A multi-alternative set analytic hierarchy process weight determination method for aviation standard evaluation

Abstract

The application discloses a multi-alternative set hierarchical analysis weight determination method for aviation standard evaluation, which comprises the following steps: obtaining an index set with multiple alternatives in an aviation standard index system; dividing the index set into multiple sub-index sets according to evaluation division rules; comparing the indexes in the sub-index sets two by two to obtain corresponding pair comparison matrices; calculating the weight vectors of the corresponding sub-index sets by using a logarithmic linear regression method for each pair comparison matrix; and cyclically splicing and calculating the weight vectors of all the sub-index sets to determine the weights of all the alternatives in the index set. The application can significantly reduce the weight determination calculation amount of the indexes in the multi-alternative set and effectively guarantee the consistency of the evaluation.

Description

Technical Field

[0001] This invention belongs to the field of technical standard evaluation, and specifically relates to a weighting method for a multi-alternative itemset hierarchical analysis for aviation standard evaluation. Background Technology

[0002] As research on aviation standards and standardization deepens, the evaluation methods for aviation standards are becoming increasingly complex, and the system of indicator structures used for aviation standard evaluation is expanding. In order to assign weights to the indicators in the indicator system, in addition to direct allocation, the Analytic Hierarchy Process (AHP) is also a key tool in this step.

[0003] The typical Analytic Hierarchy Process (AHP) comprises three levels: the alternative set, the criteria set, and the target set. These levels correspond to the alternative set, the evaluation criteria set, and the target set, respectively. The decision-making process using AHP can be summarized in three steps. The first step is to pairwise compare and score the importance of each element in the alternative set to a given criterion. Then, the weight vector of the alternative's importance to the corresponding criterion is calculated using the pairwise comparison matrix (PCM) generated from these scores. This step is also called hierarchical single ranking. The second step is to generate ranking weights for the importance of each criterion to the target in the target layer using the same method. The final step is to aggregate the weight vectors of the alternatives under each criterion according to the weights of the criteria to the target in the previous step to obtain the total ranking weight of all alternatives to the target. This is also called hierarchical overall ranking. When applying AHP to aviation standard evaluation, the elements of the alternative set correspond to the indicators used to evaluate aviation standards. The alternative set is specialized into the indicator set, and the hierarchical single ranking and weight allocation of the alternatives becomes the hierarchical single ranking and weight allocation of the indicators.

[0004] However, as the number of indicators at the same level in the aviation standard evaluation index system gradually increases, the number of pairwise comparisons required for the hierarchical single-ranking evaluation in AHP increases very rapidly. Taking the weighting problem of a set of six candidate indicators as an example, if pairwise comparisons are performed directly, 15 comparisons are needed to give a complete pairwise comparison matrix. This process is time-consuming and laborious, leading to a rapid increase in computational burden, and the consistency of evaluation for a large number of indicators is also difficult to guarantee. In the past, when encountering a large number of candidate indicators, the common practice was to reduce the candidate set based on some similarity, or to rearrange some candidate indicators to other levels for evaluation. However, indicators often have different focuses and are difficult to incorporate into other levels, and constantly adjusting the index system structure for the convenience of weighting can also destroy the integrity of the index system. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a weighting method for hierarchical analysis of multiple alternative itemsets for aviation standard evaluation, which solves the problem of reducing computational load and ensuring evaluation consistency when there are too many indicators in the multiple alternative itemsets.

[0006] To achieve the above objectives, this invention provides a weighting method for a multi-alternative itemset hierarchical analysis for aviation standard evaluation, comprising:

[0007] S1. Obtain the set of indicators with multiple alternatives in the aviation standard indicator system;

[0008] S2. Divide the indicator set into multiple sub-indicator sets according to the evaluation set rules;

[0009] S3. Perform pairwise comparisons on the indicators within the sub-indicator set to obtain the corresponding pairwise comparison matrix;

[0010] S4. For each pairwise comparison matrix, use log-linear regression to calculate the weight vector of the corresponding sub-index set;

[0011] S5. Calculate the weight vector of all sub-indicator sets by iteratively concatenating them, and assign weights to all indicators within the indicator sets:

[0012] ;

[0013] in, For indicator set The weight vector corresponding to all internal indicators, The number of sub-indicator sets. For indicator set weight vector With sub-indicator set weight vector The first splicing factor during splicing, For the first The weight vector of each subset of indicators, For indicator set weight vector and weight vector The second splicing coefficient during splicing. for The weight vector corresponds to the sub-index set Part of for The weight vector corresponds to the sub-index set The part.

[0014] Furthermore, the evaluation diversity rules include:

[0015] If the number of indicators exceeds the evaluation threshold, then the system will be split into subsets.

[0016] ,in, express The Sub-indicator set, It is the number of sub-indices;

[0017] right same The intersection is empty or contains only one element.

[0018] Furthermore, the evaluation diversity rule also includes:

[0019] use same When the intersection is empty, the resulting subset of indicators consists of indicators with consistency.

[0020] use same When a subset is partitioned with only one element in the intersection, the resulting subset consists of either consistent indicators or a set of consistent indicators plus an inconsistent indicator from the intersection.

[0021] Further, step S4, calculating the weight vector of the corresponding sub-index set for each pairwise comparison matrix using log-linear regression, includes:

[0022] S41. Let the unknown weight vector be... ,in , express The Middle The elements are in The weights to be determined in the middle;

[0023] S42. Constructing a log-linear regression problem: ,in, For sub-indicator set The Middle The first indicator is relative to the first Importance scores of each indicator The natural logarithm, It is a subset of indicators The Middle Each indicator in The natural logarithm of the undetermined weights. It is a subset of indicators The Middle Each indicator in The natural logarithm of the undetermined weights. It is a Kronecker notation if and only if When it exists ;

[0024] S43. Solving the constructed log-linear regression problem, the solution is: ,in, Represents the generalized inverse of a matrix. Sub-index set The least squares solution vector corresponding to the linear regression problem mentioned above. Size is 0-1 matrix, Sub-index set The number of indicator pairs that were not compared in importance. Sub-index set The number of indicators in the data. No. A vector consisting of all existence terms in the pairwise comparison matrix of each subset of indices.

[0025] S44. Based on the normalization conditions, from each The optimal weight vector is obtained by inverse solving. , That is, the sub-index set The corresponding weight vector.

[0026] Furthermore, S5, which iteratively concatenates and calculates the weight vector of all sub-indicator sets to assign weights to all alternatives within the indicator set, includes:

[0027] S51, Order , The initial weight vector to be merged;

[0028] S52, Calculation Corresponding weight vector And order ;

[0029] S53, Judgment Whether it is true or not, if so, then what is obtained at this time? That is The corresponding weight vector; otherwise, execute S52.

[0030] Further, the calculation in S52 Corresponding weight vector ,include:

[0031] like same If the intersection is empty, then Corresponding weight vector for:

[0032] ;

[0033] in, for Corresponding weight vector The item, For sub-indicator set Corresponding weight vector The item, for The Middle Individual indicators for the indicator set The Middle The importance score of each indicator To use log-linear regression to analyze the sub-indicator set The weight vector is obtained by calculating the pairwise comparison matrix.

[0034] Further, the calculation in S52 Corresponding weight vector It also includes:

[0035] like and If the intersection is a set of singletons, then Corresponding weight vector for:

[0036] ;

[0037] in, From Delete the first one Each component Received Dimensional vector.

[0038] As one aspect of this invention, the present invention also provides a method for weighting alternative stratum indicators for evaluating the standardization of aviation turbine fuel testing standards, comprising the steps of:

[0039] M1. Obtain the experimental standard documents for the aviation turbine fuel to be evaluated;

[0040] M2. Use layout recognition tools to identify the experimental standard documents for aviation turbine fuel and obtain the document's constituent elements;

[0041] M3. Based on the constituent elements of the document, obtain the alternative layer indicators required for normative evaluation from the aviation standards and technical role indicator system, specifically:

[0042] When the constituent elements of a document include text elements expressed in words, the alternative level indicators to be used for obtaining normative evaluation include readability indicators, logical indicators, and structural rationality indicators.

[0043] When the constituent elements of a document include non-text elements expressed in tables, formulas, or graphs, the alternative level indicators to be used for obtaining the normative evaluation shall correspondingly include table normative indicators, formula normative indicators, and graph normative indicators.

[0044] M4. The acquired readability indicators, logical indicators, and structural rationality indicators are classified into the text sub-indicator set, and the acquired graphic standardization indicators, table standardization indicators, and formula standardization indicators are classified into the non-text sub-indicator set.

[0045] M5. Perform pairwise comparisons on the indicators in the text sub-indicator set and the non-text sub-indicator set respectively to obtain the corresponding pairwise comparison matrix.

[0046] M6. Calculate the weight vectors of the text sub-indicator set and the non-text sub-indicator set according to the corresponding pairwise comparison matrix, and assign weights to the indicators in each sub-indicator set.

[0047] M7. Select one indicator from both the text sub-indicator set and the non-text sub-indicator set, compare and score them, and obtain an importance score. ;

[0048] M8. Concatenate and calculate the weight vectors of the text sub-indicator set and the non-text sub-indicator set to assign weights to all indicators within the obtained normative evaluation candidate layer;

[0049] ;

[0050] in, The weights of indicators arbitrarily extracted from the non-textual subset. The weights of indicators arbitrarily extracted from the text subset. The importance score is used to compare two arbitrarily selected indicators. This is the weight vector for the non-textual sub-indicators, corresponding to the weights of the readability index, logicality index, and structural rationality index. This is the weight vector for the text sub-indicator set, corresponding to the weights of the graphical standardization index, the tabular standardization index, and the formula standardization index.

[0051] The beneficial effects of this invention are as follows:

[0052] 1. This invention divides the indicator set with too many alternative indicators in the same level single ranking into multiple sub-indicator sets, calculates the corresponding weight vector for each sub-indicator set, and then uses a cyclic concatenation calculation method to obtain the weight of all alternative items in the indicator set, which greatly reduces the workload and calculation of comparison and scoring caused by directly performing hierarchical analysis on the indicator system.

[0053] 2. This invention provides two evaluation subset methods and a method for calculating the weights of all alternatives within an index set. The two subset methods include one where the intersection of adjacent subsets is empty and the other where the intersection of adjacent subsets is a single element. These two subset methods are used to calculate... Corresponding weight vector In the end, all of them can obtain a consistent weighting of all alternatives within the index set;

[0054] 3. The two settling methods for multi-option weighting provided in this invention facilitate the generation of consistent pairwise comparison matrices. This is because the grouping approach generates fewer pairwise comparisons of elements, and in small-scale cases, it is easier to ensure consistency between options. Furthermore, the requirement for the number of comparison coefficients ensures that no new inconsistencies are added to the overall multiset, nor are inconsistencies within a single itemset propagated externally. This effectively protects consistency and improves the accuracy of AHP's overall weight allocation of indicators. Attached Figure Description

[0055] Figure 1 This is a flowchart of a weighting method for a multi-alternative itemset hierarchical analysis for aviation standard evaluation according to the present invention;

[0056] Figure 2 This is a schematic diagram illustrating the division of the alternative indicator set when there are multiple indicators in the aviation standard evaluation system of one embodiment of the present invention;

[0057] Figure 3 This is a diagram illustrating the index structure of an aviation standards and technology effectiveness evaluation system according to an embodiment of the present invention.

[0058] Figure 4 This is a diagram illustrating the normative sub-indicator structure of an aviation standards and technology effectiveness evaluation system according to an embodiment of the present invention.

[0059] Figure 5 This is a schematic diagram illustrating the division of the alternative indicator set when adding new indicators to the aviation standard evaluation system according to an embodiment of the present invention. Detailed Implementation

[0060] To make the objectives, technical solutions, and advantages of the present invention clearer, further explanation is provided below in conjunction with the accompanying drawings and embodiments.

[0061] In the weighting problem of aviation standard evaluation index system, a situation arises where there are too many alternative indicators in a single ranking at the same level. To address the issues of cumbersome pairwise comparison processes and inconsistent pairwise comparison matrices that can occur in such cases, the following method was used in the process to reduce the number of pairwise comparisons and maintain evaluation consistency:

[0062] Example 1:

[0063] As attached Figure 1 As shown, as one aspect of the present invention, the present invention provides a weighting method for a multi-alternative itemset hierarchical analysis for aviation standard evaluation, which includes the following steps:

[0064] S1. Obtain the set of indicators with multiple alternatives from the aviation standard indicator system. ;

[0065] The following displays all use a single set of indicators with multiple alternatives from the aviation standard indicator system. For example, see attached Figure 2 As shown.

[0066] S2. Divide the indicator set into multiple sub-indicator sets according to the evaluation set rules;

[0067] Based on the calculation conditions for cyclic splicing and further research, The partitioning must satisfy the following evaluation set rules:

[0068] If the number of indicators exceeds the evaluation threshold, the system will be divided into sub-systems; generally, if there are more than 5 indicators than the evaluation threshold, the system can be divided.

[0069] , will complete the indicator set Represent as The union of subsets of indicators, where express The Sub-indicator set, It is the number of sub-indices;

[0070] right same The intersection is empty or contains only one element.

[0071] use same When the intersection of the subsets is empty, the resulting subsets consist of consistent indicators. (Consistent indicators mean that the overall judgment logic reflected in the "judgment matrix" composed of these indicators is consistent, and the calculated weights are valid. A "consistent" judgment matrix means that when comparing the pairwise importance of each indicator, its internal logic is self-consistent and without serious contradictions. Only judgment matrices that pass the consistency test have meaningful weight ranking results that can be used for subsequent evaluation and decision-making.)

[0072] use same When a subset of indices has only one element in its intersection, the resulting subset consists of either consistent indices or a set of consistent indices plus an inconsistent indices from the intersection.

[0073] For a set of subsets where the intersection contains only one element, for example, we can... All indicators are arranged in a chain sequence (meaning that subsets can be distributed using a chain-like adjacency overlap method, where each subset is connected to its immediate and adjacent subsets only at a "linkage point"). Indicators with consistency are concentrated in a segment of the chain sequence. During subset distribution, priority is given to ensuring that subsets contain consistent indicators, and then adjacent subsets share a single common intersection element. This design aims to make it easier for experts to compare indicators using the seven-level scaling method, given consistent indicators. For adjacent inconsistent subset indicators, when comparing indicators using the seven-level scaling method (as shown in Table 1), experts only need to evaluate the relationship between the single inconsistent intersection element indicator and the indicators within the subset. Compared to traditional pairwise comparisons of multiple inconsistent indicators, this significantly reduces the difficulty of indicator comparison and makes it easier to ensure consistency between options in small-scale scenarios, thus protecting the consistency of the evaluation.

[0074] Table 1. Meaning of the Seven-Level Scale

[0075]

[0076] The seven-level scaling method plays a crucial core role in the analytic hierarchy process. In the weighting of indicators in the aviation standard indicator system, experts use their professional knowledge to quantitatively evaluate two indicators, such as "How important is factor A relative to factor B?" and convert it into a precise numerical rating. As shown in Table 1 above, when factor A is very important relative to factor B, the numerical rating is 7; when it is very unimportant, the numerical rating is 1 / 7.

[0077] S3. Perform pairwise comparisons on the indicators within the sub-indicator set to obtain the corresponding pairwise comparison matrix;

[0078] After the index set is divided Each sub-indicator set Several pairwise comparison matrices are obtained by comparing the indicators within the matrix. ,in Indicates the first Sub-indicator set The number of elements (indicators) within. Indicates the first Sub-indicator set The Middle The first indicator is relative to the first The importance score for each indicator. The comparative scoring aims to compare the importance of two indicators to the standard evaluation objective, and a seven-point scale can be used. To account for the difficulties in practically comparing indicators, each... The corresponding comparative scores may be incomplete (i.e., there may be missing items).

[0079] S4. For each pairwise comparison matrix, use log-linear regression to calculate the weight vector of the corresponding sub-index set;

[0080] For each pairwise comparison matrix in the previous step The corresponding sub-indicator set was calculated using the log-linear regression method. weight vector .

[0081] S41. Let the unknown weight vector be... ,in , express The Middle The elements are in The weights to be determined in the middle;

[0082] S42. Constructing a log-linear regression problem:

[0083] ;

[0084] in, For sub-indicator set The Middle The first indicator is relative to the first The natural logarithm of the importance of each indicator It is a subset of indicators The Middle Each indicator in The natural logarithm of the undetermined weights. It is a subset of indicators The Middle Each indicator in The natural logarithm of the undetermined weights. It is a Kronecker notation if and only if When it exists .

[0085] S43. Solving the constructed log-linear regression problem, the solution is: ,in, Represents the generalized inverse of a matrix. Sub-index set The least squares solution vector corresponding to the linear regression problem mentioned above. For sub-indicator set Undetermined weight vector The vector obtained by taking the natural logarithm of each term yes Importance scores for all existing elements The vector formed by taking the natural logarithm and arranging the vectors in lexicographical order by their subscript indices. ,remember Sub-index set The number of indicator pairs that were not compared in importance is: It is the size of A 0-1 matrix that satisfies the condition for all elements with a value of 1. , There is only one line (express The (Line) makes: .

[0086] Solve the above log-linear regression problem to find the optimal weight vector. This can be represented in matrix form as follows:

[0087] ;

[0088] According to linear regression theory, the above problem has a solution:

[0089] ;

[0090] in, Sub-index set The least squares solution vector corresponding to the linear regression problem mentioned above.

[0091] S44. Based on the normalization conditions, from each The optimal weight vector is obtained by inverse solving. , That is, the sub-index set The corresponding weight vector.

[0092] Based on the normalization conditions, from each The optimal weight vector is obtained by inverse solving. :

[0093] ;

[0094] in, Indicates based on pairwise comparison matrices Sub-indicator set calculated by log-linear regression method Corresponding weight vector, sub-index set Each indicator in The weights in the vector are the corresponding terms.

[0095] S5. Calculate the weight vector of all sub-indicator sets by iteratively concatenating the vectors, assigning weights to all alternatives within the indicator sets, including:

[0096] S51, Order , The initial weight vector to be merged;

[0097] make , . The initial weight vector to be merged represents the initial weight vector of the method. It represents the number of merged sub-indices and also indicates the cyclic index of the method.

[0098] S52, Calculation Corresponding weight vector And order ;

[0099] At this point, depending on the subset partitioning method, there are two ways to calculate. Corresponding weight vector The details are as follows:

[0100] The first method:

[0101] If the settling method is same If the intersection is empty, then the splicing conditions required for simplified calculations are as follows: We select a pair of indicators and score their importance. Without loss of generality, let this pair of indicators be... and , respectively represent The first in Individual indicators (set) Total (indicators) and The first in Individual indicators (set) Total (1 indicator), and let the importance score of the latter to the former be 1. Then it can be given by the following formula. Corresponding weight vector :

[0102] ;

[0103] in, for Corresponding weight vector The Item, indicating This indicator is in Weight within, For sub-indicator set Corresponding weight vector The item, for The Middle Each indicator The Middle The importance score of each indicator To use log-linear regression to analyze the sub-indicator set The weight vector is obtained by calculating the pairwise comparison matrix.

[0104] The second method:

[0105] If the settling method is and If the intersection is a set of singletons, it can be directly given by the following formula. Corresponding weight vector :

[0106] ;

[0107] in, From Delete the first one Each component Received For ease of writing later, we assign a dimensional vector. .

[0108] get Afterwards, the poem was composed. .

[0109] S53, Judgment Whether it is true or not, if so, then what is obtained at this time? That is The corresponding weight vector; otherwise, execute S52.

[0110] Repeat S52 until ,at this time That is The corresponding weight vector is also the weight vector after merging at the end of the method. Using the previously obtained... Group splicing coefficient, The following is a block vector expression:

[0111] ;

[0112] in, The weight vector corresponding to the indicator set. The number of sub-indicator sets in the indicator set. for weight vector and weight vector The first splicing factor during splicing, To use the log-linear regression method to analyze the first... The weight vector is calculated from the pairwise comparison matrix of each subset of indicators. for weight vector and weight vector The second splicing coefficient during splicing. For traversal arrive Integer indicators; for The weight vector corresponding to Part of it; for The weight vector corresponding to Part of for The weight vector corresponding to Each part represents the weight vector of the corresponding sub-indicator set, thus obtaining the weight of each indicator in the sub-indicator set (see S44 for details).

[0113] The first method (diversity method) is adopted. same When the intersection is empty, It is called the first The first concatenation coefficient corresponding to this method loop, where , yes The first in Each indicator The first in The importance score of the indicator. When the first... When the second splicing uses the first method (the diversity method is...), same (intersection is empty) It is called the first The second concatenation coefficient corresponding to the next iteration of the method.

[0114] The second method (diversity method) is adopted. and When the intersection is a set of singletons, It is called the first The first concatenation coefficient corresponding to this method loop, where When the first When the second splicing method is used (the diversity method is...) same The intersection is a set of singletons. It is called the first The second concatenation coefficient corresponding to the next iteration of the method.

[0115] The above method provides ample freedom in both the way alternative indicator sets are divided and in the method of merging sub-indicator sets. Specifically, for the sub-indicator set column... Any rearrangement ( It is a set (to its own bijection), as long as the rearranged sub-index set still satisfies: for same Given the condition that either there is no intersection or the intersection contains only one element, there exists a... same When there is no intersection, a scheme is adopted to select the indicators between the two for importance comparison and scoring, so that the results of the method running in the order of the rearranged sub-indicator set are the same as the results of running in the order of the original indicator set.

[0116] In other words, under certain conditions, the calculation results of the method are independent of the order in which the weight vectors of each sub-index set are concatenated, which facilitates the implementation of the method.

[0117] Furthermore, the above method can significantly reduce the workload and computational burden of comparative scoring caused by directly performing hierarchical analysis on the indicator system. Through theoretical analysis, it is given... Corresponding pairwise comparison matrix Number of comparisons required At most The number of comparisons required in the above process satisfy The two are related. .when When it is relatively large, Often much smaller .fixed If it remains unchanged, it can still be calculated. Therefore, at least approximately One comparison is enough, that is to say When the number of sub-indicator sets is the same, the more uniform the size of each sub-indicator set, the fewer comparisons are required in the method; the number of comparisons required when equally dividing the index sets is the least. On the other hand, the total complexity of solving the normal equation in linear regression is... The complexity of the method when equally dividing the index set is... The latter significantly reduces the computational cost of solving the normal equation for linear regression. Of course, in practice, we cannot only consider the number of comparisons and computational cost. When the importance of some indicators is relatively easy to determine, allowing for larger sub-indicator sets can also facilitate the integration of more information into the weight vectors of the sub-indicator sets and even the weight vectors of the complete indicator set.

[0118] The following example illustrates the application of the above method:

[0119] In the evaluation of product standards in the aviation industry, research on the effectiveness of standards and technologies has given rise to a complex standard system (as shown in the appendix). Figure 3(As shown). The evaluation index system for the role of standards and technology is a set of indicators that quantifies the effectiveness of the standard-setting process in constraining product research and production. Its evaluation object is standards and standard systems in the aviation field. In constructing this index system, the interaction mechanism between standards and technology is divided into two main parts: standard characterization elements and technology characterization elements.

[0120] Specifically, the standard characterization elements focus on the standard itself, quantifying its ability as a normative document to impose external constraints and guidance on technology through a series of indicators such as binding force and normativity in the standard's constraint parameters. The technology characterization elements, on the other hand, focus on the technology itself, measuring its maturity, solidification potential, and inherent need for standards through two indicators: standard-technology adaptability and standardization readiness level.

[0121] The establishment of this indicator system is based on a multi-level, multi-dimensional tree-structure model. The design of each sub-indicator under the normative and constraining aspects stems from the normative role of various elements in aviation standard documents on technology and the constraining effect of the text, while also referencing models from the fields of natural language processing and image processing, making it a completely new indicator system. The remaining indicators, such as standard technology adaptability and standardization readiness level, have appeared in previous studies in the field of standardization.

[0122] To adapt to the standard evaluation tasks in the aviation field, many of these indicators have been specifically adjusted for the aviation sector. For example, the standard technology fit indicator is calculated as the difference between the industry average technology (characterized by some component performance indicators) and the standard's requirements for the corresponding technology, reflecting the degree of fit between aviation standards and existing industry technologies. The calculation process for this indicator references the characteristics of commonly used performance indicators in the aviation field (such as component tensile strength, maximum load, and impurity rate). By classifying the characteristics of these indicators (extremely large, interval type, extremely small, etc.) and conducting research on technical capabilities within the aviation industry, a standard technology fit calculation method adapted to the aviation field was obtained. Furthermore, the values ​​for indicators such as lexical professionalism and semantic accuracy of content words under readability in the indicator system are obtained by calculating the matching degree between the corpus in the standard documents and the corpus in a dedicated aviation lexicon (aviation dictionary). By constructing and using an aviation lexicon, these indicators can more accurately adapt to the tasks of aviation standard evaluation. Finally, the evaluation parameters of all indicators in the system (which determine which indicator values ​​correspond to good and which correspond to poor) are also determined based on the analysis of hundreds of aviation standard experiments and expert opinions in related fields. Therefore, the evaluation index system for the role of standards and technology is an index system applicable to the field of aviation standard evaluation.

[0123] The acquisition of indicator values ​​integrates expert evaluation with automated processing. After obtaining the values ​​of the leaf indicators, all indicator data are aggregated using a fuzzy comprehensive evaluation method. This method can scientifically handle ambiguity and subjective opinions in the evaluation, and through hierarchical weighted calculation, it combines a large number of low-level indicators into a comprehensive evaluation vector, which can clearly present the comprehensive effectiveness of the standard and even the standard system.

[0124] Example 2:

[0125] The following example, using the technical description in the GB / T 38203-2019 standard for testing aviation turbine fuel, demonstrates the process of applying the invention content to weight the aforementioned normative indicators.

[0126] This invention provides a method for weighting alternative stratum indicators for evaluating the standardization of aviation turbine fuel testing standards, comprising the following steps:

[0127] M1. Obtain the experimental standard documents for the aviation turbine fuel to be evaluated;

[0128] GB / T 38203-2019 provides the implementation requirements and methods for each stage of the aviation turbine fuel experiment. The standard's demonstration of this technology should conform to certain norms so that users can quickly grasp and implement the technology.

[0129] M2. Use layout recognition tools to identify the experimental standard documents for aviation turbine fuel and obtain the document's constituent elements;

[0130] To automatically separate and process text, images, tables, and formulas, PaddleX's open-source layout recognition tool and EasyOCR were used to extract the content of standard files.

[0131] M3. Based on the constituent elements of the document, obtain the alternative layer indicators required for normative evaluation from the aviation standards and technical role indicator system, specifically:

[0132] When the constituent elements of a document include text elements expressed in words, the alternative level indicators to be used for obtaining normative evaluation include readability indicators, logical indicators, and structural rationality indicators.

[0133] When the constituent elements of a document include non-text elements expressed in tables, formulas, or graphs, the alternative level indicators to be used for obtaining the normative evaluation shall correspondingly include table normative indicators, formula normative indicators, and graph normative indicators.

[0134] To extract the standardization of technical descriptions from texts, alternative indicators for evaluating standardization within the aviation standards and technical function indicator system are divided into three categories: readability, logic, and structural rationality. Readability is evaluated based on the professionalism and conciseness of the technical descriptions, and then synthesized into a readability index. Logic evaluates the degree to which the standard text conforms to grammatical norms; the absence of grammatical errors ensures logical coherence within sections, making the standard technical content easy to understand. Structural rationality analyzes the overall content arrangement of the standard document, evaluating whether the content arrangement under each level (section) heading is sufficiently unified and organized. The acquisition of these textual indicators relies on a professional thesaurus constructed from an aviation dictionary and a general terminology database, along with the open-source LTP natural language processing tool. As for the standardization of technical descriptions by the three non-text elements of figures, tables, and formulas, the measurement is based on the degree to which the representation of figures, tables, and formulas conforms to the requirements of GB / T 1.1-2020 "Standardization Work Guidelines". Specifically, open-source tools such as PaddleOCR, Pix2text, and the computer graphics algorithm package (cv2) are used for measurement and comparison.

[0135] M4. The acquired readability indicators, logical indicators, and structural rationality indicators are classified into the text sub-indicator set, and the acquired graphic standardization indicators, table standardization indicators, and formula standardization indicators are classified into the non-text sub-indicator set.

[0136] After obtaining the six normative indicators consisting of text and non-text, it is necessary to assign weights to them. This process is carried out using the Analytic Hierarchy Process (AHP). Given the large number of indicators (directly comparing each of the six normative sub-indicators requires 15 comparisons to obtain a complete pairwise comparison matrix), the inherent division of text and non-text in the technical description, and the difficulty in providing importance scores between text and non-text indicators, it is appropriate to use the invention content to subdivide the indicator set (consisting of these six indicators) before further processing.

[0137] Specifically, Figure 4 The six sub-indicators in the normative framework are considered as a set of indicators. .right There is a natural division: .in yes The set of indicators consists of three text metrics: readability, logic, and structural rationality. yes The latter three non-textual indicators consist of a set of indicators: graphical standardization, tabular standardization, and formula standardization.

[0138] M5. Perform pairwise comparisons on the indicators in the text sub-indicator set and the non-text sub-indicator set respectively to obtain the corresponding pairwise comparison matrix.

[0139] Regarding the standardization of solution preparation techniques in GB / T 38203-2019, experts from the aerospace and related fields were first invited to use a seven-level scaling method to analyze the specifications. and When comparing the importance of each indicator pairwise, experts unanimously agreed that among the technical descriptions mentioned above, text readability is slightly more important than logic and structural rationality, and logic is slightly more important than structural rationality. This is because ensuring that every sentence in the technical descriptions in the standard is quickly familiar and understandable to industry users is paramount, while grasping the overall structure naturally takes a relatively secondary role. Furthermore, figures, tables, and formulas, as supplementary forms of textual description, are equally important. Therefore, the experts' opinions formed the following pairwise comparison matrix:

[0140] ;

[0141] M6. Calculate the weight vectors of the text sub-indicator set and the non-text sub-indicator set according to the corresponding pairwise comparison matrix, and assign weights to the indicators in each sub-indicator set.

[0142] Based on the comparison matrix above, the following can be calculated: and The corresponding weight vector:

[0143]

[0144] ;

[0145] in, The first, second, and third items respectively represent The readability, logic, and structural rationality of the text are all important. The weight values ​​in the middle, The first, second, and third items respectively represent The standardization of graphics, tables, and formulas in [the text] The weight values ​​in the data.

[0146] M7. Select one indicator from both the text sub-indicator set and the non-text sub-indicator set, compare and score them, and obtain an importance score. ;

[0147] Now we invite experts to further examine readability ( The first indicator in the graph) and graph normalization ( The importance score is determined by comparing the first indicator with the second, thus showing that the former is slightly more important than the latter. =3. At this point, experts believe that the standardization of non-textual elements, as supplementary forms of textual expression, cannot be ranked on par with that of textual elements. Therefore, the standardization of non-textual elements is slightly less important than the readability of text.

[0148] M8. Concatenate and calculate the weight vectors of the text sub-indicator set and the non-text sub-indicator set to assign weights to all indicators within the obtained normative evaluation candidate layer;

[0149] The weight vector is:

[0150] ;

[0151] in, Weights of indicators arbitrarily extracted from a non-textual subset (non-textual subset) The first indicator in the data is 0.333. The weights of indicators arbitrarily extracted from a subset of text indicators ( The first indicator in the data is 0.584. As an importance score, This is the weight vector for the non-textual sub-indicators, corresponding to the weights of the readability index, logicality index, and structural rationality index. This is the weight vector for the text sub-indicator set, corresponding to the weights of the graphical standardization index, the tabular standardization index, and the formula standardization index. Represents the complete set of indicators The weight vector, It is the initial merge weight vector when the algorithm is executed. The first, second, and third items represent The three text metrics in The weight values ​​in the middle, Items 4, 5, and 6 indicate The three non-textual metrics in The weight values ​​in the data.

[0152] The above process reduces the number of pairwise comparisons from 15 to 7 by dividing the indicator set, thereby reducing the potential inconsistency caused by multiple comparisons between different types of indicators and improving the efficiency of weighting.

[0153] Example 3:

[0154] As a specific scenario of the multi-alternative set hierarchical analysis (AHP) weighting method for aviation standard evaluation, this invention also includes the case of adding a new set of indicators to an existing set of indicators. This is because in aviation standard evaluation, the indicator system for standards and technical roles is not initially determined. As research progresses, new indicators are gradually incorporated into various levels of the indicator system, forming new sets of alternative indicators. On the one hand, these new indicators often have different focuses and are difficult to incorporate into other levels. Furthermore, constantly adjusting the indicator system structure for ease of weighting can disrupt the integrity of the indicator system. On the other hand, too many indicators also increase the burden of pairwise comparisons and computational complexity in AHP. Therefore, while ensuring the indicator system remains unchanged, an indicator weighting method capable of handling the merging of old and new alternative sets is needed.

[0155] Therefore, as another aspect of the present invention, the present invention also provides a method for weighting multiple alternative item sets when dynamically adding aviation standard evaluation indicators, comprising the following steps:

[0156] P1. Each time an indicator is added, determine the new indicator structure after the addition;

[0157] P2. For the weighting problem of the new indicator system, the indicator set corresponding to each level of the single ranking process is divided into old and new indicators, such as... Figure 5 As shown.

[0158] The following presentations all use individual sets of standard constraint parameters in the standard and technology role evaluation system. For example, the same principle applies to the weighting method of indicators under standard constraint parameters, which can also be used in the weighting process of indicator layers in other similar cases, such as sub-indicator layers under normative conditions. The indicators in the text have specific meanings. Represents technological advancement, Representatives demanded reasonableness, etc. After research, simplified calculation conditions for splicing allowed for... The division can be carried out using the following two methods, among which... This represents a set of existing indicators that correspond to some of the indicators used in evaluating the implementation of major standards in the aviation field. These indicators include applicability, advancement, and operability. This represents the set of newly added indicators, corresponding to those newly added in the latest research on the role of standards and technologies in the aviation field. These include binding and normative indicators. Neither of these is empty.

[0159] (Method 1) ;

[0160] (Method 2) ;

[0161] As long as the sub-indices of the two aviation standard constraint parameters are disjoint or intersect as a single-element set, the following simplified calculation steps can be performed (in Method 2, the single elements in the intersection set can be regarded as either old indicators or new indicators, and their specific meaning is not important).

[0162] P3, Obtain and The pairwise comparisons between the indicators are used to obtain the pairwise comparison matrix corresponding to the newly added indicator set;

[0163] For the above-described constrained parameter index set middle The indicators are compared pairwise (based on the results of the evaluation of the implementation of major standards). (The pairwise comparison data has been obtained) to obtain the pairwise comparison matrix corresponding to the old indicator set. Pairwise comparison matrix corresponding to the new indicator set ,in As the first in the pairwise comparison matrix Line 1 The elements of the column represent the old indicator set. The first in The first indicator is relative to the first The importance score of each indicator , As the first in the pairwise comparison matrix Line 1 The elements of the column represent the new indicator set. The first in The first indicator is relative to the first The importance score of each indicator This process involves organizing workshops with experts in the aviation and related fields, who need to reach a consensus on the importance scores between the indicators. Specifically, the comparative scoring aims to compare the importance of two indicators to the constraints of the standard on the relevant technologies, using a seven-point scale. The meaning of each score is shown in Table 1 (which further explains...). and (The meaning of ). To account for the difficulties in comparing actual indicators, The corresponding comparison and scoring process may be incomplete (i.e.) Incomplete items may appear, manifesting as certain and (Does not exist). When When it is a singleton set, the corresponding Degenerate into real numbers Of course, the new set of indicators for aviation standard constraint parameters. It is not a set of single elements.

[0164] P4. Using log-linear regression, find the optimal weight vector between the old and new indicator sets. and ;

[0165] In the formal evaluation of the implementation of major standards, the undetermined weight vector corresponding to the new indicator set in the study of the technical role of standards and the existing indicator set is as follows: Then, using log-linear regression, the optimal weight vector between the old and new indicator sets is obtained. and These two weight vectors are the same as the pairwise comparison matrix. The result is the one that best matches the importance information of each indicator. The specific steps are as follows:

[0166] P41. Let the two unknown undetermined weight vectors be:

[0167] ;

[0168] in, , Represents the old set of indicators The first in Each indicator in Undetermined weights in the middle ( ), express The number of elements in; Represents the old set of indicators The first in Each indicator in The undetermined weights in the middle. express The number of elements in ( ).

[0169] P42. Construct the following log-linear regression problems for two undetermined weight vectors:

[0170] ;

[0171] ;

[0172] in, It is the first of the old indicators. The first indicator is relative to the first The natural logarithm of the importance score of each indicator This is the first batch of newly added indicators. The first indicator is relative to the first The natural logarithm of the importance score of each indicator It is the first of the old indicators. The natural logarithm of the undetermined weights of each indicator in the existing indicator set. This is the first batch of newly added indicators. The natural logarithm of the weights to be determined for each indicator in the set of newly added indicators. and It is a Kronecker notation if and only if When it exists If and only if When it exists In other words, this method allows for pairwise matrix comparisons. Incomplete (i.e., missing items) can also be processed. The complete case. When both matrices are complete, it corresponds to all... and The case where all values ​​are 1. Specifically, in the evaluation of the implementation of major standards, the old indicator set corresponds to... New set of indicators in the study of the role of standard technology They are all complete pairwise comparison matrices.

[0173] P43. Solve the above log-linear regression problem to find the optimal weight vector. The optimization problem on P42 can be written in matrix form as follows:

[0174] ;

[0175] in, Represents the undetermined weight vector of the existing index set. The vector obtained by taking the natural logarithm of each term Represents the undetermined weight vector of the newly added indicator set. The vector obtained by taking the natural logarithm of each term. yes All existing comparison terms The vector formed by taking the natural logarithm and arranging the vectors in lexicographical order by their subscript indices. , yes All existing comparison terms The vector formed by taking the natural logarithm and arranging the vectors in lexicographical order by their subscript indices. :

[0176] .

[0177] remember and The number of missing items in the data are respectively . It is a 0-1 matrix that satisfies the following conditions: Existing in , There is only one line (express The (Line) makes: Similarly, It is also a 0-1 matrix, satisfying the following conditions: Existing in , There is only one line (express The (Line) makes: .

[0178] According to linear regression theory, the above problem has a solution:

[0179] ;

[0180] ;

[0181] in, Represents the generalized inverse of a matrix. Let represent the least squares solution vector for the first linear regression problem described above. Indicates the old set of indicators The Middle Each indicator in The natural logarithm of the medium weights, Let represent the least squares solution vector for the second linear regression problem mentioned above. Indicates the newly added indicator set The Middle Each indicator in The natural logarithm with medium weights.

[0182] P44, According to the normalization condition from and The optimal weight vector is obtained by inversely solving the problem by taking the exponent from the middle:

[0183] According to the normalization condition: and from and The optimal weight vector is obtained by inversely solving the problem by taking the exponent from the middle:

[0184] ;

[0185] ;

[0186] in, It is Euler's constant. Indicates based on pairwise comparison matrices The weight vector corresponding to the old index set calculated using log-linear regression. Indicates the old set of indicators The Middle Each indicator in The weights in Indicates based on pairwise comparison matrices The weight vector corresponding to the old index set calculated using log-linear regression. Indicates the newly added indicator set The Middle Each indicator in The weights in the equation.

[0187] P5, for The specific steps for weighting all indicators are as follows:

[0188] At this point, based on the set division method of the old and new indicator sets, there are two methods: The weighting of all indicators is as follows:

[0189] P51. If the intersection of the old and new index sets is empty, then... After randomly selecting a pair of indicators and comparing and scoring them pairwise, calculate the complete indicator set after merging the old and new item sets. The corresponding weight vector ;

[0190] The first method: If the diversity method is (Method 1) That is, the intersection of the old and the new is empty.

[0191] Based on research, if the second step uses method one for division... The simplified calculation requires the following splicing conditions: Arbitrarily select a pair of indicators for pairwise comparison and scoring. The formula for calculating the weight vector of the complete indicator set varies depending on the selected indicator pair. Without loss of generality, let this pair of indicators be... and (For example, applicability indicators and normative indicators), respectively representing The first in Each indicator (of which there are 100) (indicators) and The first in Each indicator (of which there are 100) (Indicators). Let the importance score of the latter to the former be... The complete set of indicators after merging the old and new indicator sets can be given by the following formula. The corresponding weight vector :

[0192] ;

[0193] Among them, importance score The method also involves organizing seminars for aviation experts to reach a consensus.

[0194] P52. If the intersection of the old and new indicator sets is a single element (such as the applicability indicator), then the single element simultaneously serves as... and The indicators in the calculation result are the complete indicator set after merging the old and new indicator sets. The corresponding weight vector ;

[0195] The second method: If the distribution method is (Method Two) That is, the intersection of the old and the new forms a single element.

[0196] If the second step uses method two for division ,but Having a unique element, without loss of generality, let it simultaneously serve as The first in Individual indicators and The first in Given a set of indicators, the complete set of indicators after merging the old and new items can be directly given by the following formula. Corresponding weight vector :

[0197] ;

[0198] in, From Delete the first one Each component Received Dimensional vector.

[0199] Studies have shown that the results obtained in the fourth step of the above scheme are the same as those obtained by directly applying the new technical constraints and normative indicators. The results obtained by performing hierarchical single sorting are consistent (the number of pairwise comparisons is the same). Under this premise, the former not only reduces the amount of computation required for linear regression problems, but also makes the weighting process more systematic.

[0200] This invention proposes a hierarchical analysis (AHP) weight calculation method for multiple alternative item sets, addressing the potential problems of dynamic addition and excessive indicators in standard evaluation systems. This method employs log-linear regression with incomplete PCM to calculate the weights of the divided alternative item sets separately. Through detailed classification and discussion, this invention provides a sufficient condition for the weight vector of the merged alternative item set to be proportionally concatenated with the original weight vector—the so-called concatenation condition. Applying the results under this condition, one can update the weight vector of the merged item set in real-time based on existing weight vectors in richer dynamic environments without having to calculate it from scratch. This invention also utilizes the concatenation condition to provide a fast algorithm for calculating the weight vector of large-scale item sets, effectively reducing the workload required to provide PCM and the computational workload of obtaining the weight vector from PCM in hierarchical evaluation while ensuring consistency. Several examples clearly demonstrate the effectiveness of the above theory and algorithm. The AHP weight algorithm proposed in this invention for multiple alternative item sets, by breaking down the problem into smaller parts, can better handle the weighting problem of evaluation systems with large and dynamically added indicators, significantly expanding the application scenarios of traditional hierarchical analysis weighting.

[0201] The above embodiments are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any changes made based on the design principles of the present invention, or any non-creative modifications, should fall within the scope of the present invention.

Claims

1. A weighting method for multiple alternative itemset hierarchical analysis for aviation standard evaluation, characterized in that, It includes: S1. Obtain the set of indicators with multiple alternatives from the aviation standard indicator system. ; Obtain the standard document to be evaluated. When the document's constituent elements include text elements expressed in words, the alternative level indicators to be used for the normative evaluation include readability indicators, logical indicators, and structural rationality indicators. When the constituent elements of a document include non-text elements expressed in tables, formulas, or graphs, the alternative level indicators to be used for obtaining the normative evaluation shall correspondingly include table normative indicators, formula normative indicators, and graph normative indicators. S2, Set of Indicators Divide into multiple sub-indicator sets according to the evaluation set rules; S3. Perform pairwise comparisons on the indicators within the sub-indicator set to obtain the corresponding pairwise comparison matrix; S4. For each pairwise comparison matrix, use log-linear regression to calculate the weight vector of the corresponding sub-index set; S5. Calculate the weight vector of all sub-indicator sets using a loop, resulting in the index set. Weighting of all indicators within: ； in, For indicator set The weight vector corresponding to all internal indicators, The number of sub-indicator sets. For indicator set weight vector With sub-indicator set weight vector The first splicing factor during splicing, For sub-indicator set The weight vector, For indicator set weight vector and weight vector The second splicing coefficient during splicing. for The weight vector corresponds to the sub-index set Part of for The weight vector corresponds to the sub-index set Part of it; Specifically, it includes: S51, Order , The initial weight vector to be merged represents the initial state of the method. S52, Calculation Corresponding weight vector And order ; like same If the intersection is empty, then Corresponding weight vector for: ； in, for Corresponding weight vector The item, For sub-indicator set Corresponding weight vector The item, for The Middle Individual indicators for the indicator set The Middle The importance score of each indicator To use log-linear regression to analyze the sub-indicator set The weight vector is obtained by calculating the pairwise comparison matrix; like and If the intersection is a set of singletons, then Corresponding weight vector for: ； in, From Delete the first one Each component Received dimensional vector; S53, Judgment Whether it is true or not, if so, then what is obtained at this time? That is The corresponding weight vector; otherwise, execute S52.

2. The weighting method for multiple alternative itemset hierarchical analysis for aviation standard evaluation according to claim 1, characterized in that, The evaluation set rules include: If the number of indicators exceeds the evaluation threshold, then the system will be split into subsets. ,in, express The Sub-indicator set, It is the number of sub-indicator sets; right same The intersection is empty or contains only one element.

3. The weighting method for multiple alternative itemset hierarchical analysis for aviation standard evaluation according to claim 2, characterized in that, The evaluation set rules also include: use same When the intersection is empty, the resulting subset of indicators consists of indicators with consistency. use same When a subset is partitioned with only one element in the intersection, the resulting subset consists of either consistent indicators or a set of consistent indicators plus an inconsistent indicator from the intersection.

4. The weighting method for multiple alternative itemset hierarchical analysis for aviation standard evaluation according to claim 1, characterized in that, S4. For each pairwise comparison matrix, calculate the weight vector of the corresponding sub-indicator set using log-linear regression, including: S41. Let the unknown weight vector be... ,in , express The Middle The elements are in The weights to be determined in the middle; S42. Constructing a log-linear regression problem: ； in, For sub-indicator set The Middle The first indicator is relative to the first Importance scores of each indicator The natural logarithm, It is a subset of indicators The Middle Each indicator in The natural logarithm of the undetermined weights. It is a subset of indicators The Middle Each indicator in The natural logarithm of the undetermined weights. It is a Kronecker notation if and only if When it exists ; S43. Solving the constructed log-linear regression problem, the solution is: ； in, Represents the generalized inverse of a matrix. Sub-index set The least squares solution vector corresponding to the linear regression problem mentioned above. It is the size of 0-1 matrix, Sub-index set The number of indicator pairs that were not compared in importance. Sub-index set The number of indicators in the data. It is the first A vector consisting of all existence terms in the pairwise comparison matrix of each subset of indices; S44. Based on the normalization conditions, from each The optimal weight vector is obtained by inverse solving. , That is, the sub-index set The corresponding weight vector.

5. A method for evaluating the standardization of aviation turbine fuel testing standards using the multi-alternative itemset analytic hierarchy process (AHP) weighting method for aviation standard evaluation as described in claim 1, characterized in that, It includes the following steps: M1. Obtain the experimental standard documents for the aviation turbine fuel to be evaluated; M2. Use layout recognition tools to identify the experimental standard documents for aviation turbine fuel and obtain the document's constituent elements; M3. Based on the constituent elements of the document, obtain the alternative layer indicators required for normative evaluation from the aviation standards and technical role indicator system, specifically: When the constituent elements of a document include text elements expressed in words, the alternative level indicators to be used for obtaining normative evaluation include readability indicators, logical indicators, and structural rationality indicators. When the constituent elements of a document include non-text elements expressed in tables, formulas, or graphs, the alternative level indicators to be used for obtaining the normative evaluation shall correspondingly include table normative indicators, formula normative indicators, and graph normative indicators. M4. The acquired readability indicators, logical indicators, and structural rationality indicators are classified into the text sub-indicator set, and the acquired graphic standardization indicators, table standardization indicators, and formula standardization indicators are classified into the non-text sub-indicator set. M5. Perform pairwise comparisons on the indicators in the text sub-indicator set and the non-text sub-indicator set respectively to obtain the corresponding pairwise comparison matrix. M6. Calculate the weight vectors of the text sub-indicator set and the non-text sub-indicator set according to the corresponding pairwise comparison matrix, and assign weights to the indicators in each sub-indicator set. M7. Select one indicator from both the text sub-indicator set and the non-text sub-indicator set, compare and score them, and obtain an importance score. ; M8. Concatenate and calculate the weight vectors of the text sub-indicator set and the non-text sub-indicator set to assign weights to all indicators within the obtained normative evaluation candidate layer; ； in, The weights of indicators arbitrarily extracted from the non-textual subset. The weights of any index extracted from the text subset. The importance score is used to compare two arbitrarily selected indicators. This is the weight vector for the non-textual sub-indicators, corresponding to the weights of the readability index, logicality index, and structural rationality index. This is the weight vector for the text sub-indicator set, corresponding to the weights of the graphical standardization index, the tabular standardization index, and the formula standardization index.

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