CN116934148A - Air attack target threat assessment method based on clustering combination weighting - Google Patents
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Abstract
The invention relates to a method for evaluating air attack target threat based on clustering combination weighting, and belongs to the field of battlefield situation analysis. Aiming at the defect that the subjectivity of a weight coefficient determined by a single expert is too strong when an AHP method is adopted to determine the index weight in the current air attack target threat assessment, the air attack target threat assessment method based on clustering combination weighting is provided. Determining expert weights from 2 aspects of expert experience capacity and awareness degree of given problems by adopting a group AHP method under cluster analysis to obtain index subjective weights; and combining the objective weight obtained by the mutation coefficient method to obtain a final weight, constructing a fuzzy comprehensive evaluation model introducing an Einstain operator, and calculating to obtain a threat degree value of the target. The invention avoids the defect of strong subjectivity of the weight coefficient by clustering combination weighting, fully and organically combines a qualitative method and a quantitative method, has simple and clear calculation, and can fully assist a commander in threat assessment.
Description
Technical Field
The invention relates to a method for evaluating air attack target threat based on clustering combination weighting, and belongs to the field of battlefield situation analysis.
Background
Along with the diversification of air attack targets, the protected targets and the air defense weapon system are threatened in various ways, and in the actual air defense combat process, command decision-makers need to scientifically evaluate and sort the threat degrees of the targets by combining battlefield practice, so that reliable reference basis is provided for command decisions.
Currently, the threat assessment of the air attack target mainly comprises a plurality of assessment models such as a dynamic Bayesian network, an intuitionistic fuzzy set, a Topsis method, gray ideal association and the like. The target threat assessment has the characteristics of blurring and difficulty in quantification, a blurring comprehensive assessment method is more suitable for solving the problems, in a blurring comprehensive assessment model, the determination of index weight coefficients and the selection of blurring operators are two key problems, and the current weight coefficient determination method mainly comprises a subjective method and an objective method, wherein the subjective method mainly comprises an analytic hierarchy process (AHP method), a Delphi method, a loop ratio scoring method and the like, and the methods mainly rely on expert scores for index weighting. In the implementation process, the weighting is usually carried out according to the evaluation result of one expert, and the obtained result is often greatly different from expert to expert, so that the subjective weighting is carried out by adopting a group AHP method, namely, a plurality of experts are selected for evaluation, and firstly, the experience and the capability of the expert are evaluated by giving out a standard scene and a test vector, and the expert experience weight is determined. And classifying the experts according to the proximity degree and the consistency proportion of the expert sequencing scheme for a given threat assessment problem to obtain class weights of the experts, obtaining final weights of different experts by integrating the expert experience weights and the clustering weights, and finally calculating subjective weights of the indexes by weighting integration. In general, if the higher the closeness of the ranking scheme of an expert, the higher the degree of commonality of the expert with respect to the ranking scheme, and the more authoritative the corresponding evaluation, the greater the weight of such an expert, so that the clustering analysis is performed to determine the expert class weight according to the closeness of the ranking scheme. The consistency ratio shows the consistency degree of the matrix, and the lower the consistency ratio of the judgment matrix is, the clearer the logic and the tighter the thinking of an expert during evaluation are, the more reasonable the evaluation is made, and the higher the weight is given. The objective method comprises an entropy weight method, a CRITIC method, a coefficient of variation method and the like, and the weight of the method is mainly determined by data, so that the resolution information contained in objective data can be fully reflected, but the method is easily influenced by the value of the data and has instability. In terms of operator selection, the basic fuzzy synthesis operator such as a small and large operator (V, V) only utilizes partial information such as maximum value and minimum value in membership vectors, and other vectors do not work, so that the problem of more information omission exists; the Einstain operator is a nonlinear fuzzy synthesis operator, and the defects of the basic fuzzy operator can be eliminated by performing fuzzy synthesis operation through the Einstain operator, so that the Einstain operator has higher accuracy and scientificity.
Disclosure of Invention
According to the invention, index weighting is more reasonable by adopting a method of weighting combination of a group clustering AHP method and a variation coefficient method, and a model for evaluating the air attack target threat based on clustering combination weighting and Einstain operators is constructed.
The content of the invention can be realized by the following technical means:
a method for evaluating air attack target threat based on clustering combination weighting comprises the following steps:
step 1, selecting threat assessment indexes: including target navigation path shortcuts, flying heights, flying speeds and flying times; the target route shortcut is the horizontal projection distance from the guard target to the air attack target route, the flying height and the flying speed are the flying height and the flying speed of the air attack target respectively, and the flying time is the shortest time for the air attack target to fly to the guard target;
step 2, constructing a threat membership function and a membership matrix: defining a corresponding threat membership function according to index meanings, quantifying the threat degree of each index of each target, and constructing a threat assessment membership matrix of multiple targets and multiple indexes;
step 3, threat index weighting: the subjective weight is determined through the clustering weighting of the group AHP, the objective weight is determined through the weighting of the mutation coefficient method, and finally the final index weight is obtained through subjective and objective synthesis;
step 4, fuzzy synthesis and comprehensive evaluation: and (3) selecting a nonlinear Einstain operator to perform fuzzy synthesis on the threat assessment membership matrix obtained in the step (2) and the final index weight obtained in the step (3), calculating a fuzzy synthesis vector and sequencing threat degrees.
Further, the step 2 specifically includes the following steps:
the threat membership function is constructed specifically as follows:
determining a path shortcut threat membership function: selecting the horizontal projection distance from the guard target to the air attack target channel as a channel shortcut, wherein the smaller the channel shortcut is, the higher the threat degree is, when the channel shortcut is 0, the attack intention of the target is strongest, the possibility of damaging the guard target is largest, and the threat value is 1 at the maximum; defining the path shortcut threat membership function as:
wherein k is a set value, and p is a navigation path shortcut;
flight height threat membership function determination: the target threat value is inversely related to the flying height, and when the target flying is lower than the set height, the threat value is maximally 1; defining a fly height threat membership function as:
wherein k is a set value, and h is a flying height;
and (3) determining a flight speed threat membership function: the greater the flying speed of the air attack target, the greater the resistance difficulty and the higher the threat degree; defining a flight speed threat membership function as:
μ(v)＝1-e -αv ,0<v≤3000
wherein alpha is a set value, and v is a target flying speed;
and (3) determining a flight time threat membership function: the shorter the flying time of the air attack target is, the greater the threat degree is; when the target deviates from or deviates from flying, the flying time is longer than the distant time, and the threat degree is smaller, so that the flying time reflects two conditions of the adjacent flying and the distant flying at the same time, wherein the time of the adjacent flying takes a positive value and the time of the distant flying takes a negative value; defining a flight time threat membership function as follows:
wherein ,k1 and k2 Are set values, and t is the flying time;
the threat assessment membership matrix for constructing the multi-target multi-index is specifically as follows:
giving membership x to the ith index to the kth target by threat membership function ki And a membership vector x corresponding to the target k The method comprises the following steps:
x k ＝(x k1 x k2 … x kn )
further constructing threat assessment membership matrixes of m targets:
wherein k is more than or equal to 1 and less than or equal to m, m is the target number, and n is the number of indexes.
Further, the step 3 specifically includes the following steps:
step 301, performing index weighting by adopting a group AHP clustering weighting method, namely performing index evaluation by a plurality of experts; wherein, the experience weight is determined by gray correlation analysis, and the category weight is determined by cluster analysis;
the method for determining the experience weight is as follows:
(1) Let the test vector of a given scene constitute a reference sequence vector X 0 ＝(x 0 (1),x 0 (2),…,x 0 (n)) T S experts participate in the evaluation, and the result vector given by the jth expert forms a comparison sequence vector as follows:
X j ＝(x j (1),x j (2),…,x j (n)) T
the s +1 vectors form the following matrix:
wherein n is the number of indexes, j is more than or equal to 1 and less than or equal to s;
(2) The absolute value matrix is calculated as:
wherein ,Δj (i)＝|x 0 (i)-x j (i) The I is that the j expert gives the absolute difference value of the i index and the test vector index, i is more than or equal to 1 and less than or equal to n; j is more than or equal to 1 and less than or equal to s;
for the maximum value of each row of the matrix Δ, the component maximum vector is:
for the minimum value of each row of the matrix Δ, the component minimum value vector is:
(3) Calculating a correlation coefficient and a correlation degree;
for each term in the matrix delta, calculating the association coefficient, wherein the association coefficient of the ith index given by the jth expert is as follows:
the association degree of the result vector of each expert and the test vector is obtained through an association coefficient, and the calculation formula of the association degree is as follows:
wherein ρ is a resolution coefficient, i is not less than 1 and not more than n, j is not less than 1 and not more than s, n is the number of indexes, and s is the number of experts;
(4) The experience weight of the j-th expert is obtained through the association degree:
the determination method of the category weight is as follows:
(1) The j-th expert gives a judgment matrix under a certain criterion layer as follows:
judgment matrix A of jth expert j The feature vector corresponding to the maximum feature value of (a) is the index sorting vector:
(2) Calculating a j-th expert index ranking vector U by adopting Euclidean distance j Similarity degree with other expert's ranking index vectors; judging the similarity degree and the class-class difference degree between the two sorting vectors according to the Euclidean distance, and classifying the two sorting vectors into one class when the distance is smaller than a critical value;
suppose that there is ζ in the q-th class where the j-th expert is located q The weight of the q-th class expert is:
wherein, q is more than or equal to 1 and less than or equal to z, and z is the number of classifications;
(3) The weight in the class of the jth expert in the q-th class is as follows:
wherein b is a set value, CR j CR is a consistency ratio j Judgment matrix A according to jth expert j The maximum characteristic value of (2) is calculated by the following steps:
wherein lambda is the judgment matrix A j Is the maximum eigenvalue of (2);
(4) The category weight of the jth expert is:
c j ＝λ q *z j
wherein ,λq Weighting, z, the class q expert j The weight in the class of the jth expert in the q-th class;
the final subjective weight of the jth expert is:
ψ j ＝βγ j +(1-β)c j
wherein, beta is an adjustment coefficient;
the subjective weight vector of the comprehensive obtained index is as follows:
step 302, weighting and determining objective weights by adopting a coefficient of variation method:
(1) Calculating the mean and variance of the ith index:
wherein m is the target number, x ki Calculating index resolution capability for the membership degree of the kth target belonging to the ith index;
(2) The resolving power of calculating the i-th index is as follows:
(3) The index objective weight vector obtained by normalization is as follows:
step 303, determining the final weight by the following formula:
and alpha is an influence factor of subjective weight, and is determined according to the trust degree of the expert and the accuracy of the obtained target data.
Further, the specific calculation mode of the modeling synthesis vector in the step 4 is as follows:
wherein ,is a fuzzy synthesis operation;
the fuzzy synthetic vector for the kth object is:
wherein ,wn As the final weight corresponding to index n, einstain operatorThe operation process of (1) is as follows:
compared with the prior art, the invention has the following advantages: the invention avoids the defect of strong subjectivity of the weight coefficient by clustering combination weighting, fully and organically combines a qualitative method and a quantitative method, has simple and clear calculation, and can fully assist a commander in threat assessment.
Drawings
FIG. 1 is a flow chart of a method for evaluating threat of an air attack target according to the present invention.
FIG. 2 is a graph comparing the evaluation results of the present invention.
Detailed Description
The following describes the method of the present invention in detail with reference to simulation.
As shown in fig. 1, a method for evaluating an air attack target threat based on clustering combination weighting comprises the following steps:
step 1, selecting threat assessment indexes: including target navigation path shortcuts, flying heights, flying speeds and flying times; the target route shortcut is the horizontal projection distance from the guard target to the air attack target route, the flying height and the flying speed are the flying height and the flying speed of the air attack target respectively, and the flying time is the shortest time for the air attack target to fly to the guard target;
step 2, constructing a threat membership function and a membership matrix: defining a corresponding threat membership function according to index meanings, quantifying the threat degree of each index of each target, and constructing a threat assessment membership matrix of multiple targets and multiple indexes; the method specifically comprises the following steps:
the threat membership function is constructed specifically as follows:
determining a path shortcut threat membership function: selecting the horizontal projection distance from the guard target to the air attack target channel as a channel shortcut, wherein the smaller the channel shortcut is, the higher the threat degree is, when the channel shortcut is 0, the attack intention of the target is strongest, the possibility of damaging the guard target is largest, and the threat value is 1 at the maximum; defining the path shortcut threat membership function as:
wherein k is a set value, the value of this embodiment is 5×10 -3 P is a navigation path shortcut, and the unit is km;
flight height threat membership function determination: the target threat value is inversely related to the flying height, and when the target flying is lower than the set height, the threat value is maximally 1; defining a fly height threat membership function as:
wherein k is a set value, and the value of this embodiment is 10 -8 H is the flying height and the unit is m;
and (3) determining a flight speed threat membership function: the greater the flying speed of the air attack target, the greater the resistance difficulty and the higher the threat degree; defining a flight speed threat membership function as:
μ(v)＝1-e -αv ,0<v≤3000
wherein alpha is a set value, the value of the embodiment is-0.005, v is a target flying speed, and the unit is m/s;
and (3) determining a flight time threat membership function: the shorter the flying time of the air attack target is, the greater the threat degree is; when the target deviates from or deviates from flying, the flying time is longer than the distant time, and the threat degree is smaller, so that the flying time reflects two conditions of the adjacent flying and the distant flying at the same time, wherein the time of the adjacent flying takes a positive value and the time of the distant flying takes a negative value; defining a flight time threat membership function as follows:
wherein ,k1 and k2 All are set values, this embodiment k 1 ＝2×10 -6 ，k 2 ＝10 -7 T is the flying time, unit s;
the threat assessment membership matrix for constructing the multi-target multi-index is specifically as follows:
giving membership x to the ith index to the kth target by threat membership function ki And a membership vector x corresponding to the target k The method comprises the following steps:
x k ＝(x k1 x k2 … x kn )
further constructing threat assessment membership matrixes of m targets:
wherein k is more than or equal to 1 and less than or equal to m, m is the target number, and n is the number of indexes.
Step 3, threat index weighting: the subjective weight is determined through the clustering weighting of the group AHP, the objective weight is determined through the weighting of the mutation coefficient method, and finally the final index weight is obtained through subjective and objective synthesis; the method specifically comprises the following steps:
step 301, performing index weighting by adopting a group AHP clustering weighting method, namely performing index evaluation by a plurality of experts; wherein, the experience weight is determined by gray correlation analysis, and the category weight is determined by cluster analysis;
the method for determining the experience weight is as follows:
(1) Let the test vector of a given scene constitute a reference sequence vector X 0 ＝(x 0 (1),x 0 (2),…,x 0 (n)) T S experts participate in the evaluation, and the result vector given by the jth expert forms a comparison sequence vector as follows:
X j ＝(x j (1),x j (2),…,x j (n)) T
the s +1 vectors form the following matrix:
wherein n is the number of indexes, j is more than or equal to 1 and less than or equal to s;
(2) The absolute value matrix is calculated as:
wherein ,Δj (i)＝|x 0 (i)-x j (i) The I is that the j expert gives the absolute difference value of the i index and the test vector index, i is more than or equal to 1 and less than or equal to n; j is more than or equal to 1 and less than or equal to s;
for the maximum value of each row of the matrix Δ, the component maximum vector is:
for the minimum value of each row of the matrix Δ, the component minimum value vector is:
(3) Calculating a correlation coefficient and a correlation degree;
for each term in the matrix delta, calculating the association coefficient, wherein the association coefficient of the ith index given by the jth expert is as follows:
the association degree of the result vector of each expert and the test vector is obtained through an association coefficient, and the calculation formula of the association degree is as follows:
wherein ρ is a resolution coefficient, i is not less than 1 and not more than n, j is not less than 1 and not more than s, n is the number of indexes, and s is the number of experts;
(4) The experience weight of the j-th expert is obtained through the association degree:
the determination method of the category weight is as follows:
(1) The j-th expert gives a judgment matrix under a certain criterion layer as follows:
judgment matrix A of jth expert j The feature vector corresponding to the maximum feature value of (a) is the index sorting vector:
(2) Calculating a j-th expert index ranking vector U by adopting Euclidean distance j Similarity degree with other expert's ranking index vectors; judging the similarity degree and the class-class difference degree between the two sorting vectors according to the Euclidean distance, and classifying the two sorting vectors into one class when the distance is smaller than a critical value;
suppose that there is ζ in the q-th class where the j-th expert is located q The weight of the q-th class expert is:
wherein, q is more than or equal to 1 and less than or equal to z, and z is the number of classifications;
(3) The weight in the class of the jth expert in the q-th class is as follows:
wherein b is a set value, CR j CR is a consistency ratio j Judgment matrix A according to jth expert j The maximum characteristic value of (2) is calculated by the following steps:
wherein lambda is the judgment matrix A j Is the maximum eigenvalue of (2);
(4) The category weight of the jth expert is:
c j ＝λ q *z j
wherein ,λq Weighting, z, the class q expert j The weight in the class of the jth expert in the q-th class;
the final subjective weight of the jth expert is:
ψ j ＝βγ j +(1-β)c j
wherein, beta is an adjustment coefficient;
the subjective weight vector of the comprehensive obtained index is as follows:
step 302, weighting and determining objective weights by adopting a coefficient of variation method:
(1) Calculating the mean and variance of the ith index:
wherein m is the target number, x ki Calculating index resolution capability for the membership degree of the kth target belonging to the ith index;
(2) The resolving power of calculating the i-th index is as follows:
(3) The index objective weight vector obtained by normalization is as follows:
step 303, determining the final weight by the following formula:
and alpha is an influence factor of subjective weight, and is determined according to the trust degree of the expert and the accuracy of the obtained target data.
Step 4, fuzzy synthesis and comprehensive evaluation: and (3) selecting a nonlinear Einstain operator to perform fuzzy synthesis on the threat assessment membership matrix obtained in the step (2) and the final index weight obtained in the step (3), calculating a fuzzy synthesis vector and sequencing threat degrees. The specific calculation mode of the fuzzy synthetic vector is as follows:
wherein ,is a fuzzy synthesis operation;
the fuzzy synthetic vector for the kth object is:
wherein ,wn As the final weight corresponding to index n, einstain operatorThe operation process of (1) is as follows:
examples:
suppose that in a combat, 8 batches of air attack targets are found approaching the my guard target. The target parameters obtained by the reconnaissance information system are shown in table 1, and 7 commanders and experts participating in the command decision are total. The matrix of result vectors for a given test vector and expert is:
TABLE 1 target parameters
A membership matrix is constructed and membership of the target is calculated according to the membership function in the present invention as shown in table 2.
TABLE 2 threat membership
(2) Calculating index weights
Firstly, calculating expert experience weight, and obtaining an association coefficient matrix of 7 experts as a matrix formed by a test vector and an expert result vector
The correlation degree between 7 experts and the test vector is:
(0.5566，0.5571，0.4853，0.6668，0.5821，0.7667，0.5306)
the obtained expert experience weight is as follows:
(0.1343，0.1344，0.1171，0.1609，0.1404，0.1850，0.1280)
and then calculating expert category weight, and sequentially comparing importance degrees of 4 indexes of flight time, flight speed, path shortcut and flight height by 7 commanders and experts according to characteristics of battlefield situations and guard targets, wherein the obtained judgment matrixes are respectively as follows:
the ranking vectors and the consistency ratios CR for the 7 decision makers and the experts were obtained according to the eigenvalue method, as shown in table 3.
TABLE 3 expert evaluation case
And then, calculating Euclidean distances of 7 decision makers and expert sequencing vectors, and establishing a distance matrix M.
Taking the threshold r=0.048, according to the distance matrix, the clustering result can be obtained as follows:
A＝{1,2,3,7}
B＝{4,5}
C＝{6}
the weights of the three classes of experts are respectively obtained as follows:
λ A ＝0.7619,λ B ＝0.1905,λ C ＝0.0476
the weight of each expert in each class is calculated as
λ 1 ＝0.1599,λ 2 ＝0.2098,λ 3 ＝0.1917,λ 4 ＝0.0857,λ 5 ＝0.1048,λ 6 ＝0.0476,λ 7 The final weights for each expert given by = 0.2005 are:
{0.1471，0.1721，0.1544，0.1233，0.1226，0.1163，0.1643}
the subjective weight of the index is calculated as follows:
η＝{0.5707，0.2435，0.1207，0.0651}
the objective weight is calculated by a coefficient of variation method as follows:
taking α=0.5, i.e. subjective factors and objective factors have the same influence, and calculating the comprehensive weight as follows:
W＝{0.3635，0.2898，0.1480，0.1987}
(3) Fuzzy synthesis and comprehensive evaluation
The target threat result is obtained through fuzzy synthesis:
B＝{0.873，0.717，0.938，0.557，0.339，0.638，0.591，0.482}
the target threat degree sequencing is obtained as follows:
X 3 >X 1 >X 2 >X 6 >X 7 >X 4 >X 8 >X 5
the sequencing result shows that among the 8 batches of air attack targets, the target 3 has the greatest threat degree, the target 5 has the smallest threat degree, and the obtained evaluation result accords with the actual situation.
For comparative analysis, in the constructed target threat assessment model, the threat value ranking result of the target is calculated by using the index weight obtained by a single expert and the objective weight obtained by using a coefficient of variation method.
The evaluation result obtained by using the variation coefficient weight is:
B＝{0.880，0.716，0.943，0.663，0.422，0.710，0.601，0.540}
the target threat degree sequencing is obtained as follows:
X 3 >X 1 >X 2 >X 6 >X 4 >X 7 >X 8 >X 5
the evaluation result obtained by selecting the weight of the expert 6 is as follows:
B＝{0.869，0.701，0.930，0.420，0.210，0.535，0.581，0.397}
the obtained target threat degree sequence is as follows:
X 3 >X 1 >X 2 >X 7 >X 6 >X 4 >X 8 >X 5
the evaluation results of the 3 methods are shown in fig. 2. As can be seen by comparing the evaluation results of the method and the single expert empowerment in the text, the evaluation results of the 2 methods are basically consistent, but the evaluation of the target 6 and the target 7 is different, and the analysis of the air condition data of the target 6 and the target 7 can be seen that the flying speed and the air path shortcut of the target 6 are both larger than those of the target 7, and the target 6 is flying far away currently, but the time is very short, and the high speed of the target 6 has larger threat if suddenly turns back to be flying nearby, so that the method meets the actual situation of a battlefield.
Comparing the evaluation results of the method and objective weighting herein, it can be seen that the evaluation results only differ between the targets 4 and 7, and that the analysis of the air condition data of 2 batches of targets can obtain that the threat level of the targets 7 flying nearby should be greater than that of the targets 4 flying far away under the condition that the flight speed, the path shortcuts and the flight height of 2 batches of targets are not great. According to comparison analysis, the method can better integrate experience intention and battlefield objective data of decision makers and experts, determine more reasonable index weight coefficients and enable threat assessment and sequencing results to be more reliable.
Claims (4)
1. A method for evaluating the threat of an air attack target based on clustering combination weighting is characterized by comprising the following steps:
step 1, selecting threat assessment indexes: including target navigation path shortcuts, flying heights, flying speeds and flying times; the target route shortcut is the horizontal projection distance from the guard target to the air attack target route, the flying height and the flying speed are the flying height and the flying speed of the air attack target respectively, and the flying time is the shortest time for the air attack target to fly to the guard target;
step 2, constructing a threat membership function and a membership matrix: defining a corresponding threat membership function according to index meanings, quantifying the threat degree of each index of each target, and constructing a threat assessment membership matrix of multiple targets and multiple indexes;
step 3, threat index weighting: the subjective weight is determined through the clustering weighting of the group AHP, the objective weight is determined through the weighting of the mutation coefficient method, and finally the final index weight is obtained through subjective and objective synthesis;
step 4, fuzzy synthesis and comprehensive evaluation: and (3) selecting a nonlinear Einstain operator to perform fuzzy synthesis on the threat assessment membership matrix obtained in the step (2) and the final index weight obtained in the step (3), calculating a fuzzy synthesis vector and sequencing threat degrees.
2. The method for evaluating the threat of the air attack target based on the clustering combination weighting as set forth in claim 1, wherein the step 2 specifically includes the following steps:
the threat membership function is constructed specifically as follows:
determining a path shortcut threat membership function: selecting the horizontal projection distance from the guard target to the air attack target channel as a channel shortcut, wherein the smaller the channel shortcut is, the higher the threat degree is, when the channel shortcut is 0, the attack intention of the target is strongest, the possibility of damaging the guard target is largest, and the threat value is 1 at the maximum; defining the path shortcut threat membership function as:
wherein k is a set value, and p is a navigation path shortcut;
flight height threat membership function determination: the target threat value is inversely related to the flying height, and when the target flying is lower than the set height, the threat value is maximally 1; defining a fly height threat membership function as:
wherein k is a set value, and h is a flying height;
and (3) determining a flight speed threat membership function: the greater the flying speed of the air attack target, the greater the resistance difficulty and the higher the threat degree; defining a flight speed threat membership function as:
μ(v)＝1-e -αv ,0<v≤3000
wherein alpha is a set value, and v is a target flying speed;
and (3) determining a flight time threat membership function: the shorter the flying time of the air attack target is, the greater the threat degree is; when the target deviates from or deviates from flying, the flying time is longer than the distant time, and the threat degree is smaller, so that the flying time reflects two conditions of the adjacent flying and the distant flying at the same time, wherein the time of the adjacent flying takes a positive value and the time of the distant flying takes a negative value; defining a flight time threat membership function as follows:
wherein ,k1 and k2 Are set values, and t is the flying time;
the threat assessment membership matrix for constructing the multi-target multi-index is specifically as follows:
giving the ith finger to the kth target by threat membership functionSubject membership degree x ki And a membership vector x corresponding to the target k The method comprises the following steps:
x k ＝(x k1 x k2 … x kn )
further constructing threat assessment membership matrixes of m targets:
wherein, k is more than or equal to 1 and less than or equal to m, m is the target number, i is more than or equal to 1 and less than or equal to n, and n is the number of indexes.
3. The method for evaluating the threat of the air attack target based on the clustering combination weighting as claimed in claim 2, wherein the step 3 specifically comprises the following steps:
step 301, performing index weighting by adopting a group AHP clustering weighting method, namely performing index evaluation by a plurality of experts; wherein, the experience weight is determined by gray correlation analysis, and the category weight is determined by cluster analysis;
the method for determining the experience weight is as follows:
(1) Let the test vector of a given scene constitute a reference sequence vector X 0 ＝(x 0 (1),x 0 (2),…,x 0 (n)) T S experts participate in the evaluation, and the result vector given by the jth expert forms a comparison sequence vector as follows:
X j ＝(x j (1),x j (2),…,x j (n)) T
the s +1 vectors form the following matrix:
wherein n is the number of indexes, j is more than or equal to 1 and less than or equal to s;
(2) The absolute value matrix is calculated as:
wherein ,Δj (i)＝|x 0 (i)-x j (i) The I is that the j expert gives the absolute difference value of the i index and the test vector index, i is more than or equal to 1 and less than or equal to n; j is more than or equal to 1 and less than or equal to s;
for the maximum value of each row of the matrix Δ, the component maximum vector is:
for the minimum value of each row of the matrix Δ, the component minimum value vector is:
(3) Calculating a correlation coefficient and a correlation degree;
for each term in the matrix delta, calculating the association coefficient, wherein the association coefficient of the ith index given by the jth expert is as follows:
the association degree of the result vector of each expert and the test vector is obtained through an association coefficient, and the calculation formula of the association degree is as follows:
wherein ρ is a resolution coefficient, i is not less than 1 and not more than n, j is not less than 1 and not more than s, n is the number of indexes, and s is the number of experts;
(4) The experience weight of the j-th expert is obtained through the association degree:
the determination method of the category weight is as follows:
(1) The j-th expert gives a judgment matrix under a certain criterion layer as follows:
judgment matrix A of jth expert j The feature vector corresponding to the maximum feature value of (a) is the index sorting vector:
(2) Calculating a j-th expert index ranking vector U by adopting Euclidean distance j Similarity degree with other expert's ranking index vectors; judging the similarity degree and the class-class difference degree between the two sorting vectors according to the Euclidean distance, and classifying the two sorting vectors into one class when the distance is smaller than a critical value;
suppose that there is ζ in the q-th class where the j-th expert is located q The weight of the q-th class expert is:
wherein, q is more than or equal to 1 and less than or equal to z, and z is the number of classifications;
(3) The weight in the class of the jth expert in the q-th class is as follows:
wherein b is a set value, CR j CR is a consistency ratio j Judgment matrix A according to jth expert j The maximum characteristic value of (2) is calculated by the following steps:
wherein lambda is the judgment matrix A j Is the maximum eigenvalue of (2);
(4) The category weight of the jth expert is:
c j ＝λ q *z j
wherein ,λq Weighting, z, the class q expert j The weight in the class of the jth expert in the q-th class;
the final subjective weight of the jth expert is:
ψ j ＝βγ j +(1-β)c j
wherein, beta is an adjustment coefficient;
the subjective weight vector of the comprehensive obtained index is as follows:
step 302, weighting and determining objective weights by adopting a coefficient of variation method:
(1) Calculating the mean and variance of the ith index:
wherein m is the target number, x ki Calculating index resolution capability for the membership degree of the kth target belonging to the ith index;
(2) The resolving power of calculating the i-th index is as follows:
(3) The index objective weight vector obtained by normalization is as follows:
step 303, determining the final weight by the following formula:
and alpha is an influence factor of subjective weight, and is determined according to the trust degree of the expert and the accuracy of the obtained target data.
4. The method for evaluating the air attack target threat based on clustering combination weighting according to claim 3, wherein the specific calculation mode of the modeling synthetic vector in the step 4 is as follows:
wherein ,is a fuzzy synthesis operation;
the fuzzy synthetic vector for the kth object is:
wherein ,wn As the final weight corresponding to index n, einstain operatorThe operation process of (1) is as follows:
。
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