CN114418431A - Equipment combat effectiveness dynamic comprehensive evaluation method based on fuzzy Borda sequence value - Google Patents

Abstract

The invention relates to the technical field of equipment test and identification, and discloses a comprehensive different evaluation method based on fuzzy Borda sequence values, which comprises a combat effectiveness evaluation index system and an evaluation method, a dynamic comprehensive evaluation method based on fuzzy Borda sequence values, and a key model based on dynamic comprehensive evaluation of fuzzy Borda sequence values, wherein the key model is as follows: the system comprises a pre-inspection model of the spearman grade correlation coefficient, a dynamic comprehensive evaluation model based on fuzzy Borda sequence values and a post-inspection model of the spearman grade correlation coefficient. The invention is provided aiming at the problem of inconsistent evaluation conclusions caused by different equipment combat effectiveness evaluation methods, can evaluate and sequence the various equipment combat effectiveness in a task stage, and can evaluate and sequence the various equipment combat effectiveness in the whole task process, thereby effectively solving the problem of inconsistent evaluation conclusions of the various equipment combat effectiveness, and the application directions of the method are various.

Description

Equipment combat effectiveness dynamic comprehensive evaluation method based on fuzzy Borda sequence value

Technical Field

The invention relates to the technical field of equipment test and identification, in particular to a fuzzy Borda sequence value-based dynamic comprehensive assessment method for equipment combat effectiveness.

Background

The equipment combat effectiveness evaluation is a key and hot research problem in the field of domestic and foreign combat and equipment construction at present, and a plurality of research achievements about evaluation models and evaluation methods are obtained. At present, the mainstream equipment fighting performance evaluation methods are basically based on different evaluation angles to establish related model algorithms, but different evaluation methods can possibly obtain different evaluation sequencing results for the same index system and sample data, a decision maker is difficult to determine which evaluation conclusion is more accurate, which evaluation method is more reasonable and suitable, and also difficult to find a perfect evaluation method and an objective verification judgment standard. The reason for this is that different evaluation methods have their own evaluation mechanisms; secondly, the problem of weight among indexes (or index sets) is generally involved in the data modeling process, which always causes the problems of confusion caused by human factor deviation, inconsistency of index weight with expectation, failure in embodying the importance degree of the indexes and the like, and even the same index system has different weights in different samples. Therefore, regardless of which warfare effectiveness evaluation method is selected, the advantages and disadvantages of each method cause the evaluation result to be difficult to convince.

Disclosure of Invention

Aiming at the problem of inconsistency of evaluation conclusions of equipment combat effectiveness based on different evaluation methods, the invention provides a dynamic comprehensive evaluation method based on fuzzy Borda sequence values. The method provides a thought for solving the problem of inconsistency of evaluation conclusions of various equipment combat effectiveness, and also provides a comprehensive evaluation method of the equipment combat effectiveness, so that evaluation sequencing conclusions of combat mission stages and the overall process of the combat mission can be obtained.

In order to achieve the purpose, the invention adopts the following technical scheme:

a comprehensive different evaluation method based on fuzzy Borda sequence values adopts a dynamic comprehensive evaluation model of equipment combat effectiveness, and comprises the following steps:

1) the equipment combat effectiveness evaluation refers to a process of measuring the effectiveness degree of a series of specified combat tasks by placing equipment in a combat confrontation environment, wherein two key tasks are to establish an evaluation index system and a related index data aggregation algorithm, namely an evaluation model; 1.1 establishment of the battle effectiveness evaluation index system, the first work is to establish the battle effectiveness evaluation index system, based on the decomposition characteristics of the task stage and the battle ability, and also to evaluate the simplicity of the work, to establish the hierarchical battle effectiveness evaluation index system,

the method is characterized in that the functional or performance index and the task capability index of the equipment are adopted to generally reflect the behavior of the equipment in the whole fighting process from bottom to top, the fighting performance index is measured from top to bottom through the attribute or behavior performance value of the task capability, the functional or performance index in the task time dimension, and the whole fighting process of the equipment is supposed to be decomposed into t₁,t₂,…,t_MWhen the task phases are equal, P pieces of equipment of the same type need to be evaluated and compared, the q (q is 1,2, …, P) th task capability index at the lower layer of the combat performance index is decomposed into N subordinate function or performance indexes, and the attribute or the performance value of the i (i is 1,2, …, N) th function or performance index of the M (M is 1,2, …, P) th equipment is described as the performance index of the q (q is 1,2, …, P) th task capability index at the j (j is 1,2, …, M) th task phase

The function or performance matrix of all equipment under the q task capability of the j task stage is

The matrix expresses the specific task stage, namely stage j specific task capacity, namely the evaluation index value under the task capacity q, each row corresponds to all function or performance index representation values of one equipment, each column corresponds to all equipment representation values of one function or performance index, and based on the matrix, the attribute or behavior representation supermatrix of the equipment combat effectiveness evaluation multi-stage multi-capability data profile is constructed into

1.2 the selection of the fighting performance evaluation model, the essence of equipment fighting performance evaluation is to measure the closeness and similarity between the fighting capacity of equipment for executing the specified fighting task and the fighting capacity required for completing the specified fighting task, and the closeness measurement adopts a distance scale: a weighted comprehensive average model, a comprehensive model approaching to an ideal solution, a fuzzy comprehensive evaluation model and an ADC method; the similarity measurement adopts a correlation coefficient scale: a gray correlation method, various clustering models, a weighted comprehensive average model, a comprehensive model approximate to an ideal solution and a gray correlation method;

the weighted comprehensive average model comprises a weighted comprehensive integration model based on addition weighted integration, multiplication weighted integration, an addition multiplication weighted integration method and a gain type linear weighted integration method;

the additive weighted integration method is a system evaluation method, and the expression of the integrated evaluation index value is

In the formula a_ijRegarding the index a for the evaluation object i_jSingle index evaluation value of, w_jIs an index a_jIs then according to W_iThe magnitude of the values of (A) are sorted for those of the evaluation object, or according to W_iThe evaluation values of all indexes are linearly compensated with each other, namely, the evaluation value of one index is lower, while the evaluation values of other indexes are higher, so that the comprehensive evaluation index value is still higher; improving the evaluation value of any index and improving the comprehensive evaluation index value; the comprehensive index expression of the multiplication weighted comprehensive method is

In the formula a_ijJ index value, w, for the i evaluation object_jIs the weight of the jth index, where each w is_jWhen the index value is 1/n, the method becomes an efficacy coefficient method, and the multiplication rule of the weighted average method requires that the evaluation value of each index obtains the highest level as much as possible so as to ensure that the comprehensive evaluation index value obtains a higher value; as long as the evaluation value of one index is very small, the comprehensive evaluation index value is quickly close to zero no matter how high the evaluation values of other indexes are, so that the method emphasizes the harmony of the evaluation values of all the indexes and is suitable for the condition that all the indexes have obvious association;

the addition-multiplication weighted integration method combines the addition-weighted integration method and the multiplication-weighted integration method, and the expression of the integrated evaluation value is

In the formula w_1j、w_2jAre respectively an index a_jD is the weight of the additive-weighted synthesis method.

The gain type linear weighting comprehensive method gives gain when the evaluation value of a single index is larger than the average value of the evaluation value, gives loss when the evaluation value of the single index is smaller than the average value of the evaluation value, and the expression of the comprehensive evaluation value is

In the formula a_ijJ index value, w, for the i evaluation object_jIs the weight of the jth index, u (a)_ij) Is a continuous, piecewise differentiable, non-decreasing function_ijVariation interval of [0,1 ]]Conversion to the interval [0, s]And has s > 1, u (0) ═ 0, u (0.5) < 0.5, and u (1) ═ s.

(ii) a comprehensive model approximating the ideal solution, for a normalized evaluation matrix F,

first, the positive and negative ideal solutions are calculated as

Then, the Euclidean distance between each evaluation object and the positive ideal solution and the negative ideal solution is calculated to be respectively

Finally, the relative closeness of each evaluation object is calculated, the combat effectiveness is sorted according to the value,

(III) Grey correlation method, for the standardized evaluation matrix F, determine its reference sequence

Firstly, the absolute value of the difference value between the ith index element and the reference sequence of the mth (m is 1,2, …, P) equipment is calculated to be

Secondly, determining maximum distance environment parameters

And minimum distance environmental parameters

Are respectively marked as

Then, based on the basic idea of the Deng's correlation degree, the gray correlation coefficient of the ith index element of the mth equipment is calculated as

Where ξ ∈ (0,1) is a resolution coefficient, ξ is usually 0.5. Finally, the gray correlation degree of the mth equipment and the reference sequence is calculated continuously as

The battle effectiveness can be sorted according to the grey correlation value;

2) aiming at the combat effectiveness evaluation of n equipment, firstly, an evaluation index system and an evaluation data matrix are constructed, 2 to 4 representative evaluation methods with different evaluation mechanisms are selected, the combat effectiveness evaluation is respectively carried out on each equipment, then, statistical analysis is carried out on different evaluation conclusions so as to test the consistency of different evaluation methods, a nonparametric statistical method based on grade correlation coefficients is adopted to test the closeness degree of evaluation results of different evaluation methods, and the fuzzy Borda method is adopted to synthesize different combat effectiveness evaluation results; finally, the consistency of the comprehensive assessment conclusion of the fuzzy Borda method and assessment conclusions of different assessment methods is tested, and the process is called post-test; checking the closeness degree of the fuzzy Borda method comprehensive evaluation conclusion and the different evaluation methods evaluation conclusion by adopting the spearman grade correlation coefficient, and selecting an optimal comprehensive method according to the average spearman grade correlation coefficient of the different comprehensive methods;

3) the method comprises the steps of carrying out dynamic comprehensive evaluation based on fuzzy Borda sequence values on equipment combat effectiveness based on a key model of the dynamic comprehensive evaluation based on the fuzzy Borda sequence values, wherein the model and the algorithm comprise index system construction and evaluation data description, different evaluation models and algorithms, a pre-inspection model of different evaluation methods, a dynamic comprehensive evaluation model based on the fuzzy Borda sequence values, and a post-inspection model of a comprehensive evaluation conclusion and different evaluation conclusions;

3.1 the preliminary test model of the spearman grade correlation coefficient, adopting spearman grade correlation coefficient test method to carry out the preliminary test on different evaluation methods, firstly converting the evaluation conclusion of different evaluation methods into a ranking matrix, supposing that the fighting efficiency of n devices is evaluated by m evaluation methods, obtaining the ranking matrix of the evaluation conclusion

In the formula y_ij(i-1, 2, …, n; j-1, 2, …, m) represents the evaluation ranking value of the ith equipment operational effectiveness under the jth evaluation method, and 1 is less than or equal to y_ijN is less than or equal to n; then calculate the j₁、j₂The spearman grade correlation coefficients of the sequencing results of the two evaluation methods judge whether the evaluation conclusions of the two evaluation methods have consistency or not according to the spearman grade correlation coefficients, and the calculation formula of the spearman grade correlation coefficients of the two sequencing results is

Given a significance level α, the threshold ρ is found_αWhen is coming into contact with

Then, the two evaluators under the significance level alpha are consideredThe ordering results of the method are closely related; when the evaluation conclusions of any two evaluation methods in the matrix S are consistent, judging that the evaluation conclusions of all the evaluation methods are consistent;

3.2 dynamic comprehensive assessment model based on fuzzy Borda order values, fuzzy Borda method considers two factors when combining: one is a factor of score difference of various methods, and the other is a ranking median factor, and basic steps of the dynamic comprehensive assessment of the combat effectiveness based on the fuzzy Borda method are as follows:

step one, calculating membership degrees, and setting j (j is 1,2, …, m) to n evaluation objects t_kThe evaluation is performed at the time point of (k ═ 1,2, …, N), and the i-th (i ═ 1,2, …, N) evaluation target overall evaluation value y is obtained_ij(t_k) (i ═ 1,2, …, n; j is 1,2, …, m; k is 1,2, …, N), the degree of membership is

v_ij(t_k) Is t_k(k-1, 2, …, N) th evaluation object at time j (j-1) of the ith (i-1, 2, …, N) th evaluation object_,2, …, m) membership degree, v, of "excellent" under the methods_ij(t_k) The closer to 1, the better;

step two, calculating fuzzy frequency and making f_ih(t_k) Is t_kThe number of blur frequencies of the ith (i is 1,2, …, N) evaluation object arranged at the h-th position at the time (k is 1,2, …, N), that is, the number of blur frequencies

In the formula

A description is given of whether or not the i (i ═ 1,2, …, n) th evaluation object is ranked at the h-th bit under the j (j ═ 1,2, …, m) th method, and if the i (i ═ 1,2, …, m) th evaluation object is ranked at the h-th bit under the j-th method, there is a case where the i (i ═ 1,2, …, n) th evaluation object is ranked at the h-th bit

Otherwise

Then there is an ambiguity frequency of

W_ih(t_k) The score difference factor is reflected;

step three, converting the rank of the evaluation object into a rank score, and defining a score difference for opening the score difference

In the formula Q_hiA score ranked in the h-th order in the precedence relationship for the ith evaluation object;

and step four, calculating fuzzy Borda number. Let B_iThe fuzzy Borda number score of the ith evaluation object is calculated by the following model

In the formula

The score of the ith evaluation object at the h-th position under the j method is calculated according to the score B_iAnd (6) reordering. Score B_iThe fighting efficiency of the big is excellent, and the fighting efficiency of the small is inferior;

3.3 post-inspection model of spearman grade correlation coefficient, for the post-inspection of dynamic comprehensive evaluation method, checking the closeness degree between the comprehensive evaluation ranking conclusion and the original evaluation ranking conclusion; in addition, when a plurality of comprehensive evaluation methods exist, the optimal comprehensive evaluation method is selected, wherein the post-inspection of the comprehensive evaluation method continues to adopt a Spireman grade correlation coefficient inspection method.

Due to the adoption of the technical scheme, the invention has the following advantages:

a dynamic comprehensive evaluation method based on fuzzy Borda sequence values effectively solves the problem of inconsistency of evaluation conclusions of combat effectiveness of various devices; secondly, key models and algorithms such as a pre-inspection model for different evaluation methods, fuzzy Borda sequence values for different comprehensive evaluation conclusions, the comprehensive evaluation conclusion and a post-inspection model for different evaluation conclusions are established; thirdly, the method has various application directions, and can evaluate and sequence the fighting efficiency of various equipment in the task stage and the fighting efficiency of various equipment in the whole task process.

Drawings

FIG. 1 is a hierarchical battle effectiveness evaluation index system diagram.

FIG. 2 is a flow chart of dynamic synthetic evaluation based on fuzzy Borda order values.

FIG. 3 is a diagram of the combat effectiveness index system of the ultrashort wave communication countermeasure system.

Detailed description of the invention

As shown in fig. 1,2 and 3, a dynamic comprehensive assessment method based on fuzzy Borda sequence values is a dynamic comprehensive assessment model for evaluating the combat effectiveness of different pieces of comprehensive assessment equipment based on fuzzy Borda sequence values;

1. the equipment combat effectiveness evaluation refers to a process of measuring the effectiveness degree of a series of specified combat tasks by placing equipment in a combat confrontation environment, wherein two key tasks are to establish an evaluation index system and a related index data aggregation algorithm, namely an evaluation model.

1.1 establishment of a combat effectiveness evaluation index system, aiming at the combat effectiveness evaluation work, the first work is to establish the combat effectiveness evaluation index system, and the hierarchical combat effectiveness evaluation index system which is usually established is shown in fig. 1 based on the decomposition characteristics of task stages and combat capability and also for evaluating the simplicity of the work.

FIG. 1 uses the function or performance of equipmentThe indexes and the task capacity indexes generally reflect the operational effectiveness and other behavior performances of the equipment in the whole operational process from bottom to top, and the operational effectiveness indexes are measured from top to bottom through the attributes or behavior performance values of the task capacity, the function or the performance indexes in the task time dimension. The entire combat process of hypothetical equipment can be decomposed into t₁,t₂,…,t_MIn the equal task phases, P pieces of equipment of the same type are shared to be evaluated and compared, the q (q is 1,2, …, P) th task capability index at the lower layer of the operational performance index in fig. 1 can be decomposed into N subordinate function or performance indexes, and then the q (q is 1,2, …, P) th task capability index at the j (j is 1,2, …, M) th task phase is assumed, and the attribute or performance value of the i (i is 1,2, …, N) th function or performance index of the M (M is 1,2, …, P) th equipment is described as an attribute or performance value

The function or performance matrix of all equipment under the q task capability of the j task stage is

The matrix expresses the evaluation index value under the specific task capacity (namely, the task capacity q) of the specific task stage (namely, the stage j), each row corresponds to all the function or performance index representation values of a certain equipment, and each column corresponds to all the equipment representation values of a certain function or performance index. Based on the matrix, an attribute or behavior performance supermatrix of the equipment combat effectiveness evaluation multistage multi-capability data profile can be constructed as

1.2, selecting a combat effectiveness evaluation model, wherein the essence of the equipment combat effectiveness evaluation is to measure the closeness and similarity between the combat capability of the equipment for executing a specified combat mission and the combat capability required for completing the specified combat mission, and the closeness measurement usually adopts a distance scale, such as a commonly used weighted comprehensive average model, a comprehensive model approaching an ideal solution, a fuzzy comprehensive judgment model, an ADC (analog to digital converter) method and the like; the measure of similarity usually uses a correlation coefficient scale, such as a common gray correlation method, various clustering models, and the like. The general weighted composite average model, composite model approximating the ideal solution, and gray correlation method are briefly described here.

Weighted integral average model

The weighted integration average model mainly comprises an addition weighted integration method, a multiplication weighted integration method, an addition multiplication weighted integration method, a gain type linear weighted integration method and the like.

The addition weighted integration method is a system evaluation method widely applied at present, and the expression of the integrated evaluation index value is

In the formula a_ijRegarding the index a for the evaluation object i_jSingle index evaluation value of, w_jIs an index a_jThe weight of (c). Thus can be based on W_iThe magnitude of the values of (A) are sorted for those of the evaluation object, or according to W_iThe evaluation target is classified by the scatter characteristic and the cluster characteristic. In the method, the evaluation values of all indexes can be linearly compensated with each other, namely, the evaluation value of one index is lower, while the evaluation values of other indexes are higher, so that the comprehensive evaluation index value is still higher; the comprehensive evaluation index value can be improved by improving the evaluation value of any index.

The comprehensive index expression of the multiplication weighted comprehensive method is

In the formula a_ijJ index value, w, for the i evaluation object_jIs the weight of the jth index. In the formula, when each w_jWhen the ratio is 1/n, the method becomes an efficacy coefficient method. Weighted average methodThe multiplication rule requires that the evaluation value of each index can obtain the highest level as far as possible, so that the comprehensive evaluation index value can obtain a higher value; as long as the evaluation value of a certain index is very small, the value of the overall evaluation index will quickly approach zero regardless of how high the evaluation values of the other indexes are. Therefore, the method emphasizes the harmony of the evaluation values of the indexes and is suitable for the condition that the indexes have obvious association relation.

The addition and multiplication weighted integration method combines the addition weighted integration method and the multiplication weighted integration method, and the expression of the integrated evaluation value is

In the formula w_1j、w_2jAre respectively an index a_jD is the weight of the additive-weighted synthesis method.

The gain type linear weighting comprehensive method is to give gain when the evaluation value of a single index is larger than the average value of the evaluation value, and give a discount when the evaluation value of the single index is smaller than the average value of the evaluation value, and the expression of the comprehensive evaluation value is

In the formula a_ijJ index value, w, for the i evaluation object_jIs the weight of the jth index. u (a)_ij) Is a continuous, piecewise differentiable, non-decreasing function_ijVariation interval of [0,1 ]]Conversion to the interval [0, s]And has s > 1, u (0) ═ 0, u (0.5) < 0.5, and u (1) ═ s.

Synthetic model approximating (II) to an ideal solution

With respect to the normalized evaluation matrix F,

first, the positive and negative ideal solutions are calculated as

Then, the Euclidean distance between each evaluation object and the positive ideal solution and the negative ideal solution is calculated to be respectively

And finally, calculating the relative closeness of each evaluation object, and sequencing the combat effectiveness according to the value.

Grey correlation method

For the normalized evaluation matrix F, its reference sequence is determined

Firstly, the absolute value of the difference value between the ith index element and the reference sequence of the mth (m is 1,2, …, P) equipment is calculated to be

Secondly, determining maximum distance environment parameters

And minimum distance environmental parameters

Are respectively marked as

Then, based on the basic idea of the Deng's correlation degree, the gray correlation coefficient of the ith index element of the mth equipment is calculated as

Where ξ ∈ (0,1) is a resolution coefficient, ξ is usually 0.5. Finally, the gray correlation degree of the mth equipment and the reference sequence is calculated continuously as

The battle effectiveness can be sorted according to the grey correlation value.

2. In order to solve the limitation of a single equipment combat effectiveness evaluation method and the difference of evaluation results, the fuzzy Borda sequence value-based dynamic comprehensive evaluation method is used for integrating evaluation conclusions of various evaluation methods based on the concept of academic 'combined evaluation' to obtain a comprehensive evaluation result. By integrating various evaluation conclusions, the effect of getting strong and making up for weakness can be achieved by utilizing more information, and the effectiveness and the reliability of evaluation are improved. The basic idea of dynamic comprehensive evaluation based on fuzzy Borda order values is presented in FIG. 2.

For the battle effectiveness evaluation of n pieces of equipment, firstly, an evaluation index system and an evaluation data matrix are constructed according to the part 1, and 2 to 4 representative evaluation methods with different evaluation mechanisms are selected to respectively evaluate the battle effectiveness of each equipment. It should be noted that, when the weight calculation of the evaluation index is performed in the evaluation process, in order to avoid the influence of subjective factors on the evaluation result and fully consider the importance degree of the index itself, it is recommended to select a weight calculation model combining subjective and objective, so that the subjective and objective methods can mutually make up for the defects, and the equipment combat effectiveness can be comprehensively evaluated.

Statistical analysis of the different assessment conclusions is then required to check the consistency of the different assessment methods. Because different assessment methods can obtain different combat effectiveness assessment results from different angles, although the results may have certain differences, several assessment results should not have too large differences for the same sample. This process is commonly referred to as a pre-test, where non-parametric statistical methods based on rank correlation coefficients are used to test how closely the different evaluation methods evaluate the results.

This is followed by a comprehensive process of different evaluation methods. Common comprehensive methods for evaluating the conclusion by different evaluation methods are an average value method, a Borda method, a Copeland method, a fuzzy Borda method and the like. The three methods are combined according to the ranking of each evaluation method evaluation conclusion, and the factor of the score difference of each evaluation method evaluation conclusion is not considered; and the fuzzy Borda method not only considers the score difference factors of various evaluation methods but also considers the rank factor of the evaluation conclusion ranking result when integrating different evaluation methods. The fuzzy Borda method is adopted to synthesize different combat effectiveness evaluation results.

Finally, the consistency of the comprehensive evaluation conclusion of the fuzzy Borda method and the evaluation conclusion of different evaluation methods is tested, the process is generally called post-test, the closeness degree of the comprehensive evaluation conclusion of the fuzzy Borda method and the evaluation conclusion of different evaluation methods is tested by adopting a spearman grade correlation coefficient, and an optimal comprehensive method can be selected according to the average spearman grade correlation coefficient of different comprehensive methods.

3. The key model and algorithm of the dynamic comprehensive assessment based on the fuzzy Borda sequence value are used for carrying out dynamic comprehensive assessment based on the fuzzy Borda sequence value on the equipment combat effectiveness according to the basic thought of figure 2, and comprise index system construction and assessment data description, different assessment models and algorithms, a pre-inspection model of different assessment methods, a dynamic comprehensive assessment model based on the fuzzy Borda sequence value, a comprehensive assessment conclusion and a post-inspection model of different assessment conclusions and the like.

3.1 a spearman grade correlation coefficient pre-inspection model, and a spearman grade correlation coefficient inspection method is adopted to carry out pre-inspection on different evaluation methods. The method comprises the steps of firstly converting evaluation conclusions of different evaluation methods into a ranking matrix, supposing that the fighting efficiency of n equipment is evaluated by using m evaluation methods, and obtaining the ranking matrix of the evaluation conclusions

In the formula y_ij(i-1, 2, …, n; j-1, 2, …, m) represents the evaluation ranking value of the ith equipment operational effectiveness under the jth evaluation method, and 1 is less than or equal to y_ij≤n。

Then calculate the j₁、j₂The spearman grade correlation coefficients of the sequencing results of the two evaluation methods judge whether the evaluation conclusions of the two evaluation methods have consistency or not according to the spearman grade correlation coefficients, and the calculation formula of the spearman grade correlation coefficients of the two sequencing results is

Given a significance level α, the threshold ρ can be found_αWhen is coming into contact with

In the mean time, the ranking results of the two evaluation methods under the significance level alpha are considered to have close relationship. When the evaluation conclusions of any two evaluation methods in the matrix S have consistency, judging that the evaluation conclusions of all the evaluation methods have consistency.

3.2 dynamic comprehensive assessment model based on fuzzy Borda order values, fuzzy Borda method considers two factors when combining: one is a factor of the difference in scores of the various methods, and the other is a rank factor in the ranking. The fuzzy Borda method based battle efficiency dynamic comprehensive evaluation comprises the following basic steps:

step one, calculating the membership degree. Let n evaluation targets t be evaluated by j (j ═ 1,2, …, m) th method_kThe evaluation is performed at the time point of (k ═ 1,2, …, N), and the i-th (i ═ 1,2, …, N) evaluation target overall evaluation value y is obtained_ij(t_k) (i ═ 1,2, …, n; j is 1,2, …, m; k is 1,2, …, N), the degree of membership is

v_ij(t_k) Is t_k(k ═ 1,2, …, N) at the time point i (i ═ 1,2, …, N) evaluation targets belong to the degree of membership of "excellent", v ═ v, under the j (j ═ 1,2, …, m) method_ij(t_k) The closer to 1, the better.

And step two, calculating fuzzy frequency. Let f_ih(t_k) Is t_kThe number of blur frequencies of the ith (i is 1,2, …, N) evaluation object arranged at the h-th position at the time (k is 1,2, …, N), that is, the number of blur frequencies

In the formula

A description is given of whether or not the i (i ═ 1,2, …, n) th evaluation object is ranked at the h-th bit under the j (j ═ 1,2, …, m) th method, and if the i (i ═ 1,2, …, m) th evaluation object is ranked at the h-th bit under the j-th method, there is a case where the i (i ═ 1,2, …, n) th evaluation object is ranked at the h-th bit

Otherwise

Then there is an ambiguity frequency of

W_ih(t_k) The score difference factor is reflected.

And step three, converting the ranking of the evaluation objects into ranking scores. To separate score differences, define

In the formula Q_hiThe score ranked at h-th in the order of preference for the ith evaluation subject.

And step four, calculating fuzzy Borda number. Let B_iThe fuzzy Borda number score of the ith evaluation object is calculated by the following model

In the formula

The score of the ith evaluation object at the h-th position under the j method is calculated according to the score B_iAnd (6) reordering. Score B_iThe fighting efficiency of the bigger is excellent, and the fighting efficiency of the smaller is inferior.

3.3 post-inspection model of spearman grade correlation coefficient, for the post-inspection of dynamic comprehensive evaluation method, mainly inspecting the closeness degree between the comprehensive evaluation ranking conclusion and the original evaluation ranking conclusion; in addition, when a plurality of comprehensive evaluation methods exist, the optimal comprehensive evaluation method can be selected according to the comprehensive evaluation methods. The post-test of the comprehensive evaluation method continues to adopt a spearman grade correlation coefficient test method.

4. Dynamic comprehensive evaluation example for combat effectiveness of general defense equipment

The combat mission of a certain type of ultrashort wave ground communication countermeasure system is to carry out electromagnetic deterrence and electromagnetic blockade on an enemy ultrashort wave communication system in a certain combat region and to implement supporting interference on enemy ultrashort wave voice, data communication and the like. The system for evaluating the combat effectiveness of the ultrashort wave ground communication countermeasure system is established according to the combat mission thereof as shown in fig. 3.

The battle mission process of the ultrashort wave ground communication countermeasure system can be divided into a plurality of stages of pre-war reconnaissance, pre-war key reconnaissance, target direction finding, target attack, battle ending and the like. In order to verify the effectiveness of the dynamic assessment method for the fighting effectiveness, 6 ultrashort wave ground communication countermeasure systems of the same type (assumed to be a system I, a system II, a system III, a system IV, a system V and a system VI) and assessment data of a certain fighting task stage are selected for calculation. The data matrix of the bottom layer indexes of 6 systems and 4 kinds of fighting capacities is shown as follows after the bottom layer indexes are subjected to qualitative and quantitative conversion and polarity conversion.

Each row of the 4 matrixes corresponds to 6 evaluated object systems, and each column respectively represents the bottom evaluation index data of different fighting capacities in a certain fighting task stage. Similar calculation can be carried out on other task stages, and the assessment results of all the task stages are weighted, so that the fighting effectiveness of the whole process of the fighting task can be assessed and sorted.

Consistency check calculation of 4.13 evaluation methods, carrying out the operation efficiency of the operation task stage by adopting 3 evaluation methods, namely an addition weighted comprehensive model, a comprehensive model approaching to an ideal solution and a gray correlation method, wherein the weights among the reconnaissance capability, the direction finding capability, the interference capability and the command capability are assumed to be (0.3,0.2,0.3 and 0.2) (and the evaluation results are obtained as shown in table 1 on the assumption that the indexes of the bottom layer under each operation capability are equally important.

TABLE 1 tactical effectiveness evaluation ranking results of different evaluation methods

The consistency of the 3 evaluation methods is subjected to a prior inspection calculation, wherein

Given a significance level α of 0.05, the critical value ρ was found_0.050.829, since r₁₂＞ρ_0.05、r₁₃＞ρ_0.05、r₂₃＞ρ_0.05Then, the 3 evaluation methods herein are considered consistent at the significance level α, and a comprehensive evaluation can be performed.

Fuzzy Borda order value calculation of 4.23 evaluation methods, first, the membership degree of 6 systems belonging to "excellent" in 3 different evaluation methods was calculated, and the results are shown in Table 2.

TABLE 26 membership degrees for different evaluation methods of the systems

The number of blur frequencies ranked in h-th order by i (i ═ 1,2, …,6) th evaluation system is shown in table 3.

TABLE 36 fuzzy frequency table of system

Then, calculation of converting the sorted ranks into the rank scores was performed, and the calculation results are shown in table 4.

Table 4 conversion of rank order to rank order score table

Finally, 6 systematic fuzzy Borda number scores are calculated, and the calculation results and the battle efficiency ranking results are shown in Table 5.

TABLE 5 fuzzy Borda number based composite assessment score and ranking

4.3 consistency check calculation of the comprehensive evaluation model and 3 evaluation methods, and the Stelman grade correlation coefficient calculation based on the fuzzy Borda method comprehensive evaluation model and 3 evaluation methods, including

At a given significance level α of 0.05, due to r_m1＞ρ_0.05、r_m2＞ρ_0.05、r_m3＞ρ_0.05Then the significance level alpha is considered to be based on blurThe comprehensive evaluation method of the Borda method has higher consistency with an addition weighted comprehensive average model, a comprehensive model approximate to an ideal solution and a gray correlation method. The comprehensive evaluation method based on the fuzzy Borda method is reasonable, effective and feasible, and can objectively and comprehensively carry out comprehensive evaluation on the quality grade of the fighting efficiency of the equipment. The fuzzy Borda comprehensive evaluation model is a comprehensive model of three single evaluation models, original evaluation information of equipment fighting efficiency and effective information reflected by a single evaluation method can be comprehensively utilized, advantage complementation can be realized, and evaluation conclusion is more scientific and accurate.

Claims (1)

1. A fuzzy Borda sequence value-based dynamic comprehensive assessment method for equipment combat effectiveness is characterized by comprising the following steps: the method comprises the following steps:

1) the equipment combat effectiveness evaluation refers to a process of measuring the effectiveness degree of a series of specified combat tasks by placing equipment in a combat confrontation environment, wherein two key tasks are to establish an evaluation index system and a related index data aggregation algorithm, namely an evaluation model;

1.1 establishment of the battle effectiveness evaluation index system, the first work is to establish the battle effectiveness evaluation index system, based on the decomposition characteristics of the task stage and the battle ability, and also to evaluate the simplicity of the work, to establish the hierarchical battle effectiveness evaluation index system,

the method is characterized in that the functional or performance index and the task capability index of the equipment are adopted to generally reflect the behavior of the equipment in the whole fighting process from bottom to top, the fighting performance index is measured from top to bottom through the attribute or behavior performance value of the task capability, the functional or performance index in the task time dimension, and the whole fighting process of the equipment is supposed to be decomposed into t₁,t₂,…,t_MIn the equal task stages, P pieces of equipment of the same type are shared, the fighting performance is evaluated and compared, the q (q is 1,2, …, P) th task capability index at the lower layer of the fighting performance index is decomposed into N subordinate functions or performance indexes, and then for the q (q is 1,2, …, P) th task capability index at the j (j is 1,2, …, M) th task stage, the M (M is 1,2, …, P) th task capability index is assumed1,2, …, P) th (i ═ 1,2, …, N) function or performance index attribute or performance value is described as

The function or performance matrix of all equipment under the q task capability of the j task stage is

The matrix expresses the specific task stage, namely stage j specific task capacity, namely the evaluation index value under the task capacity q, each row corresponds to all function or performance index representation values of one equipment, each column corresponds to all equipment representation values of one function or performance index, and based on the matrix, the attribute or behavior representation supermatrix of the equipment combat effectiveness evaluation multi-stage multi-capability data profile is constructed into

1.2 the selection of the fighting performance evaluation model, the essence of equipment fighting performance evaluation is to measure the closeness and similarity between the fighting capacity of equipment for executing the specified fighting task and the fighting capacity required for completing the specified fighting task, and the closeness measurement adopts a distance scale: a weighted comprehensive average model, a comprehensive model approaching to an ideal solution, a fuzzy comprehensive evaluation model and an ADC method; the similarity measurement adopts a correlation coefficient scale: a gray correlation method, various clustering models, a weighted comprehensive average model, a comprehensive model approximate to an ideal solution and a gray correlation method;

the weighted comprehensive average model comprises a weighted comprehensive integration model based on addition weighted integration, multiplication weighted integration, an addition multiplication weighted integration method and a gain type linear weighted integration method;

the additive weighted integration method is a system evaluation method, and the expression of the integrated evaluation index value is

In the formula a_ijRegarding the index a for the evaluation object i_jSingle index evaluation value of, w_jIs an index a_jIs then according to W_iThe magnitude of the values of (A) are sorted for those of the evaluation object, or according to W_iThe evaluation values of all indexes are linearly compensated with each other, namely, the evaluation value of one index is lower, while the evaluation values of other indexes are higher, so that the comprehensive evaluation index value is still higher; improving the evaluation value of any index and improving the comprehensive evaluation index value; the comprehensive index expression of the multiplication weighted comprehensive method is

In the formula a_ijJ index value, w, for the i evaluation object_jIs the weight of the jth index, where each w is_jWhen the index value is 1/n, the method becomes an efficacy coefficient method, and the multiplication rule of the weighted average method requires that the evaluation value of each index obtains the highest level as much as possible so as to ensure that the comprehensive evaluation index value obtains a higher value; as long as the evaluation value of one index is very small, the comprehensive evaluation index value is quickly close to zero no matter how high the evaluation values of other indexes are, so that the method emphasizes the harmony of the evaluation values of all the indexes and is suitable for the condition that all the indexes have obvious association;

the addition-multiplication weighted integration method combines the addition-weighted integration method and the multiplication-weighted integration method, and the expression of the integrated evaluation value is

In the formula w_1j、w_2jAre respectively an index a_jD is the weight of the addition weighted synthesis method;

the gain type linear weighting comprehensive method gives gain when the evaluation value of a single index is larger than the average value of the evaluation value, gives loss when the evaluation value of the single index is smaller than the average value of the evaluation value, and the expression of the comprehensive evaluation value is

In the formula a_ijJ index value, w, for the i evaluation object_jIs the weight of the jth index, u (a)_ij) Is a continuous, piecewise differentiable, non-decreasing function_ijVariation interval of [0,1 ]]Conversion to the interval [0, s]And has s > 1, u (0) ═ 0, u (0.5) < 0.5, u (1) ═ s;

(ii) a comprehensive model approximating the ideal solution, for a normalized evaluation matrix F,

first, the positive and negative ideal solutions are calculated as

Then, the Euclidean distance between each evaluation object and the positive ideal solution and the negative ideal solution is calculated to be respectively

Finally, the relative closeness of each evaluation object is calculated, the combat effectiveness is sorted according to the value,

(III) Grey correlation method, for the standardized evaluation matrix F, determine its reference sequence

Firstly, the absolute value of the difference value between the ith index element and the reference sequence of the mth (m is 1,2, …, P) equipment is calculated to be

Secondly, determining maximum distance environment parameters

And minimum distance environmental parameters

Are respectively marked as

Then, based on the basic idea of the Deng's correlation degree, the gray correlation coefficient of the ith index element of the mth equipment is calculated as

Where xi e (0,1) is a resolution coefficient, xi is usually 0.5, and finally, the gray correlation degree of the mth equipment and the reference sequence is calculated as

The battle efficiency can be sorted according to the value of the grey correlation degree;

2) aiming at the combat effectiveness evaluation of n equipment, firstly, an evaluation index system and an evaluation data matrix are constructed, 2 to 4 representative evaluation methods with different evaluation mechanisms are selected, the combat effectiveness evaluation is respectively carried out on each equipment, then, statistical analysis is carried out on different evaluation conclusions so as to test the consistency of different evaluation methods, a nonparametric statistical method based on grade correlation coefficients is adopted to test the closeness degree of evaluation results of different evaluation methods, and the fuzzy Borda method is adopted to synthesize different combat effectiveness evaluation results; finally, the consistency of the comprehensive assessment conclusion of the fuzzy Borda method and assessment conclusions of different assessment methods is tested, and the process is called post-test; checking the closeness degree of the fuzzy Borda method comprehensive evaluation conclusion and the different evaluation methods evaluation conclusion by adopting the spearman grade correlation coefficient, and selecting an optimal comprehensive method according to the average spearman grade correlation coefficient of the different comprehensive methods;

3) the method comprises the steps of carrying out dynamic comprehensive evaluation based on fuzzy Borda sequence values on equipment combat effectiveness based on a key model of the dynamic comprehensive evaluation based on the fuzzy Borda sequence values, wherein the model and the algorithm comprise index system construction and evaluation data description, different evaluation models and algorithms, a pre-inspection model of different evaluation methods, a dynamic comprehensive evaluation model based on the fuzzy Borda sequence values, and a post-inspection model of a comprehensive evaluation conclusion and different evaluation conclusions;

3.1 the preliminary test model of the spearman grade correlation coefficient, adopting spearman grade correlation coefficient test method to carry out the preliminary test on different evaluation methods, firstly converting the evaluation conclusion of different evaluation methods into a ranking matrix, supposing that the fighting efficiency of n devices is evaluated by m evaluation methods, obtaining the ranking matrix of the evaluation conclusion

In the formula y_ij(i-1, 2, …, n; j-1, 2, …, m) represents the evaluation ranking value of the ith equipment operational effectiveness under the jth evaluation method, and 1 is less than or equal to y_ijN is less than or equal to n; then calculate the j₁、j₂The spearman grade correlation coefficients of the sequencing results of the two evaluation methods judge whether the evaluation conclusions of the two evaluation methods have consistency or not according to the spearman grade correlation coefficients, and the calculation formula of the spearman grade correlation coefficients of the two sequencing results is

Given a significance level α, the threshold ρ is found_αWhen is coming into contact with

In time, the sequencing results of the two evaluation methods under the significance level alpha are considered to have close relationship; when the evaluation conclusions of any two evaluation methods in the matrix S are consistent, judging that the evaluation conclusions of all the evaluation methods are consistent;

3.2 dynamic comprehensive assessment model based on fuzzy Borda order values, fuzzy Borda method considers two factors when combining: one is a factor of score difference of various methods, and the other is a ranking median factor, and basic steps of the dynamic comprehensive assessment of the combat effectiveness based on the fuzzy Borda method are as follows:

step one, calculating membership degrees, and setting j (j is 1,2, …, m) to n evaluation objects t_kThe evaluation is performed at the time point of (k ═ 1,2, …, N), and the i-th (i ═ 1,2, …, N) evaluation target overall evaluation value y is obtained_ij(t_k) (i ═ 1,2, …, n; j is 1,2, …, m; k is 1,2, …, N), the degree of membership is

v_ij(t_k) Is t_k(k ═ 1,2, …, N) at the time point i (i ═ 1,2, …, N) evaluation targets belong to the degree of membership of "excellent", v ═ v, under the j (j ═ 1,2, …, m) method_ij(t_k) The closer to 1, the better;

step two, calculating fuzzy frequency and making f_ih(t_k) Is t_kThe number of blur frequencies of the ith (i is 1,2, …, N) evaluation object arranged at the h-th position at the time (k is 1,2, …, N), that is, the number of blur frequencies

In the formula

A description is given of whether or not the i (i ═ 1,2, …, n) th evaluation object is ranked at the h-th bit under the j (j ═ 1,2, …, m) th method, and if the i (i ═ 1,2, …, m) th evaluation object is ranked at the h-th bit under the j-th method, there is a case where the i (i ═ 1,2, …, n) th evaluation object is ranked at the h-th bit

Otherwise

Then there is an ambiguity frequency of

W_ih(t_k) The score difference factor is reflected;

step three, converting the rank of the evaluation object into a rank score, and defining a score difference for opening the score difference

In the formula Q_hiA score ranked in the h-th order in the precedence relationship for the ith evaluation object;

step four, calculating fuzzy Borda number; let B_iThe fuzzy Borda number score of the ith evaluation object is calculated by the following model

In the formula

The score of the ith evaluation object at the h-th position under the j method is calculated according to the score B_iReordering; score B_iThe fighting efficiency of the big is excellent, and the fighting efficiency of the small is inferior;

3.3 post-inspection model of spearman grade correlation coefficient, for the post-inspection of dynamic comprehensive evaluation method, checking the closeness degree between the comprehensive evaluation ranking conclusion and the original evaluation ranking conclusion; in addition, when a plurality of comprehensive evaluation methods exist, the optimal comprehensive evaluation method is selected, wherein the post-inspection of the comprehensive evaluation method continues to adopt a Spireman grade correlation coefficient inspection method.

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