorting. Set the following parameters:

[0090] Let:

[0091] γ i = f i + e i (Equation 6-8), the centrality of D i , indicating the relative importance of D i ;

[0092] δ i = f i - e i (Equation 6-9), the reasonability of D i . When δ i > 0, it means that D i is a cause (active) factor;

[0093] ω i = f i / γi (Equation 6-10) represents the ratio of influence scale to centrality, reflecting the basic influence of factor D i in the system;

[0094] Z i =γ i / 1 - e i , representing the effective centrality of D i ... Equation 6-11;

[0095] K i =min{(ω i / 1 - f i ), 1}, representing the maximum estimated value of the influence scale of D i ... Equation 6-12;

[0096] H i =f i / 1 - e i , representing the minimum estimated value of the influence scale of D i ... Equation 6-13.

[0097] 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).

[0098] Sorting ω i from large to small 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.

[0099] S15. If there are evaluation factors with negative reason degrees, they will 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 vector of the influence factors in the evaluation scheme are determined.

[0100] If there are evaluation factors with negative reason degrees, they will 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 reason degree of each evaluation factor.

[0101] During the evaluation process, factors of the system may be selected and interfering factors excluded.

[0102] For δ i Factors with δ < 0 are generally excluded. For example, in case D4, the cause degree δ3 of D3 = -0.2382 < 0, which should be excluded.

[0103] In order to make the evaluation factors of multiple solutions uniform, only factors that do not meet the evaluation conditions for all solutions can be excluded. If influencing factors are excluded, the influence scale should be recalculated until the evaluation conditions are met.

[0104] Example 3

[0105] The method for constructing an evaluation coefficient matrix takes multiple solutions to be evaluated as rows and evaluation factors as columns. By subjectively assigning values or obtaining data for the indicators, an initial coefficient matrix is constructed; subsequently, the matrix is normalized according to the attributes of qualitative and quantitative indicators. The methods for obtaining the normalized coefficient matrix include:

[0106] S21. Take multiple solutions 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 solutions, and n is the number of evaluation factors not excluded, is the initial assignment of the jth evaluation factor of the ith solution;

[0107] Take comparison evaluation solution A i as the row and the influence factor assignment of solution A i as the column to construct an evaluation solution coefficient matrix

[0108]

[0109] S22. Assign values to each element of the initial coefficient matrix : If it is a qualitative indicator, use the scale value given by the expert method and normalize it. The scale interval is divided according to actual needs, generally [1, 9].

[0110] If it is a quantitative indicator, use the monitoring data or calculation result as the initial assignment and normalize it;

[0111] Illustrated by Example 1, assuming they are all qualitative indicators, on the basis of the previous cases, add three more cases. Assume each case has 4 influencing factors. If the comparison assignment result is 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:

[0112]

[0113] Illustrated by Example 2, assume x i1 and x i3 are qualitative indicators, x i2 and x i4 are quantitative indicators. Taking as four cases, if the assignment results of the scheme comparison are x i1 = {3, 6, 7}, x i3 = {1, 2, 5}, and the monitored and calculated results are x i2 = {0.98, 1.13, 1.07}, x i4 = {1900, 2010, 1985}, then the constructed coefficient matrix (hybrid matrix) is:

[0114]

[0115] If is a qualitative matrix, perform normalization processing using Equation 6-15;

[0116] If it is the initial assignment in the qualitative sub-matrix, the processing formula is

[0117] That is, in the above Example 1, the new matrix after normalization processing is:

[0118]

[0119] However, in general, is a hybrid matrix, so execute S23.

[0120] S23. According to the different attributes of the qualitative and quantitative indicators, separate the initial coefficient matrix into multiple sub-matrices, including a qualitative sub-matrix and one or more quantitative sub-matrices;

[0121] That is is a hybrid matrix. First, separate the matrix according to the qualitative and quantitative indicator categories (assuming there are v, such as dependent variable growth type, dependent variable decline type, fluctuation type), and organize it into sub-matrices G1, G2…G v . The qualitative sub-matrix is processed according to Equation 6-15; when processing the quantitative sub-matrix, let the reasonable target value of the evaluation factor be Kij , then process according to the following formula:

[0122]

[0123] K ij Determination method of : When there is a reasonable target standard value X, directly adopt Equation 6-16; when it is necessary to evaluate the deviation degree, determine it according to the following formula: Let: the target value be X, and there is

[0124] As in Example 1 above, the new matrix after normalization processing is:

[0125]

[0126] S24. Perform normalization processing on the qualitative sub-matrix and multiple quantitative sub-matrices;

[0127] S25. Combine the processed qualitative sub-matrix and quantitative sub-matrix to form a comprehensive evaluation coefficient matrix G, and the comprehensive evaluation coefficient matrix is used to characterize uncertainty and multi-type attributes simultaneously.

[0128] Example 4

[0129] In view of the uncertainty of the evaluation index, in order to better evaluate and express the attributes of the evaluation index, an evaluation scale fuzzy evaluation method with interval expression can be adopted [i] . In this paper, the interval assignment object, interval assignment method, and algorithm are improved. ① The influence value of a single factor on the system in the influence degree analysis is expressed as an interval index, and ② the mutual influence degree of the influencing factors on the evaluation factor is considered in the algorithm.

[0130] For the convenience of calculation, the following operation rules and judgment rules are defined.

[0131] (1) Denote a = [a - , a + = x{x|a - ≤ x ≤ a +}, and call a an interval number; when N = {1, 2…n}, M = {1, 2…m}, define two operation methods of interval numbers: ① a + b = [a - , a + + [b - , b + = [a - + b - , a + + b + , ② λa = [λa - , λa + , where λ ≥ 0;

[0132] (2) Let a = [a- , a + , b = [b - , b + , and denote l a = a + - a - , l b = b + - b - , then the result represented by Equation 6 - 19 is called the possibility of a ≥ b. At this time, 0 ≤ p(a ≥ b) ≤ 1, p(a ≥ b) + p(b ≥ a) = 1, and p(a ≥ b) has complementarity.

[0133]

[0134] The specific method includes:

[0135] S31. Determine the interval assignment method, including interval assignment using centrality and reasonability; or interval assignment using impact scale and effective centrality;

[0136] S32. If interval assignment is performed using centrality and reasonability, then let ω ij = [γ ij - |δ ij |, γ ij + |δ ij |], i ∈ m, j ∈ n, where ω ij is the influence degree, γ ij is the centrality of the jth evaluation factor of the ith scheme, and δ ij is the reasonability of the jth evaluation factor of the ith scheme; to make the measurement standards of each index consistent, when determining the numerical values of the fuzzy scale interval, calculate f i , e i , γ i , δ i , ω i and other values according to (Equations 6 - 1 to 6 - 9) in Example 2. The basic value γ ij takes the value of ω ij . The deviation value δ ij is calculated. When δ i > 0, the value of δ i can be directly taken; when δ i < 0, take the absolute value |δ i | of δ i .

[0137] For example, list 4 cases D, A, B, C. The evaluation matrix of the importance degree of all factors constructed according to the method in Example 2 is:

[0138]

[0139] Then its interval assignment matrix is as follows:

[0140]

[0141] S33. If interval assignment is carried out using the influence scale and effective centrality, then let ω ij = [f ij , Z ij , where f ij is the influence scale of the j-th evaluation factor of the i-th scheme, and Z ij is the effective centrality of the j-th evaluation factor of the i-th scheme;

[0142] S34. Using all ω ij as elements, construct the influence coefficient matrix W.

[0143] S35. Let: ɑ ij be the weight vector α ij = {ω i1 , ω i2 …ω ij} of the attribute set ω ij = {α i1 , α i2 …α ij}, α ij > 0 and i ∈ m, j ∈ n.

[0144] According to the independence of the index factors in the system, there are two methods to determine the weight vector:

[0145] S351. If the evaluation factors are independent of each other, that is, the factors are orthogonal or nearly orthogonal, the weight vector of the j-th evaluation factor of the i-th scheme. This method can be directly used to obtain the weight vector for those lacking big data.

[0146] S352. If there are mutual influences among the evaluation factors, then weight assignment is carried out through the basic influence, and the de-fuzzified basic influence is used as the weight. It is necessary to assign weights separately according to the importance of each index in the system, and subjective assignment can be used. Generally, the independence of the indexes is relative, and the discreteness of subjective assignment is large, making it difficult to express the true weights. In order to more objectively express the mutual feedback effects of the factors in the system, the attribute set ω ij is used as the calculated quantitative parameter, and after de-fuzzification, α ij = Ω ij ………… Equation 6-20.

[0147] S36. Aggregate the attribute values of each evaluation factor of each evaluation object, and calculate the basic value α ij, and then calculate the comprehensive attribute value ε i : Among them, G ij is the element of the normalization coefficient matrix, α ij is the weight, ω ij is the element of the influence degree coefficient matrix;

[0148] Calculate the calculation example of the comprehensive attribute value of D4:

[0149]

[0150] Assume that all the values of the coefficient matrix G ij are 1. After calculation, the obtained comprehensive attribute values are: ε A = [24.06, 35.78], ε B = [34.23, 44.59], ε C = [24.88, 34.96].

[0151] The above evaluation method defaults that the importance of all factors is 1. If the importance of some special factors needs to be considered, it is adjusted with coefficients during the fourth-step comprehensive attribute aggregation (Equation 6-21).

[0152]

[0153] Among them: ρ i is the adjustment coefficient.

[0154] S37. According to the comprehensive attribute values of each evaluation plan, calculate the possibility p between any two plans ij = p(ε i ≥ ε k ), and construct the possibility complementary judgment matrix P = (p ij ) n×n ;

[0155] Make pairwise comparisons of ε i (i ∈ n), perform sorting and solution, and obtain the sorting vector of matrix P, that is, calculate the sorting vector τ i = (τ1, τ2…τ n ) T ,

[0156] Sort each evaluation plan according to the magnitude of the component values in the sorting vector.

[0157] Use the above case to illustrate. Establish a complementary judgment matrix P for 4 matrices D, A, B, C, etc., perform sorting, and solve the sorting vector τ ij . After calculation, the results are as follows:

[0158]

[0159] τ i =(0.158, 0.238, 0.283, 0.238) T

[0160] If only considering the factor influence degree, the complementary judgment matrix is as follows:

[0161]

[0162] Its sorting vector is: τ i =(0.258, 0.251, 0.241, 0.247) T

[0163] Therefore, through the same-caliber comparison of 4 comparison objects, if only considering the influence degree of each scheme factor, the sorting of the pros and cons is D > A > C > B, and the optimal scheme is D, which is very different from the empirical judgment; if considering the comprehensive factors, the sorting of the pros and cons is B > A > C > D, and the optimal scheme is B, which is the same as the empirical judgment. Therefore, the comprehensive influencing factors must be considered. The evaluation method can be adopted.

[0164] Similarly, similar results can also be obtained by solving the mixed matrix.

[0165] Example Five

[0166] 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.

[0167] 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 know that computer storage media are not limited to the above several. The above-mentioned system memory and mass storage devices can be collectively referred to as memory.

[0168] 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.

[0169] 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.

[0170] 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 representations 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.

[0171] Furthermore, the terms "first" and "second" are only used for descriptive purposes and cannot be construed as indicating or implying relative importance or implicitly specifying the quantity of the indicated technical features. Thus, the features defined with "first" and "second" may explicitly or implicitly include at least one of these features. In the description of this application, the meaning of "a plurality" is at least two, such as two, three, etc., unless otherwise specifically defined.

[0172] Those skilled in the art should understand that the above embodiments are only 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 variations can be made based on the above invention, and these changes or variations are still within the scope of the present invention.

Claims

1. A fuzzy evaluation method based on interval assignment of evaluation indicators, characterized in that Including: Construct an evaluation system, determine multiple evaluation schemes and multiple evaluation factors, where the evaluation factors include qualitative indicators and quantitative indicators; Analyze the influence scales between the evaluation factors, determine the influence scales of each evaluation factor, and screen the evaluation factors according to the influence scales to obtain the final influence scale; Construct and normalize the coefficient matrix of the evaluation scheme to obtain the normalized coefficient matrix; According to the analysis results of the influence scales of each evaluation scheme, perform interval assignment on the influence scales of each evaluation factor of each evaluation scheme to obtain the influence degree coefficient matrix; Determine the weight vector of each evaluation factor; Calculate the comprehensive attribute value of each evaluation scheme through the normalized coefficient matrix, the influence degree coefficient matrix and the weight vector; Construct a possibility complementary judgment matrix based on the comprehensive attribute value, calculate the sorting vector, and sort each evaluation scheme according to the sorting vector.

2. The fuzzy evaluation method based on interval assignment of evaluation indexes according to claim 1, characterized in that The method for performing influence scale analysis includes: Construct an initial influence matrix X according to the mutual influence relationship between the evaluation factors; 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, T = Y·(I - Y) -1 , where I is the identity matrix; 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; 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; If there are evaluation factors with negative reasonability, eliminate them and recalculate iteratively until the final influence scale that meets the evaluation requirements is formed, and determine the basic influence factor vector of the evaluation scheme and the basic influence force vector of the influence factors in the evaluation scheme.

3. A fuzzy evaluation method based on interval assignment of evaluation indexes according to claim 1, characterized in that, The method for obtaining the normalized coefficient matrix includes: 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 that have not been eliminated is the initial assignment of the \(j\)-th evaluation factor of the \(i\)-th solution For each element of the initial coefficient matrix perform the following 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 the qualitative indicators and quantitative indicators, including a qualitative sub-matrix and one or more quantitative sub-matrices; Normalize the qualitative sub-matrix and multiple quantitative sub-matrices; Merge the processed qualitative sub-matrix and quantitative sub-matrices to form a comprehensive evaluation coefficient matrix G, and the comprehensive evaluation coefficient matrix is used to characterize uncertainty and multi-type attributes simultaneously.

4. A fuzzy evaluation method based on interval assignment of evaluation indexes 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. A fuzzy evaluation method based on interval assignment of evaluation indexes according to claim 3, characterized in that, The method for obtaining the influence degree coefficient matrix includes: Determine the interval assignment method, including interval assignment using centrality and reasonability; or interval assignment using influence scale and effective centrality; If interval assignment is performed using centrality and reasonability, let ω ij = [γ ij - |δ ij |, γ ij + |δ ij |], i ∈ m, j ∈ n, where ω ij is the influence degree, γ ij is the centrality of the j-th evaluation factor of the i-th scheme, and δ ij is the reasonability of the j-th evaluation factor of the i-th scheme; If interval assignment is carried out using influence scale and effective centrality, let ω ij ={f ij , Z ij , where f ij is the influence scale of the jth evaluation factor of the ith scheme, and Z ij is the effective centrality of the jth evaluation factor of the ith scheme; Take all ω ij as elements to construct the influence coefficient matrix W.

6. A fuzzy evaluation method based on interval assignment of evaluation indicators according to claim 5, characterized in that, The method for determining the weight vector of each evaluation factor includes: Judge whether there is mutual influence between the evaluation factors; If the evaluation factors are independent of each other, the weight vector of the j-th evaluation factor of the i-th solution If there is mutual influence between the evaluation factors, assign weights through the basic influence force, and use the de-fuzzified basic influence force as the weight.

7. A fuzzy evaluation method based on interval assignment of evaluation indexes according to claim 6, characterized in that, The method for calculating the comprehensive attribute value includes: Among them, G ij is an element of the normalization coefficient matrix, α ij is the weight, ω ij is an element of the influence degree coefficient matrix; If it is necessary to separately adjust the importance degree of a certain influencing factor, then its comprehensive attribute value where ρ i is the adjustment coefficient.

8. A fuzzy evaluation method based on interval assignment of evaluation indexes according to claim 7, characterized in that, The method for sorting each evaluation scheme includes: According to the comprehensive attribute values of each evaluation scheme, calculate the possibility degree \(p\) between any two schemes ij = \(p(\varepsilon i \geq\varepsilon k \)), and construct a complementary judgment matrix of possibility degrees \(P=(p ij ) n×n ;\ Calculate the sorting vector τ according to the possibility complementary judgment matrix i =(τ1, τ2…τ n ) T , Sort each evaluation scheme according to the magnitude of each component value in the sorting vector.

9. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the method described in any one of claims 1-8.

10. A computer program product comprising a computer program / instructions, characterized in that, When the computer program / instructions are executed by a processor, it implements the method described in any one of claims 1-8.

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