WO2019196437A1 - Index decision method - Google Patents

Abstract

An index decision method, comprising the following steps: establishing an index system M according to the attribute of an evaluated object; creating an expert set comprising multiple expert systems, and establishing an expert system measurement function according to the rationality measurement result of each expert system for each index in the index system M; respectively establishing a probability density function (I) of the measurement result of the expert set for each index, and establishing a probability density function (II) of an index measurement reference value function; establishing a probability density function (III) of a difference between the probability density function (I) and the probability density function (II), and a probability density function (IV) of an index selection reference value function; and for each index, respectively establishing a probability density function (V) of a difference between the probability density function (III) and the probability density function (IV), and determining the rationality of the index according to a rationality expectation value of the probability density function (V). By means of discrete sampling, the probability density distribution of the expert system for the rationality measurement result of the index is obtained, and the efficiency and accuracy of the rationality determination of the index are improved.

Description

Indicator decision method Technical field

The present invention relates to the field of control and decision making, and more particularly to an indicator decision making method.

Background technique

Measurement and evaluation are important means for humans to understand nature and explore nature. Under the unified measurement index and evaluation criteria, the object's attributes (such as length, quality) are measured, and the rationality of things or behaviors is evaluated to obtain objective and fair results. The evaluation of things or behaviors (objects to be evaluated) often requires multiple indicators to be “measured” from different dimensions. Therefore, the selection of the indicator itself is of great significance for the state assessment and scientific research, so it is necessary to “measure” the rationality of the indicator.

In the process of establishing an indicator system, there are often many indicators proposed by the designer. The indicators of "good" rationality can fully reflect the characteristics of the object being evaluated; the indicators of "poor" rationality cannot fully reflect the characteristics of the object being evaluated, that is, there is a large error. For the measurement of the rationality of an indicator, it will introduce the factors of the individual experts, or be interfered by other experts, and then there will be errors in the measurement of the rationality of the indicators. Therefore, it is necessary to rely on the experience of multiple experts to independently measure the rationality of the indicators, and finally to give a conclusion in a quantitative way, that is, whether to retain the indicator.

The design theory of the indicator system, the method of proposing the indicators, and the rationality of the indicators largely reflect the overall business level of the evaluation agencies and evaluators. Therefore, measuring the rationality of indicators is an important research content in modern evaluation methods, and also an indispensable analysis and research method in the further development of evaluation methods, which has played a positive role in promoting the development of scientific evaluation.

The traditional method of index decision making is based on expert experience, that is, using anonymous scoring. Each expert independently measures the rationality of the evaluation indicators and gives the authoritative coefficient of the experts. When all the experts have measured the rationality of the indicator, the average and standard deviations are calculated to form a statistically significant collective measurement result.

The inventors found that in the existing index decision method, no confidence interval information of the decision result is given. After each expert makes a reasonable measure of each indicator, the measurement results are calculated according to the longitudinal dimension of the indicator, the mean value, the full frequency, and the coefficient of variation, and then whether the human judgment indicators are reasonable in the three data. In this way, the independent single-index rationality evaluation work is divided into three types of data, and the information independently judged by the experts is not placed in the environment of the entire indicator system for decision-making, and the judgment efficiency is low and the expert information is lost.

In addition, when using the authoritative coefficient, the scores and authoritative coefficients of the same expert are not considered to obtain a comprehensive measurement result. The authoritative coefficient is only used to indicate whether the expert's authority on the indicator of this rationality is high (the result is significant when the average is greater than 0.7, the result is credible), and the authoritative fluctuation of the expert (the variance of all authoritative coefficients).

In addition, although each expert independently evaluates the same indicator, after multiple experts measure the same indicator, the measurement results are not excluded from the abnormal values, and this bias will be used by conventional statistical methods. Substitute into the rationality calculation. In particular, the coefficient of variation method is used to judge the volatility of the expert measurement results. When the average value is close to zero, the small disturbance will also have a huge impact on the coefficient of variation, thus causing insufficient accuracy of the indicator decision. Therefore, it is necessary to develop an efficient and robust indicator decision-making method.

Summary of the invention

The object of the present invention is to propose an index decision method to overcome the problem of low accuracy and low efficiency of the existing index decision making method.

The invention proposes an indicator decision method, which comprises the following steps:

Step 1: Establish an indicator system M according to the attributes of the object to be evaluated;

Step 2: Form a set of experts including multiple expert systems, and establish an expert system measurement function according to the rationality measurement results of each indicator in the indicator system M by each expert system;

Step 3: Establish a probability density function for the measurement results of each indicator for the expert set separately

Step 4: Establish a probability density function g _{H of the} indicator measurement reference value function;

Step 5: Establish a probability density function

Probability density function of the difference from the probability density function g _H

And a probability density function g _{C of the} indicator selection reference value function;

Step 6: Establish a probability density function for each indicator

The probability density function g _D of the difference from the probability density function g _C , and the rationality of the index is judged according to the reasonable expectation value of the probability density function g _D .

Preferably, the object to be evaluated has n attributes, and the indicators of the attributes are respectively denoted as m ₁ , m ₂ , m ₃ , . . . , m _i , . . . , m _n-1 , m _n , and the indicator system M is M{m|m ₁ , m ₂ , m ₃ , . . . , m _i , . . . , m _n-1 , m _n }.

Preferably, the expert system measurement function is E _i,j as shown in the following formula (1):

E _i,j (e _i,j ,C _a,j ,C _s,j )=λ·e _i,j ·(C _a,j +C _s,j )/2,0<λ≤1

E _i,j (e _i,j ,C _a,j ,C _s,j )=e _i,j ,λ=0 (1)

Where λ is the regulation factor, e _i,j , C _a,j , C _s,j respectively represent the scoring result, the measurement basis coefficient, and the measurement basis coefficient obtained by the expert system E _j for the rationality measurement of the index m _i in the indicator system M, Familiarity degree coefficient, where i=1,...,n,j=1,...,p,p is the number of expert systems.

Preferably, 0 ≤ C _{a , j} ≤ 1 _{, 0} ≤ C _{s, j} ≤ 1.

Preferably, p ≥ 10.

Preferably, the step 3 includes:

31 sub-steps of: for each metric m _i, the set of all the experts in the expert system for the measurement model index is defined as m _i Y _i;

Sub-step 32: For each index m _i , the p input quantities X ₁ , . . . , X _j , . . . , X _{p of the} measurement model Y _i are determined, which respectively correspond to the measurement results e ^{λ of} the expert system for the index m _{i i,1} ,...,e ^λ _i,j ,...,e ^λ _i,p , where e ^λ _i,j represents the value of the expert system measurement function E _i,j , calculated according to the following formulas (2) and (3), respectively Average of p inputs

And the degree of uncertainty Z:

among them,

The standard deviation of p measurement results e ^λ _i,1 ,...,e ^λ _i,j ,...,e ^λ _i,p ;

Sub-step 33: For each index m _i , the target is simulated with its corresponding mean value X and the square of the uncertainty degree Z, and the p input quantities X ₁ , . . . , X _j , . . . , X _p are respectively randomly generated. Assignment, calculate the mean and variance of X ₁ to X _p , and repeat the process S times to obtain the probability density function of the measurement model Y _i

Its expected value

Variance is

Where X represents a random variable.

Preferably, the step 4 includes:

Sub-step 41: For the index m _i , where i=1, . . . , n, the sample vector V _Yi =(y _i,1 ,y _i,2 ,...,y _i,S ) is established, where y _i,t (t=1, . . . , S) represents the expected value and variance of the measurement model Y _i after the tth random assignment of the p input quantities X ₁ , . . . , X _j , . . . , X _p in the sub-step 33;

Sub-step 42: Calculate the value of the index measurement reference value function H based on the sample vector V _Yi for i=1, . . . , n, respectively, as shown in the following formula (4):

H _i =h(V _Yi )=h(y _i,1 ,y _i,2 ,...,y _i,S ) (4)

Where h represents the median or average of the distribution function represented by the measurement model Y _i ; sub-step 43: the value of the reference value function H is measured according to the index, and the probability density function of the index measurement reference function H is established as g _H ; at the same time establish a discrete model G _{H of the} index measurement reference value function _H ;

Sub-step 44: Compare the expected and variance of the theoretical calculation with the expected and variance of the probability density function g _H obtained in sub-step 43, respectively.

Preferably, the step 5 includes:

Sub-step 51: a function Q _i of the difference between the measurement model Y _i and the index measurement reference value function H is established for each index m _i , respectively, where i=1, . . . , n:

Q _i =Y _i -H (5)

Sub-step 52: for each index m _i , the expected value and the variance of the distribution to which the measurement model Y _i is calculated for each random assignment based on the p input quantities X ₁ , . . . , X _j , . . . , X _p respectively , the value Q _{i,t of the} function Q _i is calculated as shown in the formula (6), where t=1,...,S:

Q _i,t =y _i,t -H _i (6)

Sub-step 53: Establish a median or average function C for all functions Q _i , where i=1,...,n, ie:

C=h(Q ₁ ,Q ₂ ,...,Q _i ,...,Q _n ) (7)

And, for each random assignment, the value of the median or mean function C is calculated based on the value Q _{i,t of the} function Q _i , ie:

C _t =h(Q _1,t ,Q _2,t ,...,Q _i,t ,...,Q _n,t ) (8)

Thus, the probability density function g _C of the median or mean function C, the median or mean function C, ie the index selection reference value function, is obtained.

Preferably, the step 6 includes:

Sub-step 61: for each index, respectively establish a relationship model D _i =Q _i -C between the function Q _i and the function C, where i=1,...,n;

Sub-step 62: For each indicator, for t = 1, ..., S, calculate the value of the relational model D _i , respectively, as shown in the following formula (8):

D _i,t =Q _i,t -C _t (9)

Based on the calculation result of formula (9), for each index, the probability density distribution function g _{Di of the} relational model D _i can be separately established, and the reasonableness expectation value E(g _Di ) of each index can be calculated by the probability density distribution function g _Di And standard deviation σ(g _Di );

Sub-step 63: For each indicator, the rationality of the indicator is judged according to the reasonable expectation value of its corresponding probability density distribution function g _Di .

Preferably, the indicator decision method further includes:

Step 7: Perform a significant test on the outcome of the indicator decision.

Preferably, the step 7 includes:

Sub-step 71: Establish a median function O of the relational model D _i , ie:

O=h(D ₁ , D ₂ ,...,D _i ,...,D _n ) (9)

Sub-step 72: For each random assignment, the value of the median function O is calculated based on the value D _{i,t of the} relational model D _i , as shown in the following formula (10):

O _t =h(D _1,t ,D _2,t ,...,D _i,t ,...,D _n,t ) (10)

Obtain the discrete model G _O of the median function O according to the value of the median function O, and record the probability density function of the median function O as g _O ;

Sub-step 73: Determine the anomaly distribution by chi-square test, including:

Build test function

As shown in formula (11):

Wherein, the degree of freedom is v=n-1;

According to the degree of freedom v and the first significance level α, from

Check the critical value in the value table

in case

It is considered that the rationality measurement is significant after the test, and the index decision result is desirable; on the contrary, the index decision result is not acceptable.

Another aspect of the present invention provides a computer readable storage medium having stored thereon a computer program, wherein the program is executed by a processor to implement the following steps:

Step 1: Establish an indicator system M according to the attributes of the object to be evaluated;

Step 2: Form a set of experts including multiple expert systems, and establish an expert system measurement function according to the rationality measurement results of each indicator in the indicator system M by each expert system;

Step 3: Establish a probability density function for the measurement results of each indicator for the expert set separately

Step 4: Establish a probability density function g _{H of the} indicator measurement reference value function;

Step 5: Establish a probability density function

Probability density function of the difference from the probability density function g _H

And a probability density function g _{C of the} indicator selection reference value function;

Step 6: Establish a probability density function for each indicator

The probability density function g _D of the difference from the probability density function g _C , and the rationality of the index is judged according to the reasonable expectation value of the probability density function g _D .

Preferably, the object to be evaluated has n attributes, and the indicators of the attributes are respectively denoted as m ₁ , m ₂ , m ₃ , . . . , m _i , . . . , m _n-1 , m _n , and the indicator system M is M{m|m ₁ , m ₂ , m ₃ , . . . , m _i , . . . , m _n-1 , m _n }.

Preferably, the expert system measurement function is E _i,j as shown in the following formula (1):

E _i,j (e _i,j ,C _a,j ,C _s,j )=λ·e _i,j ·(C _a,j +C _s,j )/2,0<λ≤1

E _i,j (e _i,j ,C _a,j ,C _s,j )=e _i,j ,λ=0 (1)

Where λ is the regulation factor, e _i,j , C _a,j , C _s,j respectively represent the scoring result, the measurement basis coefficient, and the measurement basis coefficient obtained by the expert system E _j for the rationality measurement of the index m _i in the indicator system M, Familiarity degree coefficient, where i=1,...,n,j=1,...,p,p is the number of expert systems.

Preferably, 0 ≤ C _{a , j} ≤ 1 _{, 0} ≤ C _{s, j} ≤ 1.

Preferably, p ≥ 10.

Preferably, the step 3 includes:

31 sub-steps of: for each metric m _i, the set of all the experts in the expert system for the measurement model index is defined as m _i Y _i;

Sub-step 32: For each index m _i , the p input quantities X ₁ , . . . , X _j , . . . , X _{p of the} measurement model Y _i are determined, which respectively correspond to the measurement results e ^{λ of} the expert system for the index m _{i i,1} ,...,e ^λ _i,j ,...,e ^λ _i,p , where e ^λ _i,j represents the value of the expert system measurement function E _i,j , calculated according to the following formulas (2) and (3), respectively Average of p inputs

And the degree of uncertainty Z:

among them,

The standard deviation of p measurement results e ^λ _i,1 ,...,e ^λ _i,j ,...,e ^λ _i,p ;

Sub-step 33: for each indicator m _i , with its corresponding average

And the square of the uncertainty degree Z is a numerical simulation target, and the p input quantities X ₁ ,..., X _j ,..., X _p are randomly assigned respectively, the average value and variance of X ₁ to X _p are calculated, and the process is repeated. S times, the probability density function of the measurement model Y _i is obtained.

Its expected value

Variance is

Where X represents a random variable.

Preferably, the step 4 includes:

Sub-step 41: for the index m _i , where i=1, . . . , n, respectively establish a sample vector V _Yi =(y _i,1 , y _i,2 , . . . , y _i,S ), where y _{i, t} (t=1, . . . , S) represents the expected value and variance of the measurement model Y _i after the tth random assignment of the p input quantities X ₁ , . . . , X _j , . . . , X _p in sub-step 33;

Sub-step 42: Calculate the value of the index measurement reference value function H based on the sample vector V _Yi for i=1, . . . , n, respectively, as shown in the following formula (4):

H _i =h(V _Yi )=h(y _i,1 ,y _i,2 ,...,y _i,S ) (4)

Where h represents the median or average of the distribution function represented by the measurement model Y _i ;

Sub-step 43: The probability density function of the index measurement reference value function H is established as g _{H according} to the value of the index measurement reference value function H; and the discrete model G _{H of the} index measurement reference value function H is established at the same time;

Sub-step 44: Compare the expected and variance of the theoretical calculation with the expected and variance of the probability density function g _H obtained in sub-step 43, respectively.

Preferably, the step 5 includes:

Sub-step 51: a function Q _i of the difference between the measurement model Y _i and the index measurement reference value function H is established for each index m _i , respectively, where i=1, . . . , n:

Q _i =Y _i -H (5)

Sub-step 52: for each index m _i , the expected value and the variance of the distribution to which the measurement model Y _i is calculated for each random assignment based on the p input quantities X ₁ , . . . , X _j , . . . , X _p respectively , the value Q _{i,t of the} function Q _i is calculated as shown in the formula (6), where t=1,...,S:

Q _i,t =y _i,t -H _i (6)

Sub-step 53: Establish a median or average function C for all functions Q _i , where i=1,...,n, ie:

C=h(Q ₁ ,Q ₂ ,...,Q _i ,...,Q _n ) (7)

And, for each random assignment, the value of the median or mean function C is calculated based on the value Q _{i,t of the} function Q _i , ie:

C _t =h(Q _1,t ,Q _2,t ,...,Q _i,t ,...,Q _n,t ) (8)

Thus, the probability density function g _C of the median or mean function C, the median or mean function C, ie the index selection reference value function, is obtained.

Preferably, the step 6 includes:

Sub-step 61: for each index, respectively establish a relationship model D _i =Q _i -C between the function Q _i and the function C, where i=1,...,n;

Sub-step 62: For each indicator, for t = 1, ..., S, calculate the value of the relational model D _i , respectively, as shown in the following formula (8):

D _i,t =Q _i,t -C _t (9)

Based on the calculation result of formula (9), for each index, the probability density distribution function g _{Di of the} relational model D _i can be separately established, and the reasonableness expectation value E(g _Di ) of each index can be calculated by the probability density distribution function g _Di And standard deviation σ(g _Di );

Sub-step 63: For each indicator, the rationality of the indicator is judged based on the reasonable expectation value of the probability density function g _D .

Preferably, the indicator decision method further includes:

Step 7: Perform a significant test on the outcome of the indicator decision.

Preferably, the step 7 includes:

Sub-step 71: Establish a median function O of the relational model D _i , ie:

O=h(D ₁ , D ₂ ,...,D _i ,...,D _n ) (9)

Sub-step 72: For each random assignment, the value of the median function O is calculated based on the value D _{i,t of the} relational model D _i , as shown in the following formula (10):

O _t =h(D _1,t ,D _2,t ,...,D _i,t ,...,D _n,t ) (10)

Obtain the discrete model G _O of the median function O according to the value of the median function O, and record the probability density function of the median function O as g _O ;

Sub-step 73: Determine the anomaly distribution by chi-square test, including:

Build test function

As shown in formula (11):

Wherein, the degree of freedom is v=n-1;

According to the degree of freedom v and the first significance level α, from

Check the critical value in the value table

in case

It is considered that the rationality measurement is significant after the test, and the index decision result is desirable; on the contrary, the index decision result is not acceptable.

The invention has the beneficial effects that the probability density distribution of the reasonableness measurement results of the expert system is obtained by means of discrete sampling, and the efficiency and accuracy of the rationality determination of the index are improved.

DRAWINGS

The above as well as other objects, features and advantages of the present invention will become more apparent from the detailed description.

FIG. 1 shows a flowchart of an indicator decision method according to an exemplary embodiment of the present invention;

2-1 to 2-8 respectively show schematic diagrams of probability density functions corresponding to the measurement results of the indicators m ₁ to m ₈ of the index decision method according to an exemplary embodiment of the present invention;

3 is a schematic diagram showing a probability density function of an indicator measurement reference value function of an indicator decision method according to an exemplary embodiment of the present invention;

4-1 to 4-8 respectively show schematic diagrams of probability density functions corresponding to differences between the indices m ₁ to m ₈ and the index measurement reference value function of the indicator decision method according to an exemplary embodiment of the present invention;

FIG. 5 is a diagram showing a probability density function of a median function of an index decision method according to an exemplary embodiment of the present invention.

detailed description

The invention will be described in more detail below with reference to the accompanying drawings. While the invention has been described in terms of the preferred embodiments of the present invention Rather, these embodiments are provided so that this disclosure will be thorough and complete.

The embodiment of the present invention provides an indicator decision method, and FIG. 1 shows a flowchart of an indicator decision method according to an exemplary embodiment, which includes the following steps:

Step 1: Establish an indicator system M according to the attributes of the object to be evaluated.

It is assumed that the object to be evaluated has n attributes, and the indices of these attributes are respectively denoted as m ₁ , m ₂ , m ₃ , . . . , m _i , . . . , m _n-1 , m _n , and the index system M is established according to the attributes of the object to be evaluated. That is, M{m|m ₁ , m ₂ , m ₃ , . . . , m _i , . . . , m _n-1 , m _n }.

Step 2: Form a set of experts containing multiple expert systems, and establish an expert system measurement function according to the rationality measurement results of each indicator in the indicator system M by each expert system.

Specifically, a set of experts including p expert systems is constructed, and the p expert systems are respectively recorded as E ₁ , E ₂ , E ₃ , . . . , E _j , . . . , E _p-1 , E _p . In order to ensure the accuracy and rationality of the decision, in general, p ≥ 10.

Each expert system separately measures the plausibility of each indicator in the indicator system M, gives the score results, and gives the measurement basis coefficient C _a and the familiarity degree coefficient C _s for each indicator. The value must satisfy the constraint of 0 ≤ C _a ≤ 1, 0 ≤ C _s ≤ 1. When C _a is 0, it means that there is no judgment. When C _a is 1, it means judgment based on practical experience; when C _s is 0, it means that it is completely unfamiliar with the indicator. When C _s is 1, it means that it is very familiar with the field of the indicator. .

In general, the measurement basis and familiarity of an expert system for each indicator in the indicator system M are basically the same, so for an expert system, the measurement basis coefficient and familiarity coefficient for each indicator are also the same. Specifically, for the expert system E _j (where j=1, . . . , p), it performs plausibility measurement on the index m _i (where i=1, . . . , n) in the indicator system M, and gives a score result e _i,j , and gives the measurement basis coefficient C _a,j and the familiarity degree coefficient C _s,j for the index m _i , so that the expert system measurement function E _i,j can be obtained as shown in the following formula (1):

E _i,j (e _i,j ,C _a,j ,C _s,j )=λ·e _i,j ·(C _a,j +C _s,j )/2,0<λ≤1

E _i,j (e _i,j ,C _a,j ,C _s,j )=e _i,j ,λ=0 (1)

Where λ is the control factor used to control whether expert measurement coefficients are added to the measurement function. The value of the expert system measurement function E _i,j is denoted as e ^λ _i,j , which represents the measurement of the indicator m _i by the expert system E _j .

In this step, the rationality measurement is performed on each index in the indicator system M through the actual expert system, and the expert system measurement function is established, and the expert system measurement function is used as the simulation reference for the subsequent steps.

In a preferred case, the expert system measures any two function values e ^λ _i,l and e ^λ _{i,k of the} function E _i,j (where 1≤l≤p, 1≤k≤p, and l≠k) The covariance and correlation coefficient between the two are zero, that is, there is no information exchange between each expert system, and there is no influence between them.

Step 3: Establish a probability density function for the measurement results of each indicator for the expert set separately

Specifically, step 3 includes:

Sub-step 31: For each indicator m _i , where i=1, . . . , n, the measurement model for the indicator m _i is defined by all expert systems in the expert set as Y _i . Preferably, the output of the measurement model Y _i follows a normal distribution.

Sub-step 32: For each index m _i , the p input quantities X ₁ , . . . , X _j , . . . , X _{p of the} measurement model Y _i are determined, which respectively correspond to the measurement results e ^λ of the indicator m _i of each expert system. _i,1 ,...,e ^λ _i,j ,...,e ^λ _i,p , calculate the average of p inputs according to the following formulas (2) and (3), respectively

And the degree of uncertainty Z:

among them,

Is the standard deviation of p measurements e ^λ _i,1 ,...,e ^λ _i,j ,...,e ^λ _i,p .

Sub-step 33: for each indicator m _i , with its corresponding average

And the square of the uncertainty degree Z is a numerical simulation target, and the p input quantities X ₁ ,..., X _j ,..., X _p are randomly assigned respectively, the average value and variance of X ₁ to X _p are calculated, and the process is repeated. S times.

When the value of S is sufficiently large, the average value of the simulation is

The difference between them will be small enough to simulate the variance and the square of the uncertainty

The difference between them will also be small enough that the obtained measurement model Y _i can accurately simulate the actual expert system.

After S random assignments, the probability density function of the measurement model Y _i is obtained.

Its expected value

Variance is

Where X represents a random variable.

Preferably, the number of random assignments S should be more than 100000 times, so that the expected value of the simulated measurement model Y _i is as close as possible

The variance of the simulated measurement model Y _i is as close as possible to the square of the uncertainty

Probability density function

Expected value

Representing all expert systems for the plausibility measurement of the indicator m _i , standard deviation

Represents the uncertainty of the comprehensive measurement results of the indicator rationality.

Through the above steps, the probability density function of the measurement result of the expert system for each index is established for each index m ₁ ,...,m _i ,...,m _n in the index system M, respectively.

...,

..., g _Yn , and then the measurement results of the expert system are all presented as a probability density function. The expert system evaluates the rationality of the index m _i , then the probability density function

Expected value

Large, standard deviation

It reflects the degree of uncertainty in the evaluation results. Expected value is

The confidence probability in the interval range is 95.45%.

Step 4: Establish a probability density function g _{H of the} indicator measurement reference value function.

Specifically, step 4 includes the following sub-steps:

Sub-step 41: For the index m _i (i=1, . . . , n), according to the result of step 33, respectively establish a sample vector V _Yi =(y _i,1 , y _i,2 ,...,y _i,S ), where y _i,t (t=1, . . . , S) represents the measurement model Y after the tth random assignment of the p input quantities X ₁ , . . . , X _j , . . . , X _p in sub-step 33 The expected value and variance of _i . After the sample vector V _{Yi has} been subjected to S random assignments, the measurement model Y _{i of} each index m _i obeys the distribution expected in sub-step 33. Preferably, Y _i is the mean

Variance is

Normal distribution model.

Sub-step 42: Calculate the value of the index measurement reference value function H based on the sample vector V _Yi for i=1, . . . , n, respectively, as shown in the following formula (4):

H _i =h(V _Yi )=h(y _i,1 ,y _i,2 ,...,y _i,S ) (4)

Where h represents the median or average of the probability density function represented by the measurement model Y _i ; preferably, h represents the median, and at this time, the obtained result H is also a probability density function, which represents all The distribution of the median (or average) of the measurement model of the indicator.

Sub-step 43: The discrete model G _{H of the} index measurement reference value function H is established according to the value of the index measurement reference value function _H , and the probability density function of the index measurement reference value function is g _H .

Based on the value of the reference value function H measured in the sub-step 42 measurement, the discrete model G _H of the index measurement reference value function H can be established, and the probability density function of the index measurement reference value function is denoted as g _H .

The expected value of the probability density function g _H represents the measured reference value (median or mean) of all indicator measurements, and the variance represents the degree of uncertainty of the measurement represented by the measured reference. Next, it is necessary to determine the difference between each indicator and the measurement reference value, and the degree of uncertainty of the difference.

Sub-step 44: The theoretically calculated expected value and variance are compared with the expected values and variances of the probability density function g _H obtained in sub-step 43, respectively, to monitor their simulations.

The theoretical calculation method is: the expected value of the probability density function corresponds to all indicators.

Median; the variance of the probability density function is

[Median of Z for all indicators] ² , where σ(g _Y ) is the median of the standard deviation of all measurement models y _i,t . When the number of simulations is sufficiently large, the theoretical calculation results will be very close to those obtained by the simulation.

Step 5: Establish a probability density function

Probability density function of the difference from the probability density function g _H

And a probability density function g _C of the reference value function of all the differences (the reference value is named as the index selection reference value function).

Specifically, step 5 includes the following sub-steps:

Sub-step 51: a function Q _i of the difference between the measurement model Y _i and the index measurement reference value function H is established for each index m _i , respectively, where i=1, . . . , n:

Q _i =Y _i -H (5)

Sub-step 52: for each index m _i , the expected value and the variance of the distribution to which the measurement model Y _i is calculated for each random assignment based on the p input quantities X ₁ , . . . , X _j , . . . , X _p respectively , the value Q _{i,t of the} function Q _i is calculated as shown in the formula (6), where t=1,...,S:

Q _i,t =y _i,t -H _i (6)

Based on the calculation result of the formula (6), for each index, a discrete model G _{Qi of a} function of the difference between the integrated measured value and the index measurement reference value function can be separately established, and the probability density function is denoted as g _Qi .

Sub-step 53: Establish a median or average function C for all functions Q _i (where i=1, . . . , n), ie:

C=h(Q ₁ ,Q ₂ ,...,Q _i ,...,Q _n ) (7)

For each random assignment, the value of the median or mean function C is calculated based on the value Q _{i,t of the} function Q _i , ie:

C _t =h(Q _1,t ,Q _2,t ,...,Q _i,t ,...,Q _n,t ) (8)

Thereby, the probability density function g _C of the median or mean function C can be obtained, and the median or average function C is the index selection reference value function.

The expected value diff _ref-m of the probability density function g _C is the median of all E(g _Q1 ), ..., E(g _Qi ), ..., E(g _Qn ). The expected value reflects the degree of deviation between the measured value of the indicator by the expert system and the reference value of the indicator measurement. The variance of the probability density function g _C reflects the range of fluctuations in the degree of deviation. Through step 5, the difference between the measurement and the reference value of each indicator and the degree of uncertainty of the difference can be obtained, and then the index selection reference value with better robustness can be obtained.

Step 6: Establish a probability density function for each indicator

The probability density function g _D of the difference from the probability density function g _C , and the rationality of the index is judged according to the reasonable expectation value of the probability density function g _D .

Specifically, step 6 includes the following sub-steps:

Sub-step 61: For each indicator, a relationship model D _i =Q _i -C between the function Q _{i ,} and the function C is respectively established, where i=1, . . . , n.

Sub-step 62: For each indicator, for t = 1, ..., S, calculate the value of the relational model D _i , respectively, as shown in the following formula (8):

D _i,t =Q _i,t -C _t (9)

Based on the calculation result of formula (9), for each index, the probability density function g _{Di of the} relational model D _i can be separately established, and the probability expectation value E(g _Di ) and the standard of each index can be calculated by the probability density function g _Di The deviation σ(g _Di ).

Sub-step 63: For each indicator, the rationality of the indicator is judged according to its corresponding probability density function g _Di rationality expectation value.

For the index m _i , if the reasonable expectation value E(g _Di )>0 of the corresponding probability density function g _Di is 0, it means that the index meets the rationality requirement by the expert system measurement, and the rationality expansion uncertainty is 2σ(g _Di ) The confidence probability is 95.45%; if the corresponding probability density function g _{Di has} a reasonable expectation value E(g _Di ) ≤ 0, it means that the indicator does not satisfy the rationality requirement through the expert system measurement, and the irrationality expansion uncertainty is 2σ. (g _Di ), the confidence probability is 95.45%. Indicators that do not meet the reasonableness requirements cannot be used to evaluate the object being evaluated.

Step 7: Perform a significant test on the outcome of the indicator decision.

Specifically, step 7 includes the following sub-steps:

Sub-step 71: Establish a median function O of the relational model D _i , ie:

O=h(D ₁ , D ₂ ,...,D _i ,...,D _n ) (9)

Where h is the median.

Sub-step 72: For each random assignment, the value of the median function O is calculated based on the value D _{i,t of the} relational model D _i , as shown in the following formula (10):

O _t =h(D _1,t ,D _2,t ,...,D _i,t ,...,D _n,t ) (10)

Where t=1,...,S;

According to the value of the median function O, the discrete model G _O of the median function O can be obtained, and the probability density function of the median function O is denoted as g _O .

Sub-step 73: The anomaly distribution is determined by a chi-square test. Specifically, first build a test function

Wherein, the degrees of freedom v=n-1; E(g _Di ) and σ(g _Di ) are the reasonable expectation values and standard deviations of the index m _i respectively; E(g _O ) is the median function O of the index m _i Expected value.

Then, according to the degree of freedom v and the first significance level α (for example, 95%),

Check the critical value in the value table

in case

It is considered that the rationality measurement is significant after the test, and the index decision result is desirable; on the contrary, under the confidence level of the first significant level, the decision result is considered to be poorly credible, and the decision result is not desirable, that is, the decision process of the indicator needs Redesign indicators and replace experts for new plausibility measurements.

Example

In an exemplary embodiment, the indicator decision method is used to perform the indicator decision, which specifically includes the following steps:

Step 1: Establish an indicator system M according to the attributes of the object to be evaluated.

The object to be evaluated has eight attributes, and the indices of these attributes are respectively denoted as m ₁ , m ₂ , m ₃ , . . . , m _i , . . . , m ₇ , m ₈ , and the index system M can be denoted as M{m|m ₁ . m ₂ , m ₃ , ..., m _i , ..., m ₇ , m ₈ }.

Step 2: Set up an expert set containing 10 expert systems, and establish an expert system measurement function based on the results of each expert system's plausibility measurement for each indicator in the indicator system M.

In the present embodiment, the measurement basis coefficient C _a and the familiarity degree coefficient C _s are both 1, and the regulation factor λ=0. The results of each expert system's plausibility measurement for each indicator are shown in Table 1 below:

Table 1 Expert system measures the rationality of indicators

Step 3: Establish a probability density function for the measurement results of each indicator for the expert set separately

First, for each indicator, calculate the average of p inputs according to equations (2) and (3).

And the degree of uncertainty Z, as shown in Table 2 below:

Table 2 average

And uncertainty Z

Then, 10,000 random assignments are made for each indicator, so that the probability density function of each measurement model can be obtained, which obeys a normal distribution. Through multiple random assignments, the average value of the simulation is

Approach, square of variance and uncertainty

The difference between them is small enough. Table 3 shows the mean and variance obtained for each indicator simulation, and Figures 2-1 to 2-8 show the probability density function diagrams of the measurement models corresponding to the indicators m ₁ to m ₈ , respectively.

Table 3 average and variance results

Through step 3, the measurement results of the expert set for each indicator are expressed as a probability density function.

Step 4: Establish a probability density function g _{H of the} indicator measurement reference value function.

Specifically, the probability density function of the measurement model of each indicator has been obtained in step 3. In this step, the median of the probability density function can be directly obtained by using formula (4), and the function of the index measurement reference value can be obtained. The probability density function g _H is shown in Figure 3. Expected value of the probability density function

Is 8.2047, the median of the expected values of all measurement models Y _i ; the standard deviation of the probability density function is 0.3491.

Finally, the theoretical calculation results are compared with the simulated results to monitor the simulation. Specifically, calculate corresponding to all indicators

The median is 8.10, and the median of Z for all indicators is 0.70.

(the median of all Z) ²

When the number of simulations is infinite, the theoretical calculations will be closer to those obtained by simulation.

Step 5: Establish a probability density function

Probability density function of the difference from the probability density function g _H

And the probability density function g _{C of the} indicator selection reference value function.

Specifically, the function Q _{i is} established according to the sub-step 51 and the sub-step 52, and the average value and the variance of the probability density function are obtained as shown in Table 4. FIGS. 4-1 to 4-8 respectively show the corresponding to the index m ₁ to Schematic diagram of the probability density function of the difference between m ₈ and the indicator measurement reference function:

Table 4 Mean and variance of the probability density function of the function Q _i

Then, according to sub-step 53, a median function C of all functions Q _i is established, the probability density function g _{C of which} is shown in FIG.

Step 6: Establish a probability density function for each indicator

The probability density function g _D of the difference from the probability density function g _C , and the rationality of the index is judged according to the reasonable expectation value of the probability density function g _D .

Specifically, sub-step 61 and sub-step 62 are performed to obtain the value of the relational model D _i and the reasonable expectation value.

And the variance σ ² (g _Di ), as shown in Table 5, and then judging the rationality of each index according to sub-step 63. In the present embodiment, the m ₁ , m ₂ , m ₄ reasonable expectation value is greater than zero, and the index is qualified. ; m ₃ , m ₅ , m ₆ , m ₇ , m ₈ reasonable expectation value is less than zero, the index is unqualified.

Table 5 Average and variance of the relational model D _i

Step 7: Perform a significant test on the outcome of the indicator decision. Specifically, the median function O of the relational model D _i is numerically simulated to obtain an expected value E(g _O ) of the O-obeyed distribution. The calculation table for the chi-square test is shown in Table 6 below:

Table 6 Chi-square test calculation form

Wherein, the degree of freedom v=n-1=7, when the 95% confidence level is found in the critical value table, the critical value is 14.0671, and the test function value

Is 11.4471, according to

Judging that the reasonableness measurement results are significant, the index decision results are desirable.

The embodiment of the invention further provides a computer readable storage medium, on which a computer program is stored, wherein when the program is executed by the processor, the following steps are implemented:

Step 1: Establish an indicator system M according to the attributes of the object to be evaluated;

Step 2: Form a set of experts including multiple expert systems, and establish an expert system measurement function according to the rationality measurement results of each indicator in the indicator system M by each expert system;

Step 3: Establish a probability density function for the measurement results of each indicator for the expert set separately

Step 4: Establish a probability density function g _{H of the} indicator measurement reference value function;

Step 5: Establish a probability density function

Probability density function of the difference from the probability density function g _H

And a probability density function g _{C of the} indicator selection reference value function;

Step 6: Establish a probability density function for each indicator

The probability density function g _D of the difference from the probability density function g _C , and the rationality of the index is judged according to the reasonable expectation value of the probability density function g _D .

Preferably, the object to be evaluated has n attributes, and the indexes of the attributes are respectively denoted as m ₁ , m ₂ , m ₃ , . . . , m _i , . . . , m _n-1 , m _n , and M is M{m| m ₁ , m ₂ , m ₃ , ..., m _i , ..., m _n-1 , m _n }.

Preferably, the expert system measurement function is E _i,j as shown in the following formula (1):

E _i,j (e _i,j ,C _a,j ,C _s,j )=λ·e _i,j ·(C _a,j +C _s,j )/2,0<λ≤1

E _i,j (e _i,j ,C _a,j ,C _s,j )=e _i,j ,λ=0 (1)

Where λ is the regulation factor, e _i,j , C _a,j , C _s,j respectively represent the scoring result, the measurement basis coefficient, and the measurement basis coefficient obtained by the expert system E _j for the rationality measurement of the index m _i in the indicator system M, Familiarity degree coefficient, where i=1,...,n,j=1,...,p,p is the number of expert systems.

Preferably, the step 3 includes:

31 sub-steps of: for each metric m _i, the set of all the experts in the expert system for the measurement model index is defined as m _i Y _i;

Sub-step 32: For each index m _i , the p input quantities X ₁ , . . . , X _j , . . . , X _{p of the} measurement model Y _i are determined, which respectively correspond to the measurement results e ^{λ of} the expert system for the index m _{i i,1} ,...,e ^λ _i,j ,...,e ^λ _i,p , where e ^λ _i,j represents the value of the expert system measurement function E _i,j , calculated according to the following formulas (2) and (3), respectively Average of p inputs

And the degree of uncertainty Z:

among them,

The standard deviation of p measurement results e ^λ _i,1 ,...,e ^λ _i,j ,...,e ^λ _i,p ;

Sub-step 33: for each indicator m _i , with its corresponding average

And the square of the uncertainty degree Z is a numerical simulation target, and the p input quantities X ₁ ,..., X _j ,..., X _p are randomly assigned respectively, the average value and variance of X ₁ to X _p are calculated, and the process is repeated. S times, the probability density function of the measurement model Y _i is obtained.

Its expected value

Variance is

Where X represents a random variable.

Preferably, the step 4 includes:

Sub-step 41: For the index m _i , where i=1, . . . , n, the sample vector V _Yi =(y _i,1 ,y _i,2 ,...,y _i,S ) is established, where y _i,t (t=1, . . . , S) represents the expected value and variance of the measurement model Y _i after the tth random assignment of the p input quantities X ₁ , . . . , X _j , . . . , X _p in the sub-step 33;

Sub-step 42: Calculate the value of the index measurement reference value function H based on the sample vector V _Yi for i=1, . . . , n, respectively, as shown in the following formula (4):

H _i =h(V _Yi )=h(y _i,1 ,y _i,2 ,...,y _i,S ) (4)

Where h represents the median or average of the distribution function represented by the measurement model Y _i ; sub-step 43: the value of the reference value function H is measured according to the index, and the probability density function of the index measurement reference function H is established as g _H ; at the same time establish a discrete model G _{H of the} index measurement reference value function _H ;

Sub-step 44: Compare the expected and variance of the theoretical calculation with the expected and variance of the probability density function g _H obtained in sub-step 43, respectively.

Preferably, the step 5 includes:

Sub-step 51: a function Q _i of the difference between the measurement model Y _i and the index measurement reference value function H is established for each index m _i , respectively, where i=1, . . . , n:

Q _i =Y _i -H (5)

Sub-step 52: for each index m _i , the expected value and the variance of the distribution to which the measurement model Y _i is calculated for each random assignment based on the p input quantities X ₁ , . . . , X _j , . . . , X _p respectively , the value Q _{i,t of the} function Q _i is calculated as shown in the formula (6), where t=1,...,S:

Q _i,t =y _i,t -H _i (6)

Sub-step 53: Establish a median or average function C for all functions Q _i , where i=1,...,n, ie:

C=h(Q ₁ ,Q ₂ ,...,Q _i ,...,Q _n ) (7)

And, for each random assignment, the value of the median or mean function C is calculated based on the value Q _{i,t of the} function Q _i , ie:

C _t =h(Q _1,t ,Q _2,t ,...,Q _i,t ,...,Q _n,t ) (8)

Thus, the probability density function g _C of the median or mean function C, the median or mean function C, ie the index selection reference value function, is obtained.

Preferably, the step 6 includes:

Sub-step 61: for each index, respectively establish a relationship model D _i =Q _i -C between the function Q _i, and the function C, where i=1,...,n;

Sub-step 62: For each indicator, for t = 1, ..., S, calculate the value of the relational model D _i , respectively, as shown in the following formula (8):

D _i,t =Q _i,t -C _t (9)

Based on the calculation result of formula (9), for each index, the probability density distribution function g _{Di of the} relational model D _i can be separately established, and the reasonableness expectation value E(g _Di ) of each index can be calculated by the probability density distribution function g _Di And standard deviation σ(g _Di );

Sub-step 63: For each indicator, the rationality of the indicator is judged based on the reasonable expectation value of the probability density function g _D .

Preferably, the indicator decision method further includes:

Step 7: Perform a significant test on the outcome of the indicator decision.

Preferably, the step 7 includes:

Sub-step 71: Establish a median function O of the relational model D _i , ie:

O=h(D ₁ , D ₂ ,...,D _i ,...,D _n ) (9)

Sub-step 72: For each random assignment, the value of the median function O is calculated based on the value D _{i,t of the} relational model D _i , as shown in the following formula (10):

O _t =h(D _1,t ,D _2,t ,...,D _i,t ,...,D _n,t ) (10)

Obtain the discrete model G _O of the median function O according to the value of the median function O, and record the probability density function of the median function O as g _O ;

Sub-step 73: Determine the anomaly distribution by chi-square test, including:

Build test function

As shown in formula (11):

Wherein, the degree of freedom is v=n-1;

According to the degree of freedom v and the first significance level α, from

Check the critical value in the value table

in case

It is considered that the rationality measurement is significant after the test, and the index decision result is desirable; on the contrary, the index decision result is not acceptable.

The embodiments of the present invention have been described above, and the foregoing description is illustrative, not limiting, and not limited to the disclosed embodiments. Numerous modifications and changes will be apparent to those skilled in the art without departing from the scope of the invention.

Claims (18)

1. An indicator decision method is characterized in that it comprises the following steps:

   Step 1: Establish an indicator system M according to the attributes of the object to be evaluated;

   Step 2: Form a set of experts including multiple expert systems, and establish an expert system measurement function according to the rationality measurement results of each indicator in the indicator system M by each expert system;

   Step 3: Establish a probability density function for the measurement results of each indicator for the expert set separately

   

   Step 4: Establish a probability density function g _{H of the} indicator measurement reference value function;

   Step 5: Establish a probability density function

   

   Probability density function of the difference from the probability density function g _H

   

   And a probability density function g _{C of the} indicator selection reference value function;

   Step 6: Establish a probability density function for each indicator

   

   The probability density function g _D of the difference from the probability density function g _C , and the rationality of the index is judged according to the reasonable expectation value of the probability density function g _D .
2. The index decision method according to claim 1, wherein the object to be evaluated has n attributes, and the indexes of the attributes are respectively denoted as m ₁ , m ₂ , m ₃ , ..., m _i , ..., m _{n -1} , m _n , the index system M is M{m|m ₁ , m ₂ , m ₃ , . . . , m _i , . . . , m _n-1 , m _n }.
3. The index decision method according to claim 2, wherein the expert system measurement function is E _i,j as shown in the following formula (1):

   E _i,j (e _i,j ,C _a,j ,C _s,j )=λ·e _i,j ·(C _a,j +C _s,j )/2,0<λ≤1

   E _i,j (e _i,j ,C _a,j ,C _s,j )=e _i,j ,λ=0 (1)

   Where λ is the regulation factor, e _i,j , C _a,j , C _s,j respectively represent the scoring result, the measurement basis coefficient, and the measurement basis coefficient obtained by the expert system E _j for the rationality measurement of the index m _i in the indicator system M, Familiarity degree coefficient, where i=1,...,n,j=1,...,p,p is the number of expert systems.
4. The method for determining an indicator according to claim 3, wherein the step 3 comprises:

   31 sub-steps of: for each metric m _i, the set of all the experts in the expert system for the measurement model index is defined as m _i Y _i;

   Sub-step 32: For each index m _i , p input quantities X ₁ , . . . , X _j , . . . , X _{p of the} measurement model Y _i are determined, which respectively correspond to the measurement results e ^λ _{i of} the expert system for the index mi _,1 ,...,e ^λ _i,j ,...,e ^λ _i,p , where e ^λ _i,j represents the value of the expert system measurement function E _i,j , which is calculated according to the following formulas (2) and (3), respectively Average of inputs

   

   And the degree of uncertainty Z:

   

   

   among them,

   

   The standard deviation of p measurement results e ^λ _i,1 ,...,e ^λ _i,j ,...,e ^λ _i,p ;

   Sub-step 33: for each indicator m _i , with its corresponding average

   

   And the square of the uncertainty degree Z is a numerical simulation target, and the p input quantities X ₁ ,..., X _j ,..., X _p are randomly assigned respectively, the average value and variance of X ₁ to X _p are calculated, and the process is repeated. S times, the probability density function of the measurement model Y _i is obtained.

   

   Its expected value

   

   Variance is

   

   Where X represents a random variable.
5. The method for determining an indicator according to claim 4, wherein the step 4 comprises:

   Sub-step 41: For the index m _i , where i=1, . . . , n, the sample vector V _Yi =(y _i,1 ,y _i,2 ,...,y _i,S ) is established, where y _i,t (t=1, . . . , S) represents the expected value and variance of the measurement model Y _i after the tth random assignment of the p input quantities X ₁ , . . . , X _j , . . . , X _p in the sub-step 33;

   Sub-step 42: Calculate the value of the index measurement reference value function H based on the sample vector V _Yi for i=1, . . . , n, respectively, as shown in the following formula (4):

   H _i =h(V _Yi )=h(y _i,1 ,y _i,2 ,...,y _i,S ) (4)

   Where h represents the median or average of the distribution function represented by the measurement model Y _i ; sub-step 43: the value of the reference value function H is measured according to the index, and the probability density function of the index measurement reference function H is established as g _H ; at the same time establish a discrete model G _{H of the} index measurement reference value function _H ;

   Sub-step 44: Compare the expected and variance of the theoretical calculation with the expected and variance of the probability density function g _H obtained in sub-step 43, respectively.
6. The method for determining an indicator according to claim 5, wherein the step 5 comprises:

   Sub-step 51: a function Q _i of the difference between the measurement model Y _i and the index measurement reference value function H is established for each index m _i , respectively, where i=1, . . . , n:

   Q _i =Y _i -H (5)

   Sub-step 52: for each index m _i , the expected value and the variance of the distribution to which the measurement model Y _i is calculated for each random assignment based on the p input quantities X ₁ , . . . , X _j , . . . , X _p respectively , the value Q _{i,t of the} function Q _i is calculated as shown in the formula (6), where t=1,...,S:

   Q _i,t =y _i,t -H _i (6)

   Sub-step 53: Establish a median or average function C for all functions Q _i , where i=1,...,n, ie:

   C=h(Q ₁ ,Q ₂ ,...,Q _i ,...,Q _n ) (7)

   And, for each random assignment, the value of the median or mean function C is calculated based on the value Q _{i,t of the} function Q _i , ie:

   C _t =h(Q _1,t ,Q _2,t ,...,Q _i,t ,...,Q _n,t ) (8)

   Thus, the probability density function g _C of the median or mean function C, the median or mean function C, ie the index selection reference value function, is obtained.
7. The method for determining an indicator according to claim 6, wherein the step 6 comprises:

   Sub-step 61: for each index, respectively establish a relationship model D _i =Q _i -C between the function Q _i, and the function C, where i=1,...,n;

   Sub-step 62: For each indicator, for t = 1, ..., S, calculate the value of the relational model D _i , respectively, as shown in the following formula (8):

   D _i,t =Q _i,t -C _t (9)

   Based on the calculation result of formula (9), for each index, the probability density distribution function g _{Di of the} relational model D _i can be separately established, and the reasonableness expectation value E(g _Di ) of each index can be calculated by the probability density distribution function g _Di And standard deviation σ(g _Di );

   Sub-step 63: For each indicator, the rationality of the indicator is judged according to the reasonable expectation value of its corresponding probability density distribution function g _Di .
8. The method for determining an indicator according to claim 7, further comprising:

   Step 7: Perform a significant test on the outcome of the indicator decision.
9. The method for determining an indicator according to claim 8, wherein the step 7 comprises:

   Sub-step 71: Establish a median function O of the relational model D _i , ie:

   O=h(D ₁ , D ₂ ,...,D _i ,...,D _n ) (9)

   Sub-step 72: For each random assignment, the value of the median function O is calculated based on the value D _{i,t of the} relational model D _i , as shown in the following formula (10):

   O _t =h(D _1,t ,D _2,t ,...,D _i,t ,...,D _n,t ) (10)

   Obtain the discrete model G _O of the median function O according to the value of the median function O, and record the probability density function of the median function O as g _O ;

   Sub-step 73: Determine the anomaly distribution by chi-square test, including:

   Build test function

   

   As shown in formula (11):

   

   Wherein, the degree of freedom is v=n-1;

   According to the degree of freedom v and the first significance level α, from

   

   Check the critical value in the value table

   

   in case

   

   It is considered that the rationality measurement is significant after the test, and the index decision result is desirable; on the contrary, the index decision result is not acceptable.
10. A computer readable storage medium having stored thereon a computer program, wherein the program is executed by a processor to implement the following steps:

    Step 1: Establish an indicator system M according to the attributes of the object to be evaluated;

    Step 2: Form a set of experts including multiple expert systems, and establish an expert system measurement function according to the rationality measurement results of each indicator in the indicator system M by each expert system;

    Step 3: Establish a probability density function for the measurement results of each indicator for the expert set separately

    

    Step 4: Establish a probability density function g _{H of the} indicator measurement reference value function;

    Step 5: Establish a probability density function

    

    Probability density function of the difference from the probability density function g _H

    

    And a probability density function g _{C of the} indicator selection reference value function;

    Step 6: Establish a probability density function for each indicator

    

    The probability density function g _D of the difference from the probability density function g _C , and the rationality of the index is judged according to the reasonable expectation value of the probability density function g _D .
11. The computer readable storage medium according to claim 10, wherein said evaluated object has n attributes, and indices of said attributes are respectively denoted as m ₁ , m ₂ , m ₃ , ..., m _i , ..., m _n-1 , m _n , the index system M is M{m|m ₁ , m ₂ , m ₃ , . . . , m _i , . . . , m _n-1 , m _n }.
12. The computer readable storage medium according to claim 11, wherein said expert system measurement function is E _i,j as shown in the following formula (1):

    E _i,j (e _i,j ,C _a,j ,C _s,j )=λ·e _i,j ·(C _a,j +C _s,j )/2,0<λ≤1

    E _i,j (e _i,j ,C _a,j ,C _s,j )=e _i,j ,λ=0 (1)

    Where λ is the regulation factor, e _i,j , C _a,j , C _s,j respectively represent the scoring result, the measurement basis coefficient, and the measurement basis coefficient obtained by the expert system E _j for the rationality measurement of the index m _i in the indicator system M, Familiarity degree coefficient, where i=1,...,n,j=1,...,p,p is the number of expert systems.
13. The computer readable storage medium of claim 12, wherein the step 3 comprises:

    31 sub-steps of: for each metric m _i, the set of all the experts in the expert system for the measurement model index is defined as m _i Y _i;

    Sub-step 32: For each index m _i , the p input quantities X ₁ , . . . , X _j , . . . , X _{p of the} measurement model Y _i are determined, which respectively correspond to the measurement results e ^{λ of} the expert system for the index m _{i i,1} ,...,e ^λ _i,j ,...,e ^λ _i,p , where e ^λ _i,j represents the value of the expert system measurement function E _i,j , calculated according to the following formulas (2) and (3), respectively Average of p inputs

    

    And the degree of uncertainty Z:

    

    

    among them,

    

    The standard deviation of p measurement results e ^λ _i,1 ,...,e ^λ _i,j ,...,e ^λ _i,p ;

    Sub-step 33: for each indicator m _i , with its corresponding average

    

    And the square of the uncertainty degree Z is a numerical simulation target, and the p input quantities X ₁ ,..., X _j ,..., X _p are randomly assigned respectively, the average value and variance of X ₁ to X _p are calculated, and the process is repeated. S times, the probability density function of the measurement model Y _i is obtained.

    

    Its expected value

    

    Variance is

    

    Where X represents a random variable.
14. The computer readable storage medium of claim 13, wherein the step 4 comprises:

    Sub-step 41: For the index m _i , where i=1, . . . , n, the sample vector V _Yi =(y _i,1 ,y _i,2 ,...,y _i,S ) is established, where y _i,t (t=1, . . . , S) represents the expected value and variance of the measurement model Y _i after the tth random assignment of the p input quantities X ₁ , . . . , X _j , . . . , X _p in the sub-step 33;

    Sub-step 42: Calculate the value of the index measurement reference value function H based on the sample vector V _Yi for i=1, . . . , n, respectively, as shown in the following formula (4):

    H _i =h(V _Yi )=h(y _i,1 ,y _i,2 ,...,y _i,S ) (4)

    Where h represents the median or average of the distribution function represented by the measurement model Y _i ; sub-step 43: the value of the reference value function H is measured according to the index, and the probability density function of the index measurement reference function H is established as g _H ; at the same time establish a discrete model G _{H of the} index measurement reference value function _H ;

    Sub-step 44: Compare the expected and variance of the theoretical calculation with the expected and variance of the probability density function g _H obtained in sub-step 43, respectively.
15. The computer readable storage medium of claim 14, wherein the step 5 comprises:

    Sub-step 51: a function Q _i of the difference between the measurement model Y _i and the index measurement reference value function H is established for each index m _i , respectively, where i=1, . . . , n:

    Q _i =Y _i -H (5)

    Sub-step 52: for each index m _i , the expected value and the variance of the distribution to which the measurement model Y _i is calculated for each random assignment based on the p input quantities X ₁ , . . . , X _j , . . . , X _p respectively , the value Q _{i,t of the} function Q _i is calculated as shown in the formula (6), where t=1,...,S:

    Q _i,t =y _i,t -H _i (6)

    Sub-step 53: Establish a median or average function C for all functions Q _i , where i=1,...,n, ie:

    C=h(Q ₁ ,Q ₂ ,...,Q _i ,...,Q _n ) (7)

    And, for each random assignment, the value of the median or mean function C is calculated based on the value Q _{i,t of the} function Q _i , ie:

    C _t =h(Q _1,t ,Q _2,t ,...,Q _i,t ,...,Q _n,t ) (8)

    Thus, the probability density function g _C of the median or mean function C, the median or mean function C, ie the index selection reference value function, is obtained.
16. The computer readable storage medium of claim 15 wherein said step 6 comprises:

    Sub-step 61: for each index, respectively establish a relationship model D _i =Q _i -C between the function Q _i, and the function C, where i=1,...,n;

    Sub-step 62: For each indicator, for t = 1, ..., S, calculate the value of the relational model D _i , respectively, as shown in the following formula (8):

    D _i,t =Q _i,t -C _t (9)

    Based on the calculation result of formula (9), for each index, the probability density distribution function g _{Di of the} relational model D _i can be separately established, and the reasonableness expectation value E(g _Di ) of each index can be calculated by the probability density distribution function g _Di And standard deviation σ(g _Di );

    Sub-step 63: For each indicator, the rationality of the indicator is judged according to the reasonable expectation value of its corresponding probability density distribution function g _Di .
17. The computer readable storage medium of claim 16, wherein the program is further executed by the processor when:

    Step 7: Perform a significant test on the outcome of the indicator decision.
18. The computer readable storage medium of claim 17, wherein the step 7 comprises:

    Sub-step 71: Establish a median function O of the relational model D _i , ie:

    O=h(D ₁ , D ₂ ,...,D _i ,...,D _n ) (9)

    Sub-step 72: For each random assignment, the value of the median function O is calculated based on the value D _{i,t of the} relational model D _i , as shown in the following formula (10):

    O _t =h(D _1,t ,D _2,t ,...,D _i,t ,...,D _n,t ) (10)

    Obtain the discrete model G _O of the median function O according to the value of the median function O, and record the probability density function of the median function O as g _O ;

    Sub-step 73: Determine the anomaly distribution by chi-square test, including:

    Build test function

    

    As shown in formula (11):

    

    Wherein, the degree of freedom is v=n-1;

    According to the degree of freedom v and the first significance level α, from

    

    Check the critical value in the value table

    

    in case

    

    It is considered that the rationality measurement is significant after the test, and the index decision result is desirable; on the contrary, the index decision result is not acceptable.

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