Large-scale heterogeneous multi-attribute equipment scheme clustering decision-making method and medium

Abstract

The invention relates to a large-scale heterogeneous multi-attribute equipment scheme clustering decision-making method and a medium. The method comprises the following steps: uniformly converting heterogeneous attribute data in a digital twin decision-making information system into binary connection numbers; determining an attribute weight by adopting an MEREC method, and constructing an attribute non-compensable value based on the attribute weight and the binary connection number; generating a scheme similar network according to the attribute non-compensable value; performing network clustering operation on the scheme similar network, and outputting a scheme clustering result; and based on the scheme clustering result, calculating the comprehensive target distance of the scheme in the cluster by adopting the grey target theory, and fusing the global value of the scheme and the comprehensive target distance to generate a final scheme score. According to the method, the problems of heterogeneous information fusion distortion, attribute non-compensatory mechanism deficiency and low large-scale scheme clustering efficiency in a digital twinborn decision scene are solved by constructing heterogeneous data unification-attribute non-compensatory mechanism modeling-network clustering-intra-cluster decision.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of complex equipment decision optimization, in particular to a large-scale heterogeneous multi-attribute equipment scheme clustering decision method and medium. BACKGROUND

[0002] Under the background of digital twin technology being widely applied in high-end equipment demonstration, the decision information system faces massive heterogeneous (such as precise numbers, interval numbers, sequence numbers, language variables, various fuzzy numbers and language term sets, etc.) and multi-scale evaluation data, and meanwhile, a large number of alternative schemes are involved in the equipment demonstration process, forming a typical large-scale heterogeneous multi-attribute decision problem. The existing researches have significant limitations in dealing with such problems: on the one hand, the fusion methods for heterogeneous information are mainly divided into two categories based on conversion (such as conversion into fuzzy numbers, interval numbers, etc.) and distance (such as distance from ideal solution), the former is easy to cause information loss in the conversion process, and the latter over-reliance on the accuracy of reference point selection and difficult to ensure the quality of homogeneous preference values, leading to decision bias; on the other hand, in the face of large-scale scheme set, the traditional decision methods have high computational complexity and low efficiency, and the existing simplification techniques (such as attribute reduction, scheme clustering, and efficient sorting algorithm) mainly focus on a single dimension (attribute heterogeneity or scheme scale), lacking of integrated methods that can effectively handle heterogeneous information fusion and large-scale scheme clustering decision, which seriously restricts the effectiveness and practicality of decision-making.

[0003] Specifically, the existing technology has three key defects: first, the information homogenization process mainly focuses on the evaluation information expressed by the decision maker, and lacks effective unified transformation methods for sensor measurement information (such as feature parameters) collected by machines, and it is difficult to fully reflect the inherent fuzziness and uncertainty in the comparison between schemes; second, the attribute measure method is too simple (often relying on a single distance or similarity), and fails to consider multiple dimensions of attribute characteristics such as distance, similarity, correlation and entropy, especially ignoring the attribute non-compensable mechanism (i.e. the short board of one attribute cannot be compensated by the advantage of other attributes) commonly existing in high-end equipment, leading to the loss of attribute characteristics and evaluation distortion between schemes; third, there is insufficient research on clustering decision for large-scale scheme characteristics, lacking of quantitative clustering standard function, making it difficult to design a unified standard to realize scientific classification of schemes and effectively coordinate the unity of global decision and local decision, and unable to fully utilize the concept of "unified evaluation of similar schemes" to improve decision efficiency.

[0004] Therefore, it is urgent to develop a new large-scale heterogeneous multi-attribute high-end equipment scheme clustering decision method for digital twin scenarios to overcome the above defects. SUMMARY

[0005] The application provides a large-scale heterogeneous multi-attribute equipment scheme clustering decision method and a medium, which aims to solve the problems of heterogeneous information fusion distortion, attribute non-compensable mechanism loss and low efficiency of large-scale scheme clustering in a digital twin decision-making scenario.

[0006] To achieve the above-mentioned purpose, the first aspect of the application provides a large-scale heterogeneous multi-attribute equipment scheme clustering decision method, comprising the following steps: unify heterogeneous attribute data in a digital twin decision-making information system into binary connection numbers; determine attribute weights by using a MEREC method, and construct attribute non-compensable values based on the attribute weights and the binary connection numbers; generate a scheme similarity network according to the attribute non-compensable values; perform a network clustering operation on the scheme similarity network, and output a scheme clustering result; based on the scheme clustering result, calculate a comprehensive target center distance of schemes in a cluster by using a grey target theory, and generate a final scheme score by fusing a global value of the scheme and the comprehensive target center distance.

[0007] Further, the heterogeneous attribute data includes sensor measurement information, and the method for converting the sensor measurement information into binary connection numbers comprises: calculate the standardized distance of a to-be-selected scheme and each scheme in a target database under the same attribute; calculate the positive evidence support degree and the negative evidence support degree of the to-be-selected scheme according to the standardized distance, wherein the positive evidence support degree represents the degree that the to-be-selected scheme is better than other schemes, and the negative evidence support degree represents the degree that the to-be-selected scheme is worse than other schemes; construct a confidence interval based on the positive evidence support degree and the negative evidence support degree, wherein the confidence interval contains the trust degree and the non-negative degree of the attribute of the scheme; map the confidence interval to a certain-uncertain space, extract the certainty component and the uncertainty component, and form a binary connection number.

[0008] Further, the heterogeneous attribute data includes expert evaluation information; the expert evaluation information is converted into binary connection numbers, and the following operations are performed according to the information type: for a language variable, a qualitative language is quantified by using a language scale function to generate a quantitative value, and a hesitancy degree is calculated, and the binary connection number is generated by combining the quantitative value and the hesitancy degree; for a hesitant fuzzy number, a geometric mean hesitancy degree is calculated, and the binary connection number is generated by combining the membership degree score and the geometric mean hesitancy degree; for a probability language term set, a quantitative value of a language term is calculated by using a score function, and the binary connection number is generated by combining the uncertainty represented by a deviation function.

[0009] Further, the method for determining attribute weight by using MEREC method comprises: extracting the certainty component and the uncertainty component in the binary connection number; calculating distance measure, similarity measure, association measure and entropy measure based on the certainty component; generating attribute non-compensable value representing attribute consistency difference between schemes by weighting and fusing the distance measure, similarity measure, association measure and entropy measure through attribute weight.

[0010] Further, the method for determining attribute weight by using MEREC method comprises: for benefit type attribute, normalizing attribute value by using maximum value of each attribute; for cost type attribute, normalizing attribute value by using inverse of minimum value of each attribute; taking natural logarithm of normalized attribute value in benefit type attribute or cost type attribute and summing up to obtain total performance value of each scheme; after removing each attribute in turn, recalculating total performance value of each scheme after removal; for each attribute, accumulating absolute deviation of original total performance value and total performance value after removal of the attribute; taking absolute deviation of each attribute and proportion of absolute deviation sum of all attributes as attribute weight value of the attribute.

[0011] Further, the network clustering operation comprises: generating comprehensive similarity matrix by using game combination optimization strategy and fusing multiple node similarity calculation methods; performing Markov clustering operation on the comprehensive similarity matrix, and sequentially performing network expansion, weight inflation and probability pruning; rechecking neighborhood link relationship of boundary node in clustering result, and adjusting cluster group to which the node belongs; merging cluster group with too small size, and outputting final scheme clustering result.

[0012] Further, the method for calculating comprehensive target distance of schemes in cluster comprises: performing reward and punishment transformation on attribute value of schemes in cluster, wherein, for benefit type attribute, using upper limit effect measure to standardize by using maximum value of attribute as reference, and for cost type attribute, using lower limit effect measure to standardize by using minimum value of attribute as reference; determining positive target heart and negative target heart of schemes in cluster based on standardized attribute value, wherein, the positive target heart is composed of optimal value of each attribute, and the negative target heart is composed of worst value of each attribute; calculating positive target distance of each scheme from positive target heart and negative target distance of each scheme from negative target heart; Taking the positive and negative target center connecting line as the reference axis, the projection value of the positive target center distance of each scheme on the axis is calculated as the comprehensive target center distance.

[0013] Further, the scheme global value is obtained by the following method: Determine the positive ideal solution based on the attribute values of all alternative schemes, wherein each attribute takes the optimal value, and the maximum value for the benefit type attribute and the minimum value for the cost type attribute; Determine the negative ideal solution based on the attribute values of all alternative schemes, wherein each attribute takes the worst value, and the minimum value for the benefit type attribute and the maximum value for the cost type attribute; For each scheme, calculate the distance between it and the positive ideal solution, which is obtained by the weighted sum of the attribute value differences, and the weight is the attribute weight; For each scheme, calculate the distance between it and the negative ideal solution, which is obtained by the weighted sum of the attribute value differences, and the weight is the attribute weight; Divide the distance between the scheme and the negative ideal solution by the sum of the distance between the scheme and the positive ideal solution and the distance between the scheme and the negative ideal solution to obtain the scheme global value.

[0014] Further, the final scheme score is generated by weighted fusion of the scheme global value and the comprehensive target center distance, and the weight coefficient is dynamically determined by the size proportion of the scheme subgroup.

[0015] To achieve the above object, the third aspect of the present application provides a computer readable storage medium, and a computer program is stored on the computer readable storage medium, and the computer program is run by a processor to execute the steps of the large-scale heterogeneous multi-attribute equipment scheme clustering decision method.

[0016] The present application has the following beneficial effects: Compared with the prior art, the large-scale heterogeneous multi-attribute equipment scheme clustering decision method and medium provided by the application solves the above problems by constructing a whole-process method system of "heterogeneous data unification-attribute irreplaceable mechanism modeling-network clustering-intra-cluster decision": first, for the distortion of heterogeneous information fusion, a unified transformation mechanism based on D-U space mapping is proposed, which converts sensor measurement information (accurate numbers, interval numbers, sequence numbers) and expert evaluation information (language variables, hesitant fuzzy numbers, probability language term sets, etc.) into binary connection number form. By separating the certain component and the uncertain component (such as mapping the confidence interval to the certain boundary point and the uncertain interval), the original data fuzziness and structural characteristics are preserved while realizing the lossless homogenization of heterogeneous information; second, for the lack of attribute irreplaceable mechanism, a multi-dimensional measurement model is constructed, the attribute weight is calculated by MEREC method, and the attribute irreplaceable value between schemes is quantified by combining distance measure, similarity measure, correlation measure and entropy measure. The global scheme value is generated by comparing the multi-dimensional feature gap between the scheme and the positive and negative ideal solutions, which accurately describes the nonlinear dependence and short board effect between attributes; finally, for the low efficiency of large-scale clustering, the scheme similarity network is constructed based on the attribute irreplaceable value, the game combination optimization strategy is used to fuse multiple node similarities, and the improved MCL algorithm is used to realize scheme clustering (including boundary rechecking and small cluster merging optimization), which significantly reduces the decision scale. The comprehensive target center distance is calculated in the cluster by using the grey target theory, and finally the ranking is generated by fusing the global value of the scheme and the variable weight score of the local target center distance, which reduces the calculation complexity while ensuring the decision accuracy, and realizes the efficient and accurate decision. BRIEF DESCRIPTION OF DRAWINGS

[0017] In order to more clearly illustrate the technical solutions in the embodiments of the application, the drawings needed in the embodiment description will be briefly introduced as follows.

[0018] Figure 1 is a large-scale heterogeneous multi-attribute equipment scheme clustering decision method framework disclosed by the embodiments of the application.

[0019] Figure 2 is a digital twin five-dimensional model structure diagram disclosed by the embodiments of the application.

[0020] Figure 3 is a D-U space coordinate diagram disclosed by the embodiments of the application.

[0021] Figure 4 is a mapping diagram of sensor measurement confidence interval in D-U space disclosed by the embodiments of the application.

[0022] Figure 5 is a D-H space mapping diagram of expert evaluation information disclosed by the embodiments of the application. Figure 5 (a) is a D-U space mapping diagram of sensor measurement information,Figure 5 (b) is a D-U space mapping of expert evaluation language variables, Figure 5 (c) is a D-U space mapping of a set of probabilistic language terms.

[0023] Figure 6 is a high-end equipment scheme optimization problem analysis graph under the influence of an attribute non-compensable mechanism, disclosed by an embodiment of the application.

[0024] Figure 7 is a project clustering network example graph, disclosed by an embodiment of the application.

[0025] Figure 8 is a comprehensive target distance diagram, disclosed by an embodiment of the application.

[0026] Figure 9 is a heat map of attribute non-compensable values between two computing schemes, disclosed by an embodiment of the application.

[0027] Figure 10 is a scheme clustering decision network graph, disclosed by an embodiment of the application.

[0028] Figure 11 is a network graph after clustering, disclosed by an embodiment of the application. DETAILED DESCRIPTION

[0029] In order for those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be described clearly and completely below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor should be within the scope of protection of the present application.

[0030] According to the embodiments of the present application, it should be noted that the steps shown in the flowchart of the drawings can be executed in a computer system such as a set of computer executable instructions, and although the logical order is shown in the following manufacturing method, in some cases, the steps shown or described can be executed in an order different from that here.

[0031] In the specific implementation of the present application, it is crucial to understand the basic concepts of digital twinning and the basic principles of set pair theory (Set Pair Analysis, SPA) and deterministic-uncertain space (D-U space), which are described in detail as follows: Digital twin refers to making full use of physical models, sensor updates, operation history and other data, integrating multi-disciplinary, multi-physical quantity, multi-scale, multi-probability simulation process, creating a virtual model of a physical entity in a virtual space, and simulating the behavior of the physical entity in the real environment with the help of data. As a mirror of the physical entity in the virtual space, it reflects the whole life cycle process of the corresponding physical entity product, and adds or expands new capabilities to the physical entity. In the high-end equipment demonstration scenario faced by the present invention, digital twin provides the advantages of high efficiency and rapid iteration. The widely used five-dimensional model of digital twin (physical entity, virtual entity, connection, twin data and service) includes: (1) wherein, is a multi-dimensional evaluation vector, represents a physical entity, represents a virtual entity, represents a service, represents twin data, represents the connection between each component. The structure of the five-dimensional model of digital twin is shown in Figure 2 When digital twin is used for equipment scheme demonstration, the decision information data structure is often multi-level, involving different scales and levels of association, and traditional information systems are difficult to capture this complexity.

[0032] When digital twin is used for equipment scheme demonstration, the decision information data structure has the characteristics of multi-level and multi-scale association. The present invention is based on the following formal definition: Definition 1: A digital twin decision information system is called , wherein is a non-empty finite object set (i.e. a set of alternative schemes), is a non-empty finite attribute set, is a non-empty finite scale set.

[0033] Any alternative scheme has different evaluation values at different information scales of attribute . Therefore, the digital twin decision information system can also be represented as: .

[0034] The digital twin decision information system will have two kinds of data, namely sensor measurement information and expert decision information. The characteristic parameter measurement value of the sensor is the characteristic layer information, and the experience knowledge of the expert is the decision layer information. The data given by the sensor is the measurement value of a certain characteristic attribute of the scheme, which represents the extension property of the target scheme, so the measurement value of the sensor needs to be converted into the degree of support or opposition to the scheme, and the expert decision information needs to be converted into the same scale.

[0035] Definition 2: Assumption It is a digital twin decision information system, in which It is a full shot ( It is an attribute In the (The range of values ​​at each scale). There exists a surjective... Make ,in It is called in the attribute From scale To scale, Information scaling transformation function.

[0036] Definition 3: Set pair analysis (SPA) is a theory that studies the interaction between certainty and uncertainty, which are ubiquitous in nature and human society. A set pair is a subsystem composed of two related sets. SPA analyzes the identity (a), difference (b), and opposition (c) existing within set pair systems, opening up new avenues for solving problems of stochastic uncertainty and fuzzy uncertainty. The connection number is the main mathematical tool of SPA, and its general expression is: in, To handle the uncertainty of features, , and For any non-negative real, and for a certain attribute, respectively, are mathematical measures of the degree of identity, difference, and opposition. The degree of opposition coefficient represents... and opposition; It is the difference coefficient, through The uncertainty in values ​​between -1 and 1 represents the uncertainty inherent in this attribute. Depending on the type of uncertainty in the problem, Can be expanded to In the form of [formula missing], in problems that do not consider the opposition of set-pair systems, the connection number can be simplified to [formula missing]. This format is suitable for handling ambiguity and uncertainty in decision-making information.

[0037] Deterministic-uncertain space is a space containing uncertainty, as defined by SPA, characterized by its composition. 3D space At least one dimension of the coordinate axis describes the measure of uncertainty. Figure 3 The composite quantity containing uncertain components in the two-dimensional DU space shown For example, in the figure Axis Description the deterministic component of the uncertainty component of the axis description the deterministic component of the uncertainty component of the

[0038] The essence of the theoretical basis of MCL algorithm is to calculate the process of Markov chain random walk in graph G, mainly including three links of expansion, inflation and pruning.

[0039] Definition 4: Set a network graph with community structure as Indicates that the network graph Loop, the adjacency matrix Standardization, so that The range of edge set elements is And . Use To represent the state transition matrix, the formula is as follows: (2) Where, is the state transition matrix The transition probability of node To node In the state transition matrix (after expansion operation) is The adjacency matrix of the network is The unit matrix is The space position index is The upper limit of the row total is Indicates that the loop is added to the matrix, and one connection edge is added to each node itself, which means that each element on the diagonal line is increased by 1 in the matrix. The matrix is normalized and standardized Processing, where Indicates the unit matrix; The column standardization factor is

[0040] The expansion operation is the process of multiplying two matrices, and the formula is: (3) Where, Indicates the expanded transition matrix, Is a binary function; , The characteristic vector / observation value is The normalized transition matrix is The expansion parameter is

[0041] The larger the expansion value , the more likely it is for the random walk to leave the cluster and enter the remaining clusters. Therefore, as the expansion value increases, the connection between the same cluster is weakened.

[0042] The expansion operation is to multiply the elements in the corresponding positions of the two matrices and normalize the columns of the matrix, that is, to multiply the elements in the corresponding positions of the two matrices and normalize the columns of the matrix. The formula is: (4) (5) wherein, is a state transition matrix is a transition probability (a matrix after the expansion operation) from a node to a node ; is an expansion parameter; is the total number of nodes in the network; represents a probability that a node transits to a community after the expansion operation; is a transition probability matrix after expansion; is a new state transition matrix after the expansion operation, which is used for the next pruning.

[0043] The accurate pruning is to retain values with large probabilities, and the probability values of the remaining nodes are zero: (6) wherein, represents a matrix after pruning, is a matrix after the expansion operation, is a pruning parameter, and the elements in the matrix are arranged in descending order in each column, and all elements after the th element are set to 0 to obtain the matrix . The expansion, expansion and pruning operations are iteratively performed until convergence, and the final matrix can be mapped to obtain the clustering (community) structure of the network. The algorithm provides core method support for the network clustering operation in step S400 of the present application.

[0044] As shown in Figure 1 , the present application provides a large-scale heterogeneous multi-attribute equipment scheme clustering decision method, which comprises the following steps: Step S100, uniformly converting heterogeneous attribute data in a digital twin decision information system into a binary connection number; Step S200, determining attribute weights by using a MEREC method, and constructing attribute irreplaceable values based on the attribute weights and the binary connection number; Step S300, generating a scheme similar network according to the attribute irreplaceable values; Step S400, performing a network clustering operation on the scheme similar network, and outputting a scheme clustering result; Step S500, based on the scheme clustering result, the grey target theory is used to calculate the comprehensive target distance of the scheme in the cluster, and the global value of the scheme and the comprehensive target distance are fused to generate the final scheme score.

[0045] In one specific embodiment of the application, as described in step S100 above, the heterogeneous attribute data in the digital twin decision information system is mainly derived from sensor measurement information and expert evaluation information, which needs to be uniformly converted into binary connection numbers . The specific processing method varies depending on the data type. Generally speaking, there are three types of high-end equipment feature data in the digital twin scenario, namely, precise numbers, interval numbers, and sequence numbers.

[0046] The attribute of the precise number type is represented by a single real value to represent the attribute of the equipment. The interval number attribute is used to describe the range type attribute of the equipment, which is an effective description method for handling complex and uncertain information. The sequence number represents the sequence data of the equipment changing with the characteristics in the time or space dimension, which is usually a continuous or ordered numerical sequence.

[0047] Let the mixed attribute feature parameter vector of the th high-end equipment scheme be , the mixed feature parameter vector of the th target scheme in the equipment target parameter database be , the distance between the th unknown target feature data and the feature parameter in the target database be denoted as , The Euclidean distance is used for normalization processing: (7) Wherein, the symbols and represent the scheme number, which is uniform in value, represents the feature attribute number; is the original distance (such as Euclidean distance) of the equipment scheme and the target scheme in attribute ; is the feature parameter value of the th high-end equipment scheme in attribute ; is the feature value of the target scheme (reference scheme) in attribute ; is the distance type identifier; The standardized distance value.

[0048] Consideration of equipment characteristic criteria and a standardized distance vector Assume that equipment characteristic attributes are all of the benefit type, and the equipment scheme set For any one scheme in , define its positive and negative evidence support: (8) (9) Wherein, is the positive evidence support; is the negative evidence support; is the alternative scheme, the index is ; is the index variable of other schemes; is other schemes The normalized distance value under attribute and scale ; is the normalized distance value of the current scheme under attribute and scale ; Let , If and are not 0, then there is: (10) Wherein, is called the positive support of the scheme , which measures the degree of advantage over other alternative schemes under attribute , is called the negative support of , which measures the degree of disadvantage over other alternative schemes under attribute ; The maximum value of the positive support degree of attribute in all schemes; The minimum value of the negative support degree of attribute in all schemes. The confidence interval of selecting scheme

[0049] under attribute is: (11) Wherein, ​​represents the degree of trust in , represents the degree of non-rejection in .

[0050] In the attribute and nature of the selected scheme The confidence interval of the mapping of the D-U space is the confidence interval , denoted as , is an interval number , where , and , when , , that is, the point is a real number. By means of the connection number, the interval number is mapped on the D-U space: (12) , where is the overall confidence state, composed of the real part (certainty) and the imaginary part (uncertainty), the real part represents the degree of trust in the scheme; the imaginary part represents the overall uncertainty of the scheme, is the uncertainty coefficient, taking a value in the range , for a given , the connection number form is obtained: (13) , where is the confidence connection number. The mapping of the confidence interval of the sensor measurement data to the two-dimensional D-U space is shown in Figure 4 . In Figure 4 , the boundary points and of the confidence interval number are certain, and the points between and are uncertain, so , that is, the certainty part can be represented as , and the uncertainty part is represented as

[0051] Expert evaluation decision information is divided into three types: language variables, fuzzy values, and language terms. Language variables refer to evaluation information represented by specific numerical values or symbols. Language variables are used for equipment attributes that can be clearly quantified. Fuzzy values are used to describe evaluations of equipment attributes with certain uncertainty or complexity. Language variables are a qualitative evaluation method suitable for equipment attributes that are difficult to accurately quantify and are expressed in natural language.

[0052] (1) Representation of language variables in D-U space Expert evaluation of decision-making information often uses precise linguistic variables as attributes, typically represented by a single linguistic symbol. It is used to represent the attributes of equipment, and usually represents a shorthand for a certain type of attribute of equipment.

[0053] It is a set of an odd number of language variables that quantifies the qualitative indicators used to evaluate language variables. Language scale function: (14) Understandably, the function of this formula is to incorporate language variables. Discrete semantic terms in The mapping is a deterministic membership degree (such as "support level").

[0054] in, For language items, For offset parameters, (Indicates the degree of semantic offset). (Normalized variables); This represents the total number of language items. For deterministic membership degree.

[0055] Then language variables The degree of hesitation is: (15) in, The degree of hesitation. There are language variables ,make , The obtained connection number form According to this method, linguistic variables are converted into binary relational expressions.

[0056] (2) Representation of hesitant fuzzy numbers in DU space The fuzzy numbers in expert evaluation decision-making information include types such as triangular fuzzy numbers, trapezoidal fuzzy numbers, discrete fuzzy numbers, intuitive fuzzy numbers, and hesitant fuzzy numbers, meaning that a certain degree of fuzziness can be included when providing attribute evaluations of equipment.

[0057] For fuzzy number attributes, taking hesitant fuzzy numbers as an example, hesitant fuzzy elements are used to represent the degree of hesitation among experts when evaluating the attribute. The mathematical expression of hesitant fuzzy elements is as follows: ,in It is a set of values ​​in [0,1], called For hesitant and ambiguous elements.

[0058] To fully account for the degree of hesitation among decision-makers, this embodiment considers both the differences in membership between elements in the hesitant fuzzy element and the different numbers of elements, and defines a geometric mean degree of hesitation to characterize the uncertain information of hesitant fuzziness.

[0059] Given that the geometric mean hesitation of an HFE is defined as: (16) in, For hesitant and blurred elements, The number of elements. yes The scoring function for each element is as follows: (17) Among them, if ,but Given a hesitant fuzzy number. ,make , The obtained connection number form .

[0060] (3) Representation of the probabilistic language term set in the DU space The linguistic terminology includes various types such as hesitant and ambiguous terminology sets, two-layer terminology sets, probabilistic terminology sets, and multi-granularity terminology sets. These are used to help experts evaluate complex and uncertain attributes, providing a rich set of means for the multi-layered and ambiguous expression of equipment attributes. This embodiment uses a probabilistic terminology set as an example, employing probabilistic terminology to represent the linguistic preferences of experts when evaluating attributes.

[0061] Let LTS be PLTS is represented as: (18) in, Basic language set, For indexing language terms, It is a linguistic term. yes The corresponding probability, express Number, This is a probability normalization constraint.

[0062] set up For any PLTS language term, the language term The small mark is The score function and its inverse function for a single language are defined as follows: (19) in, for In the language collection Subscript in; Probability-weighted semantic scores; Indicates the continuous semantic strength of language terms after standardization; A semantic description in numerical form. Indicates continuous value input; Based on numerical values Reconstructing language terminology ( (for integer order); This is a set of probabilistic language terms.

[0063] Conversion logic: Forward conversion Language item Integer mapping Standard value ; Inverse conversion Numerical value Reconstruction function Language items The scoring function is defined as: (20) in, The overall score for PLTS (used for DU space mapping); The discrete value after rounding down a single linguistic term; This is a probability-weighted approach to discrete semantic scores. set up For any PLTS, language terminology The small mark is , The deviation function is defined as follows: (twenty one) Given a probabilistic language set ,make , The resulting connection number takes the following form: (twenty two) Language variables Hesitant fuzzy numbers and probability language set Mapping on the two-dimensional DU space as follows Figure 5As shown. According to the content of the figure and the formula correlation analysis, (a), (b), (c) in the figure respectively represent the D-U space mapping relationship of the following three types of data, which correspond to the following: (a) is the D-U space mapping of sensor measurement information; (b) is the D-U space mapping of expert evaluation language variables; (c) is the D-U space mapping of the probability language term set (PLTS).

[0064] In one specific embodiment of the present application, as described in the above step S200, in a complex equipment or system, the short board or defect of a certain specific attribute cannot be compensated by the advantage of the system on other attributes. It is embodied as the relative independence of the performance values between different attributes, and each attribute has its indispensable role in realizing the overall function and cannot be simply replaced or compensated by the performance of other attributes. The mutual relationship between attributes cannot be regarded as linear or additive, but as a complex dependence and relative independence.

[0065] As shown in Figure 6 , the traditional distance measure-based method can evaluate the overall ability of the high-end equipment scheme, and select the scheme closest to the ideal solution, while the data statistics correlation measure-based method can evaluate the similarity of the ability gap on different attributes, and select the scheme similar to the ideal solution. The information entropy-based measure quantifies the information amount and uncertainty of different attributes in the scheme, and provides a reference for evaluating the stability of the overall scheme. A high entropy value can represent the diversity and complexity of attribute performance, reflecting the adaptability of the scheme in different environments. The correlation analysis-based measure represents the correlation strength and direction between two or more attributes, and measures their correlation.

[0066] Considering the influence of the non-compensable attribute mechanism, this embodiment considers distance measure, similarity measure, correlation measure and entropy measure, and considers that a better high-end equipment scheme should be a scheme that is very "similar" to the ideal scheme. The understanding of "similar" is that the distance between the development scheme and the ideal scheme is small, and the change trend of the development scheme on each attribute is similar to that of the ideal scheme. The correlation measure is a measure used to measure the relationship strength and direction between variables, which helps to identify the interaction and dependence between different attributes in high-end equipment evaluation and data analysis, and further evaluates the effectiveness of the ability arrangement. At the same time, it satisfies the characteristics of a certain complexity, which characterizes the diversity and complexity of attributes, and reflects the adaptability of the scheme in different environments.

[0067] If the D-U space exists a parameter , which quantifies the proportion of certainty and characterizes the numerical size of the D-U space, and is calculated as follows: (23) , wherein is a real quantitative value, For deterministic values, For uncertain values, .

[0068] If D-U space exists parameter , the generalized normalized D-U space distance is calculated as follows: (24) where, is the generalized normalized distance; is the quantized value of scheme A on the th attribute; is the quantized value of scheme B on the th attribute; in particular, is the number of attributes, , is the scheme A, is the scheme B, is the attribute weight, is the distance norm parameter, if , the D-U space distance degenerates to Hamming distance; if , it degenerates to Euclidean distance.

[0069] With reference to the cosine similarity, if D-U space exists parameter , the similarity measure of D-U space is calculated as follows: (25) If D-U space exists parameter , the correlation measure of D-U space elements is calculated as follows: (26) where, , is the mean value, , .

[0070] With reference to the relative entropy measure definition, if D-U space exists parameter , the entropy measure of D-U space is used to measure the difference between two probability distributions, describing the "information loss" from one distribution to another, and is calculated as follows: (27) Attribute non-recoverable value on D-U space is used to measure the attribute consistency difference between schemes, and the calculation formula is as follows: (28) wherein, is the non-compensable value; are 4 core evaluation dimensions (i.e. distance measure, similarity measure, correlation measure and entropy measure) corresponding to the equipment scheme.

[0071] The optimal value and the worst value of the attribute in all schemes respectively constitute the positive ideal solution and the negative ideal solution as the positive and negative reference points.

[0072] (29) (30) wherein, is the positive ideal solution, is the attribute quantitative value; is the attribute index; is the attribute set; is the negative ideal solution. Then for the equipment selection scheme containing attributes, the scheme attribute feature gap of each scheme with the positive and negative ideal solutions is defined respectively as: (31) wherein, is the positive distance; is the negative distance; is the single-dimensional distance function; is the positive ideal solution parameter; is the negative ideal solution parameter; is the to-be-evaluated scheme in the corresponding dimension quantitative value. Further calculate the scheme global value as: (32) wherein, is the scheme global value; is the scheme identification. Score as the quantitative value of the scheme for the next step of evaluation decision.

[0073] The MEREC weight determination method based on the D-U space is as follows: The attribute weight information is obtained by measuring the removal effect of each attribute on the overall performance of the alternative scheme. In this method, the greater the impact of deleting an attribute on the overall performance of the alternative scheme, the greater the weight should be allocated. Based on the above idea, the MEREC weight determination method based on information entropy is designed in this embodiment, and the specific steps are as follows: ​Step S201: Standardize the initial evaluation matrix. If the attribute is benefit-type, then: (33) If the attribute is of type cost, then: (34) in, This is the original evaluation value; Standardized evaluation values; For the first of all schemes The maximum value (benefit type) or minimum value (cost type) of an attribute; For the first of all schemes The minimum (benefit-oriented) or maximum (cost-oriented) value of an attribute; The number of alternative options; To evaluate the number of attributes.

[0074] Step S202: Calculate the overall performance of each alternative solution. : (35) in, For the first The overall performance index of the scheme is as follows: the larger the value, the better the scheme. This is a logarithmic transformation function.

[0075] Step S203: Calculate the performance of the solution after removing each attribute. : (36) in, Indicates the first The alternative is to remove the first option. Overall performance after considering all attributes; This represents the total number of remaining attributes after removing the attributes. Index for the remaining attributes.

[0076] Step S204: Calculate the sum of absolute deviations for each attribute: (37) in, Indicates the first The sum of absolute deviations of each attribute; This is a performance deviation. This is the scheme index.

[0077] Step S205: Obtain the objective weight of the attribute: (38) in, Indicates the first The objective weight of the attribute satisfies and .

[0078] In one specific embodiment of the present application, as described in step S300 above, this step is based on the attribute non-compensable value (characterizing the difference in attribute consistency between schemes) calculated in step S200 to construct a scheme similarity network. The network takes the alternative schemes as nodes and the similarity relationship between schemes as edges, providing a basic structure for subsequent clustering decisions. The following is the specific implementation process: In step S100, heterogeneous attribute data (including sensor measurement information and expert evaluation information) has been uniformly converted into binary connection numbers , wherein is the deterministic component, is the uncertainty component. In step S200: The MEREC method is used to determine the weight of each attribute ; and based on the weight and the binary connection number, the attribute non-compensable value is constructed; the attribute non-compensable value quantifies the difference in attribute consistency between schemes and , and the smaller the value, the higher the similarity between schemes.

[0079] Based on the attribute non-compensable value , the process of constructing the scheme similarity network is as follows: Step S301, all scheme pairs are traversed, and the attribute non-compensable value is calculated, which directly reflects the difference between schemes: The smaller the value, the more similar the schemes.

[0080] Step S302, to control the network density, a threshold value is set, which is determined based on the distribution of the values of all scheme pairs , and is usually selected as the 75% quantile (i.e., only the top 25% connections with the highest similarity are retained). When , an edge is added between the schemes and ; otherwise, there is no connection.

[0081] Step S303, taking all alternative schemes as the node set , the scheme pairs satisfying as the edge set , and forming an undirected weighted graph . The edge weight is , and the lower the weight, the stronger the similarity. To visually display the network structure, Figure 7The threshold is indicated. Similar networks to schemes 1, 4, and 5. For example, scheme 3 is similar to schemes 1, 4, and 5. Therefore, there are connecting edges; Scheme 2 and Scheme 3 Therefore, there is no connection.

[0082] In a specific embodiment of the present invention, as described in step S400 above, for large-scale solution decision-making problems, the present invention proposes a node similarity network clustering method based on game-theoretic combinatorial optimization. This method improves clustering accuracy by fusing multiple similarity metrics to avoid information loss from single methods. The core idea is to treat different similarity calculations as "game participants" and achieve a consistent optimal similarity assessment through collaborative optimization. The specific network clustering operation is as follows: Assuming to adopt Various node similarity calculation methods (such as cosine similarity, Jaccard coefficient, etc.) are used to perform pairwise similarity calculations on network nodes, generating a basic similarity set: A comprehensive similarity vector is constructed through linear combination: (39) In the formula, This represents the total number of node similarity algorithms used (such as cosine similarity, Jaccard coefficient, etc.). For algorithm indexing, Based on the similarity vector; To synthesize the similarity vector, The coefficients of the linear combination to be optimized; This is the transpose symbol.

[0083] In order to and To minimize the deviation, we need to... The linear combination coefficients to be optimized Optimize to obtain the optimal result. ,Right now: (40) In the formula, To minimize the discrepancy between the overall similarity score and the results of each algorithm; For Euclidean distance (L2 norm); The optimal weight combination to be solved is denoted as .

[0084] Using the properties of matrix differentiation, the first-order optimality condition is derived: (41) Solving this system of linear equations yields the optimal linear combination coefficients. Then by The results were normalized to obtain the final comprehensive similarity. , the formula is: (42) In the formula, is the comprehensive similarity; is the normalized weight. If a node and its neighbor nodes are located in different communities, the node is called a boundary node, so the boundary re-inspection of the node located at the boundary of the community is considered, the similarity between the node and the subgraph can be measured by the number of internal links at the intersection of the neighborhood of the node and the subgraph, in this embodiment, the definition is used for the re-inspection operation of the boundary node, and the formula is as follows: (43) In the formula, is the re-inspection operation of the boundary node, is the boundary node, is the community in which the neighbor node connected to the node is located, is the intersection of the neighbor nodes of and the target community; is the connection weight.

[0085] The pruning operation adopts the accurate deletion mode, pre-weights the matrix, and performs operation according to the logic of the MCL algorithm, that is, the MCL algorithm in the pre-order definition 4 is executed. When the iteration process is stopped, the operated matrix is mapped into a community structure. The mapped community structure is subjected to the optimization operation of boundary re-inspection and small community merging. The pseudo code of the project network clustering algorithm is as follows: In one specific embodiment of the present application, as described in the above step S500, the similar schemes are compared together, the errors and workload when a large number of schemes are compared together are reduced, for a small sample space, the grey target theory is used for decision-making, for heterogeneous attributes, the attributes are uniformly converted into effect vectors for convenient comparison. For the clustering decision network, a large number of scheme structures are formed into scheme clusters with similarity, and the grey target decision theory can realize data mining and information development as much as possible.

[0086] Suppose that a scheme cluster has scheme evaluation samples, which constitute an evaluation sample set ; a conditional scheme and attribute factors constitute the effect sample matrix of , wherein, and respectively represent , sample elements .

[0087] Since the dimensions and properties of each index are different, in order to better express the dispersion degree between the decision information and the ideal expectation, the reward and punishment transformation operator is introduced, and each index is processed by dimensionless. Let be the average value of each attribute factor, then (44) where, is the average value of attribute ; is the number of schemes; is the scheme index; is the attribute index; is the value of scheme in attribute .

[0088] Let be the effect measure of index , for benefit type index, we have (45) Similarly, for cost type index, we have (46) Thus, the normalized decision matrix can be obtained.

[0089] For each scheme cluster, let , then the positive target center, i.e. the optimal effect vector, is , let , then the negative target center, i.e. the worst effect vector, is . The positive and negative target center distance is , the positive target center distance of scheme is , and the negative target center distance is . The evaluation vector of any scheme is always between the positive and negative target centers, and the optimal scheme can be obtained by the size of the projection of the positive target center distance on the line between the positive and negative target centers. That is, the larger the projection, the better the corresponding countermeasure. The projection is the comprehensive target center distance. As shown in Figure 8 , according to the cosine theorem, the calculation formula of the projection is: (47) where, is the comprehensive target center distance (projection value), indicating the closeness of the scheme to the positive target center; is the distance between the positive and negative target centers (global distance); is the distance of the scheme to the positive target center; is the distance of the scheme to the negative target center.

[0090] The score of the scheme in the cluster is the sum of the scores of the targets in the cluster After the score is obtained (see step S200), the balance between the local and global of the comprehensive scheme is set to the weight value , which represents the preference of the decision maker for the overall and local performance of the scheme: (48) wherein, is the weight value, is the number of subgroups of the scheme, is the total number of schemes, is the subgroup index; is the total number of subgroups.

[0091] The final score of the scheme can be expressed as: (49) wherein, is the final score of the scheme, the value of which depends on the subgroup of the scheme, calculated by formula (48), is the global value of the scheme, that is, , representing the global performance of the scheme in the entire decision system. Therefore, the final selected scheme is the top schemes with the highest value.

[0092] The method of the present application will be explained in detail below with specific examples: Among various space propulsion technologies, high-end equipment of heavy-lift launch vehicle engines has many advantages such as high performance and reliability, good task adaptability, etc., and has always occupied a dominant position in space engineering applications. For different application requirements, heavy-lift launch vehicle engines have developed hundreds of engineering products of various types with different thrust levels, different propellants, different propellant supply methods, and different power cycle methods. In the process of demonstrating liquid rocket engines in the digital twin scenario, multiple enterprises are involved in the design, and each enterprise can provide multiple selection schemes, and the optimal scheme needs to be selected from them. The existing multiple experts evaluate 50 schemes, mainly discussing 6 attribute indexes such as thrust-to-weight ratio, combustion efficiency, variable speed, reliability, reusability, and complexity, and the specific parameters are shown in Table 1, and the attribute data types are {exact number, interval number, sequence number, language variable, hesitant fuzzy number, probability language term}.

[0093] Table 1 Attribute parameters of heavy-lift launch vehicle engine demonstration ​The thrust-to-weight ratio, combustion efficiency, variable speed, etc. can be output by the sensor, and the target parameter setting is 1, [0.8, 1.0], {0.80, 0.80, 0.80}. For expert evaluation decision information, the evaluation language variable of reliability performance is mainly three kinds of excellent / good / poor. The hesitation fuzzy number of multiplexing capability attribute is filled according to the optimistic principle to make its length consistent. The complexity attribute information is The probability language term set of expression form. Part of the evaluation information is shown in Table 2.

[0094] Table 2 Evaluation information of heavy-lift launch vehicle engine demonstration scheme According to formulas (7)-(11), the confidence interval of the thrust-to-weight ratio, combustion efficiency, variable speed, etc. of the heavy-lift launch vehicle engine is calculated, and formula (12) is used for D-U space mapping. At the same time, the evaluation heterogeneous information of reliability performance, multiplexing capability and complexity is mapped in D-U space. And the R value of the six attributes is calculated by formula (23).

[0095] According to formulas (23)-(28), the attribute non-compensable values between schemes are calculated, and the 75% threshold point is obtained, as shown in Figure 9 The red cells are the scheme pairs with higher similarity than the rest.

[0096] According to the attribute non-compensable values, a scheme clustering decision network diagram is constructed, as shown in Figure 10 Then, according to the algorithm, 50 schemes are clustered. When the random state matrix of the traditional MCL algorithm adds a self-loop, sets the expansion parameter e=2, the inflation parameter r=2, the maximum loop number maxloop=60, and the number of added self-loops multfactor=1, the algorithm has the best effect of community division. In this embodiment, the above parameters are set, and the experimental results are: the scheme network is divided into 9 groups, i.e. {3, 4, 7, 10, 45, 14, 47, 48, 20, 31}, {1, 2, 40, 43, 18, 26}, {32, 33, 6, 8, 22, 30}, {42, 11, 44, 21, 23, 27}, {34, 36, 38, 39, 49, 19}, {12, 13, 46, 15, 16}, {0, 35, 37, 17, 25}, {41, 29, 28, 5}, {24, 9}. The clustered network is shown in Figure 11 The scheme nodes of the same color represent that they are in the same cluster, for example, schemes 5, 28 and 41 belong to the same cluster.

[0097] According to the grey target decision theory, first, the effect vectors of all schemes are calculated. The largest number of scheme clusters is selected. For example, the effect vector of scheme cluster 1 is shown in Table 3: Table 3 Effect vector information of scheme cluster 1 The positive and negative target centers of scheme cluster 1 are calculated as follows: [0.904, 0.774, -0.130, 0.479, 1.00, 0.454], [-1.000, 0.467, -1.000, -0.613, -0.594, -1.000] According to the formula, the positive and negative target center distance is calculated as 3.214. The comprehensive target center distance of the effect vectors of each scheme in scheme cluster 1 is 2.574, 1.642, 1.921, 1.925, 1.103, 1.751, 1.276, 1.431, 1.469, 1.004, respectively.

[0098] According to the TOPSIS score of each scheme in scheme cluster 1, 0.471, 0.561, 0.473, 0.468, 0.510, 0.497, 0.533, 0.567, 0.462, 0.489, the maximum score is taken as 0.5. The final score of each scheme in scheme cluster 1 is 1.522, 1.102, 1.197, 1.196, 0.806, 1.124, 0.905, 0.999, 0.965, 0.747. Similarly, the final scores of the schemes in the remaining scheme clusters can be calculated, and finally, the optimal scheme is scheme 23 with a score of 1.47984.

[0099] In summary, the application constructs a heterogeneous data unification method, maps the data of the digital twin information decision system to the D-H space, converts it into a binary connection number, and describes the certain and uncertain information of the data. Secondly, considering the overall attribute characteristics of high-end equipment, a measure method of attribute non-compensable mechanism is proposed. And the attribute weight is solved by combining the MEREC method. Then, following the concept of "similar scheme unified evaluation", a scheme similar network is constructed. The node similarity network clustering method of game characteristics is defined to cluster the schemes, and the grey target theory is used for intra-cluster decision. Finally, the high-end equipment demonstration case under the digital twin scene is analyzed and discussed in detail. In the experiment, the discrimination degree of the decision ranking of the method is high, the time is shortened under the cluster decision mode, and it has an advantage in large-scale schemes. Considering the decision-making scene of heterogeneous data, the accuracy and reliability of the high-end equipment demonstration process are improved.

[0100] According to another aspect of the embodiments of the application, an electronic device is also provided, which includes a processor and a memory, the processor being configured to implement the steps of the method when executing a computer program stored in the memory.

[0101] In the above-described embodiments of the present application, the description of each embodiment focuses on different aspects, and the parts not described in detail in a certain embodiment can be referred to the relevant description of other embodiments.

[0102] In several embodiments provided in the present application, it should be understood that the disclosed technical contents can be implemented by other ways. Among them, the above-described device embodiments are only schematic, for example, the division of the units can be a logical function division, and in actual implementation, there can be another division way, for example, a plurality of units or components can be combined or integrated into another system, or some features can be ignored or not executed. In addition, the coupling or direct coupling or communication connection between the units or modules shown or discussed can be indirect coupling or communication connection through some interfaces, units or modules, which can be electrical or other forms.

[0103] In addition, each functional unit in each embodiment of the present application can be integrated in one processing unit, or each unit can exist physically, or two or more units can be integrated in one unit. The above-mentioned integrated unit can be realized in the form of hardware or in the form of software functional unit.

[0104] When the integrated unit is realized in the form of software functional unit and sold or used as an independent product, it can be stored in a computer readable storage medium. Based on this understanding, the technical solutions of the present application essentially or the part of the prior art that contributes or the whole or part of the technical solutions can be embodied in the form of software product, and the computer software product is stored in a storage medium, including a plurality of instructions to make a computer device (which can be a personal computer, a server or a network device, etc.) execute all or part of the steps of the method described in each embodiment of the present application. The foregoing storage medium includes: U disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), mobile hard disk, magnetic disk or optical disk and various program code storage media.

[0105] The above is only the preferred embodiment of the present application, and it should be pointed out that for ordinary skilled in the art, without departing from the principles of the present application, a number of improvements and refinements can be made, and these improvements and refinements should be considered as the protection scope of the present application.

Claims

1. A clustering decision-making method for large-scale heterogeneous multi-attribute equipment schemes, characterized in that, Includes the following steps: Transform heterogeneous attribute data in digital twin decision information systems into binary relational numbers; The MEREC method is used to determine the attribute weights, and the attribute non-compensable values ​​are constructed based on the attribute weights and the binary relationship coefficients. Generate a similar network based on the non-compensable value of the aforementioned attribute; Perform network clustering on networks similar to the proposed scheme and output the clustering results. Based on the clustering results of the schemes, the comprehensive target center distance of the schemes within the cluster is calculated using gray target theory. The global value of the scheme and the comprehensive target center distance are then fused to generate the final scheme score.

2. The clustering decision-making method for large-scale heterogeneous multi-attribute equipment schemes as described in claim 1, characterized in that, The heterogeneous attribute data includes sensor measurement information, and the method for converting the sensor measurement information into a binary relationship number includes: Calculate the standardized distance between the candidate solutions and each solution in the target database under the same attributes; Based on the standardized distance, the positive evidence support and negative evidence support of the candidate solutions are calculated respectively. The positive evidence support represents the degree to which the candidate solution is superior to other solutions, and the negative evidence support represents the degree to which the candidate solution is inferior to other solutions. A confidence interval is constructed based on the support of positive evidence and the support of negative evidence. The confidence interval includes the degree of trust in the attribute of the scheme and the degree of non-denial. The confidence interval is mapped to a deterministic-uncertain space, and the deterministic and uncertain components are extracted to form a binary correlation coefficient.

3. The clustering decision-making method for large-scale heterogeneous multi-attribute equipment schemes as described in claim 1, characterized in that, The heterogeneous attribute data includes expert evaluation information; the expert evaluation information is converted into binary contact numbers, and the following operations are performed according to the information type: For language variables, qualitative language is quantified using a language scaling function to generate quantified values, and its degree of hesitation is calculated. The quantified values ​​and degree of hesitation are then combined to generate a binary correlation coefficient. For hesitant fuzzy numbers, calculate their geometric mean hesitancy, and combine the membership score and the geometric mean hesitancy to generate a binary connection number. For a probabilistic linguistic term set, the quantification value of the linguistic term is calculated through a scoring function, and the uncertainty represented by the bias function is combined to generate a binary connection number.

4. The clustering decision-making method for large-scale heterogeneous multi-attribute equipment schemes as described in claim 2, characterized in that, The method for determining attribute weights using the MEREC method, and constructing attribute non-compensatory values ​​based on the attribute weights and the binary relationship coefficients, includes: Extract the deterministic and uncertain components from the binary connection coefficient; Calculate distance measure, similarity measure, association measure, and entropy measure based on deterministic components; By weighted fusion of distance measure, similarity measure, association measure and entropy measure, an attribute non-compensable value is generated to represent the attribute consistency difference between the representation schemes.

5. The clustering decision-making method for large-scale heterogeneous multi-attribute equipment schemes as described in claim 1 or 4, characterized in that, Methods for determining attribute weights using the MEREC method include: For benefit-type attributes, the attribute values ​​are normalized using the maximum value of each attribute; for cost-type attributes, the attribute values ​​are normalized using the reciprocal of the minimum value of each attribute. Take the natural logarithm of the normalized attribute values ​​in the benefit-type or cost-type attributes and sum them to obtain the total performance value of each scheme. After removing each attribute in turn, the total performance value of each scheme after removal is recalculated; For each attribute, sum the absolute deviations between the original total performance value of each solution and the total performance value after removing that attribute; The absolute deviation of each attribute and its proportion to the sum of the absolute deviations of all attributes are used as the attribute weight value.

6. The clustering decision-making method for large-scale heterogeneous multi-attribute equipment schemes as described in claim 1, characterized in that, Performing network clustering operations includes: A game-theoretic combinatorial optimization strategy is adopted, and multiple node similarity calculation methods are integrated to generate a comprehensive similarity matrix; Markov clustering is performed on the comprehensive similarity matrix, followed by network expansion, weight inflation, and probability pruning. The neighborhood link relationships of boundary nodes in the clustering results are re-examined, and the clusters to which the nodes belong are adjusted. Merge clusters that are too small and output the final clustering result.

7. The clustering decision-making method for large-scale heterogeneous multi-attribute equipment schemes as described in claim 1, characterized in that, Methods for calculating the overall target center distance of intra-cluster schemes include: The attribute values ​​of the schemes within the cluster are transformed to reward the best and punish the worst. Among them, the benefit-type attributes are measured by the upper limit effect and standardized with the maximum value of the attribute as the benchmark. The cost-type attributes are measured by the lower limit effect and standardized with the minimum value of the attribute as the benchmark. Based on the standardized attribute values, the positive and negative bullseyes of the schemes within the cluster are determined, wherein the positive bullseyes are composed of the optimal values ​​of each attribute, and the negative bullseyes are composed of the worst values ​​of each attribute. Calculate the positive target distance and the negative target distance of each scheme; Using the line connecting the positive and negative target centers as the reference axis, calculate the projection value of the positive target center distance of each scheme onto this axis, which is then used as the comprehensive target center distance.

8. The clustering decision-making method for large-scale heterogeneous multi-attribute equipment schemes as described in claim 1, characterized in that, The global value of the scheme is obtained through the following method: The ideal solution is determined based on the attribute values ​​of all alternative solutions, where the optimal value is taken for each attribute, the maximum value is taken for benefit-type attributes, and the minimum value is taken for cost-type attributes. The negative ideal solution is determined based on the attribute values ​​of all alternative solutions, where the worst value is taken for each attribute, the minimum value is taken for benefit-related attributes, and the maximum value is taken for cost-related attributes. For each solution, calculate its distance to the ideal solution. This distance is obtained by weighted sum of the differences between the attribute values, with the weights being the attribute weights. For each solution, calculate its distance to the negative ideal solution. This distance is obtained by weighted sum of the differences between the attribute values, with the weights being the attribute weights. The global value of the scheme is calculated by dividing the distance between the scheme and the negative ideal solution by the sum of the distances between the scheme and the positive ideal solution and the negative ideal solution.

9. The clustering decision-making method for large-scale heterogeneous multi-attribute equipment schemes as described in claim 1, characterized in that, The final score of the scheme is generated by weighted fusion of the global value of the scheme and the comprehensive target distance, and the weight coefficient is dynamically determined by the proportion of the scheme subgroup size.

10. A computer-readable storage medium storing a computer program thereon, characterized in that, When the computer program is run by the processor, it executes the steps of the clustering decision method for any of the large-scale heterogeneous multi-attribute equipment schemes as described in claims 1-8.

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