Linear structure can be understood as follows: things in this structure are next to each other, just like queuing. If you want to find it, you must read it from beginning to end.
A node refers to an object, which is regarded as a point in the whole. If other objects (nodes) have a certain relationship with themselves, they are connected by lines.
Monte Carlo method, or computer random simulation method, is a calculation method based on "random number". This method originated from the "Manhattan Project" in which the United States developed the atomic bomb in the First World War. One of the project hosts, mathematician Feng? Neumann named this method after the world-famous casino-Monte Carlo in Monaco, which cast a mysterious color on it.
The basic idea of Monte Carlo method was discovered and used long ago. As early as the17th century, people knew that the "probability" of events was determined by the "frequency" of events. /kloc-in the 0 th and 9 th centuries, people used the method of throwing needles to determine pi. The appearance of electronic computers in the 1940s, especially the appearance of high-speed electronic computers in recent years, made it possible to simulate this kind of experiments in a large number and quickly by mathematical methods.
Suppose there is a square with a side length of 1 on the plane, and there is an irregular "figure" in it. How to find the area of this "figure"? Monte Carlo method is a "randomization" method: n points are randomly thrown into a square and fall into a "figure", and the area of the "figure" is about m/n.
Polls can be used as a loose metaphor. Pollsters do not consult every registered voter, but determine the possible winners through a small-scale sample survey of voters. Its basic idea is the same.
The problems in scientific and technological calculation are much more complicated than this. Such as the pricing of financial derivatives (options, futures, swaps, etc.). ) and transaction risk estimation, the dimension of the problem (that is, the number of variables) may be as high as hundreds or even thousands. For this kind of problem, with the increase of dimension, the difficulty increases exponentially, which is called "heading dimension", and it is difficult for traditional numerical methods to deal with it (even the fastest computer). Monte Carlo method can deal with the disaster of dimensionality well, because the computational complexity of this method no longer depends on dimensionality. Problems that could not be calculated in the past can be calculated now. In order to improve the efficiency of the method, scientists have proposed many so-called "variance reduction" techniques.
Another kind of method, quasi-Monte Carlo, is similar to Monte Carlo method in form, but its theoretical basis is different, and it has also developed rapidly in recent years. The "Hua Wang Fa" put forward by China mathematician Hua He is one of them. The basic idea of this method is to replace the random number sequence in Monte Carlo method with a deterministic super-uniform distribution sequence (mathematically called a low-discipline sequence). For some problems, the actual speed of this method is generally hundreds of times faster than that proposed by Monte Carlo method, and the calculation accuracy can be obtained.
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On the basis of establishing a fuzzy comprehensive evaluation model of enterprise performance with integrated management system and introducing fuzzy mathematics theory, we can start to analyze the performance indicators of the following steps of the enterprise, and finally get the evaluation grade of enterprise management system integration performance.
Step 1: According to the established comprehensive evaluation index system of enterprise performance, calculate the weights of each evaluation aspect in the first layer, such as wA, wB, wC and wD, and get the weights of each index in the second layer, such as wij(i=A, b, c, d, j= 1 2, … 10).
Step 2: According to the actual situation of enterprises implementing the integrated management system of quality, environment and occupational health and safety and the fuzzy set of evaluation indicators, invite an expert jury to evaluate each sub-indicator of the four indicators and list the evaluation table.
Step 3: First of all, for financial evaluation indicators, ri is used to indicate the evaluation level of experts on each indicator I that affects the performance evaluation level of enterprises, and wi is used to indicate the weight level of this indicator (i= 1, 2… 10). According to the parameters listed in Table 4-8 and Table 4- 10, their respective membership functions f(x) are determined. For each term f(x), the cumulative function F(x) is calculated by integral method, and the maximum value max (F(x)) of f (x) is calculated. Assuming that X obeys the beta distribution, the Monte Carlo simulation method is used to randomly generate a uniform random number for F(x) obtained from each term, with the generation range of [0, max(F(x))], and then F(x)= the generated random number, so that an X can be obtained by inverse solution, and the obtained X is a random value representing its fuzzy set. In this way, a group of random x values can be obtained, which respectively represent the weights of various factors evaluated by experts and the random simulation values of evaluation grades.
Step 4: Calculate the grade R of enterprise performance evaluation grade in terms of financial evaluation indicators according to the following formula (1), where ri and wi are the x values calculated in the previous step respectively.
R= ( 1)
R value represents the comprehensive level of enterprise performance evaluation level in the evaluation of managers and employees, and the index β is calculated by formula (2):
β = (2)
At this point, one-step iterative calculation is completed.
Step 5: Repeat step 2 and step 3 a lot, and the number of cycles or simulations required to get the ideal results can be estimated by a test program. According to the experiments carried out by experts, the simulation results of 1000 times are ideal, and Monte Carlo simulation can be run by VB program running at high speed on personal computer.
Step 6: Determine the minimum value, maximum value, average value and standard deviation of R obtained in step 3, and then normalize it according to the selected 5-point system. The four normalized parameters are represented by a, b, μ and σ respectively. Then, these parameters are substituted into the β-M membership function, as follows:
g(x)=C(x-a)a(b-x)β (3)
c = aaββ[]a+β– 1(4)
a=P2 (5)
β= (6)
p= (7)
q= (8)
Here g(x) defines the fuzzy number that represents the comprehensive evaluation of the impact indicators by experts. β-M membership function is a membership function, not a probability density function. But it has the ideal property of β probability density distribution function, that is, it is a bounded function, which can be shifted to the right, left or expressed in a symmetrical form. In the existing form of β-M function, the parameters α and β are both non-integers, which is an advantage without complicated calculation.
Step 7: Calculate the actual fuzzy number of the expert comprehensive evaluation impact index. According to the above steps, the fuzzy set that affects the index grade in all aspects is obtained, but there is no direct method to calculate the fuzzy number. Therefore, an actual figure is needed to represent the percentage that affects the performance evaluation level of enterprises. This actual number contains fuzziness, and the actual number model shown in Figure 4-3 is adopted:
1.0
g(x) AL AR
0 a b 1.0 x
β-M membership function
According to the following formula, the evaluation value la of financial evaluation in comprehensive evaluation of enterprise performance is calculated:
LA =(AL–AR+ 1)/2(9)
Here AR is a non-fuzzy real number, al is the ARea on the left of the membership function of the obtained fuzzy set, and ar is the area on the right. The numerical distribution range of r is 0~ 1.
Step 8: Calculate LB, LC and LD of manager and employee evaluation, customer evaluation and social environment evaluation indicators according to the above steps 3 to 7.
Step 9: Calculate the final enterprise performance evaluation index according to the weights (wA, wB, wC, wD) of financial evaluation, manager and employee evaluation, customer evaluation and social environment evaluation;
EPEI = wala +wBLB+wCLC+wDLD (10)
Fourthly, the computer realizes the performance evaluation model of enterprise implementing management system integration.
According to the above calculation methods and steps, the corresponding computer program can be written to automatically evaluate the comprehensive evaluation level of the management system integration performance of the evaluated enterprise. The calculation process of the comprehensive evaluation model of enterprise performance shows that the comprehensive evaluation model of enterprise performance can be designed and realized by using Visual Basic 6.0 and Matlab 5.3.
Step 1: Just input the weight grade (wi) and evaluation grade (ri) of each evaluation index in financial evaluation in VB program, and the minimum value A, maximum value B, average value μ and standard deviation σ of calculated R can be automatically obtained by using this program;
Step 2: Input the obtained A, B, μ, σ into the set EXCEL table to obtain α, β, C values;
Step 3: Input the minimum A, maximum B, α, β and C values of R in Matlab program to get the evaluation value LA of comprehensive evaluation of enterprise performance in financial evaluation, and then get LB, LC and LD respectively according to the above steps;
Step 4: Substitute the obtained LA, LB, LC and LD into the formula (10) to get the enterprise performance evaluation index EPEI.
/data/200 108/ 1 _ 200 10830 _ 13234 . html
On the basis of establishing a fuzzy comprehensive evaluation model of enterprise performance with integrated management system and introducing fuzzy mathematics theory, we can start to analyze the performance indicators of the following steps of the enterprise, and finally get the evaluation grade of enterprise management system integration performance.
Step 1: According to the established comprehensive evaluation index system of enterprise performance, calculate the weights of each evaluation aspect in the first layer, such as wA, wB, wC and wD, and get the weights of each index in the second layer, such as wij(i=A, b, c, d, j= 1 2, … 10).
Step 2: According to the actual situation of enterprises implementing the integrated management system of quality, environment and occupational health and safety and the fuzzy set of evaluation indicators, invite an expert jury to evaluate each sub-indicator of the four indicators and list the evaluation table.
Step 3: First of all, for financial evaluation indicators, ri is used to indicate the evaluation level of experts on each indicator I that affects the performance evaluation level of enterprises, and wi is used to indicate the weight level of this indicator (i= 1, 2… 10). According to the parameters listed in Table 4-8 and Table 4- 10, their respective membership functions f(x) are determined. For each term f(x), the cumulative function F(x) is calculated by integral method, and the maximum value max (F(x)) of f (x) is calculated. Assuming that X obeys the beta distribution, the Monte Carlo simulation method is used to randomly generate a uniform random number for F(x) obtained from each term, with the generation range of [0, max(F(x))], and then F(x)= the generated random number, so that an X can be obtained by inverse solution, and the obtained X is a random value representing its fuzzy set. In this way, a group of random x values can be obtained, which respectively represent the weights of various factors evaluated by experts and the random simulation values of evaluation grades.
Step 4: Calculate the grade R of enterprise performance evaluation grade in terms of financial evaluation indicators according to the following formula (1), where ri and wi are the x values calculated in the previous step respectively.
R= ( 1)
R value represents the comprehensive level of enterprise performance evaluation level in the evaluation of managers and employees, and the index β is calculated by formula (2):
β = (2)
At this point, one-step iterative calculation is completed.
Step 5: Repeat step 2 and step 3 a lot, and the number of cycles or simulations required to get the ideal results can be estimated by a test program. According to the experiments carried out by experts, the simulation results of 1000 times are ideal, and Monte Carlo simulation can be run by VB program running at high speed on personal computer.
Step 6: Determine the minimum value, maximum value, average value and standard deviation of R obtained in step 3, and then normalize it according to the selected 5-point system. The four normalized parameters are represented by a, b, μ and σ respectively. Then, these parameters are substituted into the β-M membership function, as follows:
g(x)=C(x-a)a(b-x)β (3)
c = aaββ[]a+β– 1(4)
a=P2 (5)
β= (6)
p= (7)
q= (8)
Here g(x) defines the fuzzy number that represents the comprehensive evaluation of the impact indicators by experts. β-M membership function is a membership function, not a probability density function. But it has the ideal property of β probability density distribution function, that is, it is a bounded function, which can be shifted to the right, left or expressed in a symmetrical form. In the existing form of β-M function, the parameters α and β are both non-integers, which is an advantage without complicated calculation.
Step 7: Calculate the actual fuzzy number of the expert comprehensive evaluation impact index. According to the above steps, the fuzzy set that affects the index grade in all aspects is obtained, but there is no direct method to calculate the fuzzy number. Therefore, an actual figure is needed to represent the percentage that affects the performance evaluation level of enterprises. This actual number contains fuzziness, and the actual number model shown in Figure 4-3 is adopted:
1.0
g(x) AL AR
0 a b 1.0 x
β-M membership function
According to the following formula, the evaluation value la of financial evaluation in comprehensive evaluation of enterprise performance is calculated:
LA =(AL–AR+ 1)/2(9)
Here AR is a non-fuzzy real number, al is the ARea on the left of the membership function of the obtained fuzzy set, and ar is the area on the right. The numerical distribution range of r is 0~ 1.
Step 8: Calculate LB, LC and LD of manager and employee evaluation, customer evaluation and social environment evaluation indicators according to the above steps 3 to 7.
Step 9: Calculate the final enterprise performance evaluation index according to the weights (wA, wB, wC, wD) of financial evaluation, manager and employee evaluation, customer evaluation and social environment evaluation;
EPEI = wala +wBLB+wCLC+wDLD (10)
Fourthly, the computer realizes the performance evaluation model of enterprise implementing management system integration.
According to the above calculation methods and steps, the corresponding computer program can be written to automatically evaluate the comprehensive evaluation level of the management system integration performance of the evaluated enterprise. The calculation process of the comprehensive evaluation model of enterprise performance shows that the comprehensive evaluation model of enterprise performance can be designed and realized by using Visual Basic 6.0 and Matlab 5.3.
Step 1: Just input the weight grade (wi) and evaluation grade (ri) of each evaluation index in financial evaluation in VB program, and the minimum value A, maximum value B, average value μ and standard deviation σ of calculated R can be automatically obtained by using this program;
Step 2: Input the obtained A, B, μ, σ into the set EXCEL table to obtain α, β, C values;
Step 3: Input the minimum A, maximum B, α, β and C values of R in Matlab program to get the evaluation value LA of comprehensive evaluation of enterprise performance in financial evaluation, and then get LB, LC and LD respectively according to the above steps;
Step 4: Substitute the obtained LA, LB, LC and LD into the formula (10) to get the enterprise performance evaluation index EPEI.
/data/200 108/ 1 _ 200 10830 _ 13234 . html
On the basis of establishing a fuzzy comprehensive evaluation model of enterprise performance with integrated management system and introducing fuzzy mathematics theory, we can start to analyze the performance indicators of the following steps of the enterprise, and finally get the evaluation grade of enterprise management system integration performance.
Step 1: According to the established comprehensive evaluation index system of enterprise performance, calculate the weights of each evaluation aspect in the first layer, such as wA, wB, wC and wD, and get the weights of each index in the second layer, such as wij(i=A, b, c, d, j= 1 2, … 10).
Step 2: According to the actual situation of enterprises implementing the integrated management system of quality, environment and occupational health and safety and the fuzzy set of evaluation indicators, invite an expert jury to evaluate each sub-indicator of the four indicators and list the evaluation table.
Step 3: First of all, for financial evaluation indicators, ri is used to indicate the evaluation level of experts on each indicator I that affects the performance evaluation level of enterprises, and wi is used to indicate the weight level of this indicator (i= 1, 2… 10). According to the parameters listed in Table 4-8 and Table 4- 10, their respective membership functions f(x) are determined. For each term f(x), the cumulative function F(x) is calculated by integral method, and the maximum value max (F(x)) of f (x) is calculated. Assuming that X obeys the beta distribution, the Monte Carlo simulation method is used to randomly generate a uniform random number for F(x) obtained from each term, with the generation range of [0, max(F(x))], and then F(x)= the generated random number, so that an X can be obtained by inverse solution, and the obtained X is a random value representing its fuzzy set. In this way, a group of random x values can be obtained, which respectively represent the weights of various factors evaluated by experts and the random simulation values of evaluation grades.
Step 4: Calculate the grade R of enterprise performance evaluation grade in terms of financial evaluation indicators according to the following formula (1), where ri and wi are the x values calculated in the previous step respectively.
R= ( 1)
R value represents the comprehensive level of enterprise performance evaluation level in the evaluation of managers and employees, and the index β is calculated by formula (2):
β = (2)
At this point, one-step iterative calculation is completed.
Step 5: Repeat step 2 and step 3 a lot, and the number of cycles or simulations required to get the ideal results can be estimated by a test program. According to the experiments carried out by experts, the simulation results of 1000 times are ideal, and Monte Carlo simulation can be run by VB program running at high speed on personal computer.
Step 6: Determine the minimum value, maximum value, average value and standard deviation of R obtained in step 3, and then normalize it according to the selected 5-point system. The four normalized parameters are represented by a, b, μ and σ respectively. Then, these parameters are substituted into the β-M membership function, as follows:
g(x)=C(x-a)a(b-x)β (3)
c = aaββ[]a+β– 1(4)
a=P2 (5)
β= (6)
p= (7)
q= (8)
Here g(x) defines the fuzzy number that represents the comprehensive evaluation of the impact indicators by experts. β-M membership function is a membership function, not a probability density function. However, it has the ideal property of β probability density distribution function, that is, it is a bounded function, which can be shifted to the right, left or expressed in a symmetrical form. In the existing form of β-M function, the parameters α and β are both non-integers, which is an advantage without complicated calculation.
Step 7: Calculate the actual fuzzy number of the expert comprehensive evaluation impact index. According to the above steps, the fuzzy set that affects the index grade in all aspects is obtained, but there is no direct method to calculate the fuzzy number. Therefore, an actual figure is needed to represent the percentage that affects the performance evaluation level of enterprises. This actual number contains fuzziness, and the actual number model shown in Figure 4-3 is adopted:
1.0
g(x) AL AR
0 a b 1.0 x
β-M membership function
Calculate the evaluation value la of financial evaluation in the comprehensive evaluation of enterprise performance according to the following formula:
LA =(AL–AR+ 1)/2(9)
Here AR is a non-fuzzy real number, al is the ARea on the left of the membership function of the obtained fuzzy set, and ar is the area on the right. The numerical distribution range of r is 0~ 1.
Step 8: Calculate LB, LC and LD of manager and employee evaluation, customer evaluation and social environment evaluation indicators according to the above steps 3 to 7.
Step 9: Calculate the final enterprise performance evaluation index according to the weights (wA, wB, wC, wD) of financial evaluation, manager and employee evaluation, customer evaluation and social environment evaluation;
EPEI = wala +wBLB+wCLC+wDLD (10)
Fourthly, the computer realizes the performance evaluation model of enterprise implementing management system integration.
According to the above calculation methods and steps, the corresponding computer program can be written to automatically evaluate the comprehensive evaluation level of the management system integration performance of the evaluated enterprise. The calculation process of the comprehensive evaluation model of enterprise performance shows that the comprehensive evaluation model of enterprise performance can be designed and realized by using Visual Basic 6.0 and Matlab 5.3.
Step 1: Just input the weight grade (wi) and evaluation grade (ri) of each evaluation index in financial evaluation in VB program, and the minimum value A, maximum value B, average value μ and standard deviation σ of calculated R can be automatically obtained by using this program;
Step 2: Input the obtained A, B, μ, σ into the set EXCEL table to obtain α, β, C values;
Step 3: Input the minimum A, maximum B, α, β and C values of R in Matlab program to get the evaluation value LA of comprehensive evaluation of enterprise performance in financial evaluation, and then get LB, LC and LD respectively according to the above steps;
Step 4: Substitute the obtained LA, LB, LC and LD into the formula (10) to get the enterprise performance evaluation index EPEI.
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