Heterogeneous multi-attribute decision-making complex equipment key component identification method
By constructing a heterogeneous multi-attribute decision-making method, combining hybrid distance measurement and OPA-EWM method, the subjectivity problem in the identification of key components of complex equipment is solved, and the accurate and robust identification of key components is achieved.
Patent Information
- Application Number
- CN202411925096.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-25
- Publication Date
- 2025-04-15
AI Technical Summary
The prior art has strong subjectivity in the identification of key components of complex equipment and insufficient identification methods, which affects the health management and maintenance costs of equipment.
A system of importance evaluation indexes for complex equipment components is constructed, a heterogeneous multi-attribute decision-making method is adopted, and a component evaluation index is described using real numbers, interval numbers, intuitive fuzzy numbers, triangular fuzzy numbers and fuzzy terms. Combining the mixed distance measurement and OPA-EWM method, the subjective weight and objective weight are comprehensively considered to calculate the component's importance score.
The accurate identification of key components of complex equipment is achieved, and the identification results are more robust and reasonable, in line with the actual engineering, and the importance of key components is highlighted.
Smart Images
Figure CN119831434A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to a method for identifying key components of complex equipment, and in particular to a method for identifying key components of complex equipment based on heterogeneous multi-attribute decision making. Background Art
[0002] Complex equipment is large in size, complex in structure, powerful in function, with strong correlation between components, complex operating mechanisms, diverse faults and complex causes. As the service time continues, the performance of each component will inevitably degrade, affecting the reliability of the entire machine. Once a failure occurs, it will cause the equipment to shut down, incur huge repair costs, and may even cause major safety accidents. Currently, the identification of key components of complex equipment is mostly based on the experience of management personnel or simply selects real numbers from the aspects of component cost, reliability, etc. for comprehensive evaluation, resulting in a strong subjectivity in the identification method, which is not conducive to the healthy management of complex equipment. Summary of the invention
[0003] Purpose of the invention: The purpose of the invention is to propose a method for identifying key components of complex equipment based on heterogeneous multi-attribute decision-making, so as to achieve accurate identification of key components of complex equipment.
[0004] Technical solution: The present invention comprises the following steps:
[0005] Construct an evaluation index system for the importance of complex equipment components; evaluate each component according to the evaluation index system to obtain an initial evaluation matrix; standardize and normalize the initial evaluation matrix to obtain a normalized evaluation matrix; determine the positive and negative ideal solution vectors; calculate the positive and negative ideal distance matrices; calculate the weight of each evaluation index; calculate the importance score of each component, and determine the key components based on the importance score.
[0006] The evaluation indexes of the importance of complex equipment components include work efficiency c1, life time c2, market value c3, technology maturity c4, maintenance difficulty c5, detection difficulty c6, reliability c7, failure probability c8, tightness c9 and failure propagation probability c 10 , where c1, c3, c4, c8, c 10 It is expressed by real numbers, c2 by interval numbers, c9 by intuitionistic fuzzy numbers, c7 by triangular fuzzy numbers, and c5 and c6 by fuzzy terms.
[0007] The initial evaluation matrix is obtained by evaluating each component according to the evaluation index system. Specifically, it is assumed that the complex equipment has a total of m components, which are respectively recorded as {A1, A2, ..., A m}, according to the evaluation index {c1,c2,…,c 10}Evaluate each component one by one, and get the initial evaluation matrix A = {a ij}m×10 , where a ij For component A i The evaluation result of the j-th evaluation indicator.
[0008] The initial evaluation matrix is standardized and normalized to obtain a normalized evaluation matrix, specifically: the evaluation indicators are divided into two categories: "benefit" and "cost", among which c2 and c7 are "cost" categories, and the rest are "benefit" categories, and all indicators are converted into "benefit" categories:
[0009] For a real number a ij =r ij , the conversion formula is as follows:
[0010]
[0011] in, and is the evaluation result r of the jth evaluation index ij The maximum and minimum values of (i=1,2…,m);
[0012] For the interval number a ij =[m ij ,n ij ], the conversion formula is as follows:
[0013]
[0014] in, and is the evaluation result of the jth evaluation index [m ij ,n ij ](i=1,2…,m)where n ij The maximum value and m ij The minimum value of
[0015] For the intuitionistic fuzzy number a ij =<μ ij ,ν ij >, first convert to interval number a ij =[μ ij ,1-ν ij ], and then converted into interval number b according to formula (2) ij ;
[0016] For the triangular fuzzy number a ij =(l ij ,m ij ,n ij ), the conversion formula is as follows:
[0017]
[0018] in, and is the evaluation result of the jth evaluation index (l ij ,m ij ,n ij )(i=1,2…,m)where n ij The maximum value and l ij The minimum value of
[0019] For the fuzzy term a ij ={s i}, first converted into an intuitive fuzzy number a ij =<μ ij ,ν ij >, and then converted into interval number a ij =[μ ij ,1-ν ij ], and then converted into interval number b according to formula (2) ij ;
[0020] According to the above conversion rules, A={a ij} m×10 Transformed into normalized evaluation matrix B = {b ij} m×10 .
[0021] In the determination of the positive and negative ideal solution vectors, the positive and negative ideal solutions are respectively
[0022] For real numbers
[0023]
[0024] For the interval number
[0025]
[0026] For triangular fuzzy numbers
[0027]
[0028] The calculation of the positive and negative ideal distance matrices is specifically as follows: Calculate each element b in B ij arrive and distance, construct the positive and negative ideal separation matrix D + and D - for:
[0029]
[0030] in, and Respectively represent b ij arrive and distance;
[0031] For real numbers a and b,
[0032] d * (a,b)=|ab| (9)
[0033] For interval numbers a = [a1, a2] and b = [b1, b2],
[0034]
[0035] For triangular fuzzy numbers a = (a1, a2, a3) and b = (b1, b2, b3),
[0036]
[0037] Where λ is the adjustment coefficient.
[0038] The calculation of the weight of each evaluation index specifically includes the following steps:
[0039] Invite M experts to score the importance of each evaluation index in order, and obtain the index ranking matrix E = {E1, E2, ..., E M} T , the scores of each expert on the parts are ranked in the same order, which is given by the matrix B in order of size, and the scoring matrix F = {f ij} m×10 , where f ij is the evaluation index C of the i-th component j The ranking results on ; Get the subjective weight of each evaluation index
[0040] The objective weight of each evaluation index is determined by using the normalized evaluation matrix B and entropy weight method.
[0041] Calculate the weight w of each evaluation index j ,
[0042]
[0043] Among them, 0≤φ, and
[0044] The sorting method is as follows:
[0045] For real numbers a and b, if a≥b, a ranks higher; if a<b, b ranks higher;
[0046] For interval numbers a = [a1, a2] and b = [b1, b2], if a1 ≥ b1, a2 ≥ b2, then a is ranked first; if a1 ≥ b1, a2 < b2, then b is ranked first;
[0047] For triangular fuzzy numbers a = (a1, a2, a3) and b = (b1, b2, b3), if a2>b2, a ranks first; if a2=b2, a1≥b1, a2≥b2, a ranks first; if a2=b2, a1≥b1, a2<b2, b ranks first; if a2<b2, b ranks first.
[0048] The steps for determining the objective weight of each evaluation index are as follows:
[0049] Calculate each element b in the evaluation matrix B ij Information includedI i ' j :
[0050] For a real number r,
[0051]
[0052] Among them, r * is the design range, r≤r * , ε is the guarantee of I′(r,r * )>0;
[0053] For the interval number L = [a, b],
[0054]
[0055] Among them, L * =[a * ,b * ] is the design range, a≤a * , b≤b * , ε is the guarantee of I′(L,L * )>0;
[0056] For triangular fuzzy number N = (n1, n2, n3),
[0057]
[0058] in, is the design range, ε is the guarantee of I′(N,N * )>0;
[0059] Calculate each evaluation index C j Information entropy e j ,
[0060]
[0061] in, l=1 / lnm,0≤e j ≤1;
[0062] Calculate each evaluation index C j The objective weight of
[0063]
[0064] in,
[0065] The importance scores of each component are calculated, and the key components are determined according to the importance scores. Specifically, D + and D - Each element in calculates the importance score S(A i )(i=1,2,…,m),
[0066]
[0067] According to the importance score S(A i ) are sorted, the greater the importance, the more important the component.
[0068] Beneficial effects: The present invention is based on the collected heterogeneous information such as the function, cost, operation mechanism, historical fault information of each component of complex equipment and the topological structure of the entire equipment, which is more in line with engineering practice; the problem of identifying key components of complex equipment is regarded as a multi-attribute decision-making problem containing heterogeneous information, and real numbers, interval numbers, intuitive fuzzy numbers, triangular fuzzy numbers and fuzzy terms are used to describe the evaluation indicators of components, which overcomes the deficiency of single description of traditional evaluation information; a heterogeneous multi-attribute decision-making evaluation model based on hybrid distance measurement and OPA-EWM method is proposed, which comprehensively considers the subjective weight and objective weight of the evaluation index, and designs a hybrid distance measurement to distinguish the differences between different components, highlighting the importance of key components. Compared with the existing technology, the decision results obtained are more robust, more convincing and more reasonable. BRIEF DESCRIPTION OF THE DRAWINGS
[0069] Figure 1 is a flow chart of the present invention;
[0070] Figure 2 This is a diagram of the evaluation index system for the importance of complex equipment components of the present invention. DETAILED DESCRIPTION
[0071] The present invention will be further described below in conjunction with the accompanying drawings.
[0072] The method for identifying key components of complex equipment based on heterogeneous multi-attribute decision making in this embodiment includes the following steps:
[0073] S1. Constructing an evaluation index system for the importance of complex equipment components
[0074] The evaluation index of the importance of complex equipment components can be constructed from the aspects of component function, value, maintainability, reliability and the topological structure of the entire equipment, including work efficiency (c1), life time (c2), market value (c3), technology maturity (c4), maintenance difficulty (c5), detection difficulty (c6), reliability (c7), failure probability (c8), compactness (c9) and failure propagation probability (c10). 10 ) and other indicators, among which c1, c3, c4, c8, c 10 It is expressed by real numbers, c2 by interval numbers, c9 by intuitionistic fuzzy numbers, c7 by triangular fuzzy numbers, and c5 and c6 by fuzzy terms.
[0075] S2. Evaluate each component according to the evaluation index system to obtain the initial evaluation matrix
[0076] Assume that the complex equipment has m components (or systems), which are denoted as {A1, A2, …, A m}, according to 10 evaluation indicators {c1,c2,…,c 10}Evaluate the m components one by one and get the initial evaluation matrix A={a ij} m×10 , where a ij For component A i The evaluation result of the j-th evaluation indicator.
[0077] S3, standardize and normalize the initial evaluation matrix to obtain a normalized evaluation matrix
[0078] In the present invention, the evaluation indexes are divided into two categories: "benefit" and "cost", among which c2 and c7 are "cost" categories, and the rest are "benefit" categories. For the convenience of calculation, all indicators must be converted into "benefit" categories.
[0079] For a real number a ij =r ij , the conversion formula is as follows:
[0080]
[0081] in, and is the evaluation result r of the jth evaluation index ij The maximum and minimum values of (i=1,2…,m).
[0082] For the interval number aij =[m ij ,n ij ], the conversion formula is as follows:
[0083]
[0084] in, and is the evaluation result of the jth evaluation index [m ij ,n ij ](i=1,2…,m)where n ij The maximum value and m ij The minimum value of .
[0085] For the intuitionistic fuzzy number a ij =<μ ij ,ν ij >, can be converted into interval number a first ij =[μ ij ,1-ν ij ], and then converted into interval number b according to formula (2) ij .
[0086] For the triangular fuzzy number a ij =(l ij ,m ij ,n ij ), the conversion formula is as follows:
[0087]
[0088] in, and is the evaluation result of the jth evaluation index (l ij ,m ij ,n ij )(i=1,2…,m)where n ij The maximum value and l ij The minimum value of .
[0089] For the fuzzy term a ij ={s i}, can be converted into an intuitive fuzzy number a ij =<μ ij ,ν ij >, and then converted into interval number a ij =[μ ij ,1-ν ij ], and then converted into interval number b according to formula (2) ij .
[0090] According to the above conversion rules, A={a ij} m×10 Transformed into normalized evaluation matrix B = {bij} m×10 .
[0091] S4. Determine the positive and negative ideal solution vectors
[0092] Since all evaluation indicators have been converted into "benefit" indicators, the positive and negative ideal solutions are and
[0093] For real numbers
[0094]
[0095] For the interval number
[0096]
[0097] For triangular fuzzy numbers
[0098]
[0099] S5. Calculate positive and negative ideal distance matrices
[0100] Calculate the value of each element b in B ij arrive and distance, construct the positive and negative ideal separation matrix D + and D - :
[0101]
[0102] in, and Respectively represent b ij arrive and In order to improve the accuracy and robustness of subsequent decisions, the generalized hybrid distance is used in the present invention to capture the diversity and relevance of evaluation data.
[0103] For real numbers a and b,
[0104] d * (a,b)=|ab| (9)
[0105] For interval numbers a = [a1, a2] and b = [b1, b2],
[0106]
[0107] For triangular fuzzy numbers a = (a1, a2, a3) and b = (b1, b2, b3),
[0108]
[0109] In equations (10) and (11), λ is the adjustment coefficient, which can be adjusted according to the preferences of different decision makers, thereby allowing the application of different generalized distances. Generally, λ=1 is selected.
[0110] S6. Calculate the weight of each evaluation index, which is divided into three stages:
[0111] The first stage: Invite M experts to score the importance of each evaluation index in order, and obtain the index ranking matrix E = {E1, E2, ..., E M} T In the present invention, it is assumed that the opinions of the experts are independent of each other and have the same weights; the scores of the components by the experts are ranked in the same order, which is given by the matrix B in order of size, and the scoring matrix F = {f ij} m×10 , where f ij is the evaluation index C of the i-th component (or system) j Then, the order priority method (OPA) is used to obtain the subjective weight of each evaluation index. The sorting method is as follows:
[0112] For real numbers a and b, if a≥b, a ranks higher; if a<b, b ranks higher.
[0113] For interval numbers a = [a1, a2] and b = [b1, b2], if a1 ≥ b1, a2 ≥ b2, then a is ranked higher; if a1 ≥ b1, a2 < b2, then b is ranked higher.
[0114] For triangular fuzzy numbers a = (a1, a2, a3) and b = (b1, b2, b3), if a2>b2, a ranks first; if a2=b2, a1≥b1, a2≥b2, a ranks first; if a2=b2, a1≥b1, a2<b2, b ranks first; if a2<b2, b ranks first.
[0115] The second stage: using the normalized evaluation matrix B and the entropy weight method (EWM) to determine the objective weight of each evaluation index The specific steps are as follows:
[0116] S61: Calculate each element b in the evaluation matrix B ij Information includedI i ' j :
[0117] For a real number r,
[0118]
[0119] Among them, r * is the design range, r≤r * , ε is the guarantee of I′(r,r * )>0.
[0120] For the interval number L = [a, b],
[0121]
[0122] Among them, L * =[a * ,b * ] is the design range, a≤a * , b≤b * , ε is the guarantee of I′(L,L * )>0.
[0123] For triangular fuzzy number N = (n1, n2, n3),
[0124]
[0125] in, is the design range, ε is the guarantee that I′(N,N * )>0.
[0126] S62: Calculate each evaluation index C j Information entropy e j ,
[0127]
[0128] in, l=1 / lnm,0≤e j ≤1.
[0129] S63: Calculate each evaluation index C j The objective weight of
[0130]
[0131] in,
[0132] In the third stage, the weight w of each evaluation index is calculated j ,
[0133]
[0134] Among them, 0≤φ, and
[0135] S7. Calculate the importance score of each component and determine the key components based on the importance score
[0136] Using D + and D - Each element in calculates the importance score S(A i )(i=1,2,…,m),
[0137]
[0138] According to the importance score S(A i ) are sorted, the greater the importance, the more important the component.
[0139] The present embodiment is further explained below in conjunction with specific examples.
[0140] like Figure 1 As shown, a method for identifying key components of complex equipment based on heterogeneous multi-attribute decision-making includes the following steps:
[0141] Step 1: Construct an evaluation index system for the importance of complex equipment components. Construct an evaluation index system for the importance of complex equipment components from aspects such as component function, value, maintainability, reliability, and the topological structure of the entire equipment, such as Figure 2 As shown in the figure, it includes work efficiency (c1), life span (c2), market value (c3), technology maturity (c4), maintenance difficulty (c5), detection difficulty (c6), reliability (c7), failure probability (c8), compactness (c9) and failure propagation probability (c 10 ) and other indicators, among which c1, c3, c4, c8, c 10 It is expressed by real numbers, c2 by interval numbers, c9 by intuitionistic fuzzy numbers, c7 by triangular fuzzy numbers, and c5 and c6 by fuzzy terms.
[0142] Step 2: Evaluate each component according to the evaluation index system to obtain the initial evaluation matrix. A complex equipment has 6 components, denoted as {A1, A2, …, A6}. According to 10 evaluation indicators {c1, c2, …, c 10}Evaluate the six components one by one and get the initial evaluation matrix A = {a ij} 6×10 , as shown in Table 1. Among them, the work efficiency index is the component A within the working time of the complex equipment iThe proportion of working time, expressed as a percentage; the life time index takes the interval value of the shortest and longest service time of the component, in years; the market value index takes the actual purchase price of the component, in yuan; the technical maturity index is expressed in levels 1-9 respectively; the maintenance difficulty and detection difficulty indicators are expressed in 5 fuzzy terms: very simple (s1), simple (s2), medium (s3), difficult (s4) and very difficult (s5); the reliability index is expressed by triangular fuzzy numbers (a, b, c), where a and c are the lower and upper bounds of the reliability level (1-9), and b is the most recognized reliability level within the scoring range; the failure probability index takes the average number of failures per hour of the component, in times / hour; the closeness index is expressed by intuitionistic fuzzy sets (u, v), where u represents the close membership of the component with other components, and v represents the loose membership of the component with other components; the failure propagation probability index represents the probability that the failure of the component will cause the failure of other components, expressed in %.
[0143] Table 1. Initial evaluation matrix
[0144]
[0145] Step 3: Standardize and normalize the initial evaluation matrix to obtain a normalized evaluation matrix. In Table 1 above, work efficiency, market value, technology maturity, maintenance difficulty, detection difficulty, failure probability, tightness, and failure propagation probability are "benefit" indicators, and life time and reliability indicators are "cost" indicators. The normalized evaluation matrix B = {b ij} 6×10 , as shown in formula (19):
[0146]
[0147] Step 4: Determine the positive and negative ideal solution vectors. According to matrix B, the positive and negative ideal solutions C can be obtained. + and C - , as shown in equations (20) and (21):
[0148] C + ={1,[0.4,1],1,1,[0.8,1],[0.8,1],(0.625,0.875,1),1,[0.4,1],1} (20)
[0149] C - ={0,[0,0.4],0,0,[0,0.2],[0,0.2],(0,0.125,0.25),0,[0,0.2],0} (21)
[0150] Step 5: Calculate the positive and negative ideal distance matrices. According to matrix B and positive and negative ideal solutions C+ and C - , select λ=1, calculate the positive and negative ideal separation matrix D + and D - , as shown in equations (22) and (23):
[0151]
[0152] Step 6: Calculate the weight of each evaluation indicator.
[0153] In the first stage, the OPA method is used to determine the subjective weight of each evaluation indicator. The specific steps are as follows: Invite three experts to score the importance of each indicator in order, and obtain the indicator ranking matrix E, as shown in formula (24):
[0154]
[0155] According to the matrix B, the expert's scoring matrix F for the components is obtained as follows (25):
[0156]
[0157] The ordinal priority method (OPA) is used to obtain the subjective weight vector w of each evaluation index. SUB , as shown in formula (26):
[0158] w SUB =(0.0370.0670.0840.0290.0490.0330.2390.2980.0560.109) (26)
[0159] In the second stage, the objective weight of each evaluation index is determined by using the normalized evaluation matrix B and the entropy weight method (EWM). The specific steps are as follows: Calculate each element b in B ij Information includedI i ' j , we get the information matrix I′, as shown in equation (27):
[0160]
[0161] Calculate each evaluation index C j Information entropy e j , we get the information entropy vector e, as shown in formula (28):
[0162] e=(0.8470.8700.7030.7550.6140.3880.3700.2780.6140.879) (28)
[0163] Calculate each evaluation index C j The objective weight of Get the objective weight vector wOBJ , as shown in formula (29):
[0164] w OBJ =(0.041 0.035 0.081 0.067 0.105 0.166 0.171 0.196 0.105 0.033)(29)
[0165] In the third stage, the weight w of each evaluation index is calculated j , respectively taking φ=0.6, The comprehensive weight vector w is obtained as follows (30):
[0166] w=(0.0390.0540.0820.0440.0710.0860.2120.2570.0750.079) (30)
[0167] Step 7: Calculate the importance score of each component. + and D - Each element in calculates the importance score S(A i )(i=1,2,…,m), and obtain the importance score vector S, as shown in the following formula (31):
[0168] S=(0.3281 0.6181 0.3491 0.2790 0.3352 0.4070) (31)
[0169] Step 8: Determine the key components based on the importance scores. According to vector S, A2>A6>A3>A5>A1>A4. Therefore, A2 is the most critical component, followed by A6. In the subsequent complex equipment health management, the status of A2 and A6 should be focused on.
[0170] In order to prove the advantages of the present invention, additional explanations are given from the aspects of robustness, sensitivity and method, as follows:
[0171] In terms of robustness, since the proposed generalized mixed distance involves the parameter λ, when the value of λ is different, the generalized mixed distance calculation method used will also be different, which may affect the final recognition. Therefore, different values of λ are selected to compare the recognition results, as shown in Table 2.
[0172] Table 2. Comparison of recognition results for different λ values
[0173]
[0174] It can be seen from Table 2 that as λ increases, the importance of each component changes, but the range of change is not large, and the ranking of component importance remains basically unchanged (except that the importance of A3 and A5 is relatively close, with a slight change), indicating that the recognition result is relatively stable.
[0175] In terms of sensitivity, the comprehensive weight of the proposed evaluation index is obtained by combining the subjective weight and the objective weight, and is related to φ and The value of has a certain influence. When φ and Changes will inevitably affect the weights of each evaluation index, thus affecting the final identification. The impact of the value on the recognition results, 6 groups of different values are selected to compare the recognition results, as shown in Table 3:
[0176] Table 3. Different φ and Comparison of recognition results of values
[0177]
[0178]
[0179] It can be seen from Table 3 that as φ and The importance of each component changes with the change of , and the ranking also changes greatly. The more the subjective weight is valued, the greater the importance of A6 and the smaller the importance of A5, but the ranking of A2 and other components remains unchanged. This shows that in actual application, φ and φ can be appropriately adjusted according to the subjective preferences of complex equipment designers or managers. The value of is more conducive to identifying more important components.
[0180] In terms of method comparison, the proposed method mainly uses OPA, EWM and TOPSIS methods. OPA and EWM methods are used to determine the weight of indicators, and TOPSIS method is used to calculate the importance of components. Therefore, the method of the present invention is compared with OPA-TOPSIS and EWM-TOPSIS methods, and the results are shown in Table 4:
[0181] Table 4. Comparison of recognition results of different methods
[0182]
[0183] As can be seen from Table 4, the recognition results of the method of the present invention are not completely consistent with those of other methods, but the trends are roughly the same, which on the one hand shows the effectiveness of the method proposed in the present invention, and on the other hand shows that the weights determined by different methods have a certain influence on the recognition results. However, using the OPA method to determine the weights is too subjective, and using the EWM method to determine the weights is too objective. The weight formula proposed by the present invention takes into account both subjective and objective weights, and can also adjust the proportion of subjective and objective weights according to the manager's preferences, which has certain advantages.
Claims
1. A method for identifying key components of complex equipment based on heterogeneous multi-attribute decision making, characterized in that: The following steps are involved: Construct an evaluation index system for the importance of complex equipment components; evaluate each component according to the evaluation index system to obtain an initial evaluation matrix; Standardize and normalize the initial evaluation matrix to obtain a normalized evaluation matrix; Determine the positive and negative ideal solution vectors; Calculate positive and negative ideal distance matrices; Calculate the weight of each evaluation index; Calculate the importance score of each component and determine the key components based on the importance score.
2. According to the method for identifying key components of complex equipment by heterogeneous multi-attribute decision making in claim 1, it is characterized in that: The evaluation indexes of the importance of complex equipment components include work efficiency c1, life time c2, market value c3, technology maturity c4, maintenance difficulty c5, detection difficulty c6, reliability c7, failure probability c8, tightness c9 and failure propagation probability c 10 , where c1, c3, c4, c8, c 10 It is expressed by real numbers, c2 by interval numbers, c9 by intuitionistic fuzzy numbers, c7 by triangular fuzzy numbers, and c5 and c6 by fuzzy terms.
3. The method for identifying key components of complex equipment using heterogeneous multi-attribute decision making according to claim 2 is characterized in that: The initial evaluation matrix is obtained by evaluating each component according to the evaluation index system. Specifically, it is assumed that the complex equipment has a total of m components, which are respectively recorded as {A1, A2, ..., A m }, according to the evaluation index {c1,c2,…,c 10 }Evaluate each component one by one and get the initial evaluation matrix A = {a ij } m×10 , where a ij For component A i The evaluation result of the j-th evaluation indicator.
4. The method for identifying key components of complex equipment using heterogeneous multi-attribute decision making according to claim 3 is characterized in that: The initial evaluation matrix is standardized and normalized to obtain a normalized evaluation matrix, specifically: the evaluation indicators are divided into two categories: "benefit" and "cost", among which c2 and c7 are "cost" categories, and the rest are "benefit" categories, and all indicators are converted into "benefit" categories: For a real number a ij =r ij , the conversion formula is as follows: in, and The evaluation result r of the jth evaluation index ij The maximum and minimum values of , i = 1, 2…, m; For the interval number a ij =[m ij ,n ij ], the conversion formula is as follows: in, and is the evaluation result of the jth evaluation index [m ij ,n ij ] ij The maximum value and m ij The minimum value of , i = 1, 2…, m; For the intuitionistic fuzzy number a ij =<μ ij ,ν ij >, first convert it into an interval number a ij =[μ ij ,1-ν ij ], and then converted into interval number b according to formula (2) ij ; For the triangular fuzzy number a ij =(l ij ,m ij ,n ij ), the conversion formula is as follows: in, and is the evaluation result of the jth evaluation index (l ij ,m ij ,n ij ) ij The maximum value and l ij The minimum value of , i = 1, 2…, m; For the fuzzy term a ij ={s i }, first convert it into an intuitive fuzzy number a ij =<μ ij ,ν ij >, and then converted into interval number a ij =[μ ij ,1-ν ij ], and converted into interval number b according to formula (2) ij ; According to the above conversion rules, A={a ij } m×10 Transformed into normalized evaluation matrix B = {b ij } m×10 .
5. The method for identifying key components of complex equipment using heterogeneous multi-attribute decision making according to claim 4 is characterized in that: In the determination of the positive and negative ideal solution vectors, the positive and negative ideal solutions are respectively For real numbers For the interval number For triangular fuzzy numbers 6. The method for identifying key components of complex equipment using heterogeneous multi-attribute decision making according to claim 5 is characterized in that: The calculation of the positive and negative ideal distance matrices is specifically as follows: Calculate each element b in B ij arrive and distance, construct the positive and negative ideal separation matrix D + and D - for: in, and Respectively represent b ij arrive and distance; For real numbers a and b, d * (a,b)=|a-b| (9) For interval numbers a = [a1, a2] and b = [b1, b2], For triangular fuzzy numbers a = (a1, a2, a3) and b = (b1, b2, b3), Where λ is the adjustment coefficient.
7. The method for identifying key components of complex equipment using heterogeneous multi-attribute decision making according to claim 6 is characterized in that: The calculation of the weight of each evaluation index specifically includes the following steps: Invite M experts to score the importance of each evaluation index in order, and obtain the index ranking matrix E = {E1, E2, ..., E M } T , the scores of each expert on the parts are ranked in the same order, which is given by the matrix B in order of size, and the scoring matrix F = {f ij } m×10 , where f ij is the evaluation index C of the i-th component j The ranking results on ; Get the subjective weight of each evaluation index The objective weight of each evaluation index is determined by using the normalized evaluation matrix B and entropy weight method. Calculate the weight w of each evaluation index j , Among them, 0≤φ, and 8. The method for identifying key components of complex equipment using heterogeneous multi-attribute decision making according to claim 7 is characterized in that: The sorting method is as follows: For real numbers a and b, if a≥b, a ranks higher; if a<b, b ranks higher; For interval numbers a = [a1, a2] and b = [b1, b2], if a1 ≥ b1, a2 ≥ b2, then a is ranked first; if a1 ≥ b1, a2 < b2, then b is ranked first; For triangular fuzzy numbers a = (a1, a2, a3) and b = (b1, b2, b3), if a2>b2, a ranks first; if a2=b2, a1≥b1, a2≥b2, a ranks first; if a2=b2, a1≥b1, a2<b2, b ranks first; if a2<b2, b ranks first.
9. The method for identifying key components of complex equipment using heterogeneous multi-attribute decision making according to claim 7 is characterized in that: The steps for determining the objective weight of each evaluation index are as follows: Calculate each element b in the evaluation matrix B ij Information included I′ ij : For a real number r, Among them, r * is the design range, r≤r * , ε is the guarantee of I′(r,r * )>0; For the interval number L = [a, b], Among them, L * =[a * ,b * ] is the design range, a≤a * , b≤b * , ε is the guarantee of I′(L,L * )>0; For triangular fuzzy number N = (n1, n2, n3), in, is the design range, ε is the guarantee that I′(N,N * )>0; Calculate each evaluation index C j Information entropy e j , in, Calculate each evaluation index C j The objective weight of in, 10. The method for identifying key components of complex equipment using heterogeneous multi-attribute decision making according to claim 7 is characterized in that: The importance scores of each component are calculated, and the key components are determined according to the importance scores. Specifically, D + and D - Each element in calculates the importance score S(A i ), i=1,2,…,m, According to the importance score S(A i ) are sorted, the greater the importance, the more important the component.