A Dynamic Decision-making Method for Solving the Complexity of Attribute Weights and Time Weights

Abstract

The present invention discloses a dynamic decision-making method for solving the complexity of attribute weight and time weight, comprising: extracting decision information of each target fighter according to the battlefield environment; converting the attribute information of the target fighter into the decision information of each target fighter at different time t k The interval intuitionistic fuzzy matrix is used to obtain the decision matrix #imgabs0#. The deviation maximization method is used to obtain the attribute weight w(t) of each target fighter; the data aggregation operator IVIFPWGA is used to aggregate the different time t k The elements #imgabs2# in the decision matrix #imgabs1# are aggregated to obtain the T of each enemy fighter. i At different times t k The comprehensive interval intuitive fuzzy value #imgabs3# is obtained by the superior and inferior solution distance method TOPSIS to obtain the time weight vector λ(t); the data aggregation operator DIVIFPWGA is used to obtain the T of each enemy fighter i At each moment t k The comprehensive interval intuitive fuzzy value #imgabs4# obtains the score function #imgabs6# and the accuracy function #imgabs7# of the comprehensive interval intuitive fuzzy value #imgabs5#, sorts the score function #imgabs8#, and obtains the decision result. This method improves the reliability of the decision result, effectively reduces the time complexity of the algorithm, and can more accurately assess the threat of air combat targets.

Description

Technical Field

[0001] The present invention relates to the technical field of air combat threat assessment, and particularly to a dynamic decision-making method for solving the complexity of attribute weights and time weights. Background Art

[0002] In air combat, due to the time-varying nature of the decision-making process and the continuous changes in attributes such as the flight speed and angle of the fighter aircraft, a large amount of uncertain information is involved in the decision-making process. To obtain a more accurate evaluation result, domestic and foreign scholars have conducted extensive research on dynamic multi-objective decision-making, evolving from initially relying on target information at a single moment to making decisions based on the data changes of each target over a period of time. Most existing decision-making operators are based on the representation of static relationships between attributes and are difficult to express the correlation between decision-making data at different times. At the same time, in terms of solving time weights, most existing methods rely on subjective settings, ignoring objective factors, and the rationality of time weight settings is poor; moreover, the subjective preferences of decision-makers are ignored, making it difficult to reflect the preference information at different times. Summary of the Invention

[0003] Aiming at the problem of air combat threat assessment, the present application provides a dynamic decision-making method for solving the complexity of attribute weights and time weights, which improves the reliability of decision-making results, effectively reduces the time complexity of the algorithm, and can more accurately evaluate the threat of air combat targets.

[0004] To achieve the above object, the technical solution of the present application is: a dynamic decision-making method for solving the complexity of attribute weights and time weights, including:

[0005] Extract the decision-making information of each target fighter according to the battlefield environment;

[0006] Convert the attribute information of the target fighter into an interval-valued intuitionistic fuzzy matrix at different times t k to obtain a decision matrix

[0007] Use the deviation maximization method to obtain the attribute weight w(t) of each target fighter;

[0008] Utilize the data aggregation operator IVIFPWGA to aggregate the elements k in the decision matrix at different times t to obtain the comprehensive interval-valued intuitionistic fuzzy value i of each enemy fighter T k at different times t

[0009] Obtain the time weight vector λ(t) through the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS);

[0010] Use the data aggregation operator DIVIFPWGA to aggregate the comprehensive interval intuitionistic fuzzy values at different times t k to obtain the comprehensive interval intuitionistic fuzzy values of each enemy warplane T at each time t i k k 1

[0011] Obtain the score function and accuracy function of the comprehensive interval intuitionistic fuzzy value

[0012]

[0013] Sort the score function to obtain the decision result

[0014] Furthermore, convert the target warplane attribute information into an interval intuitionistic fuzzy matrix at different times t k to obtain the decision matrix Specifically

[0015] Let the target warplane set T = {T 1 , T 2 ,..., T n}, and the attribute sets such as speed and angle G = {G 1 , G 2 ,..., G m}. By collecting the attribute information of each target warplane at each time t k the decision matrix Let the time vector be: λ(t k ) = (λ(t 1 ), λ(t 2 ),..., λ(t p )) T , satisfying The attribute weight is ω(t k ) = (ω 1 (t k ), ω 2 (t k ),..., ω m (t k )) T , and satisfying ω j (t k ) ∈ [0, 1] and

[0016] Furthermore, the data aggregation operator IVIFPWGA converts the target fighter information into elements in the decision matrix for aggregation, obtaining the comprehensive interval intuitionistic fuzzy values of each enemy fighter at different times: Let be the interval-valued intuitionistic fuzzy numbers of the attributes of a group of enemy fighters. The definition of the data aggregation operator IVIFPWGA is as follows:

[0017]

[0018]

[0019] is the normalized Hamming distance between two interval-valued intuitionistic fuzzy numbers.

[0020] Furthermore, the data aggregation operator DIVIFPWGA utilizes the nonlinear property of the power weighted geometric mean operator to connect the interrelationships of the aggregated data: Suppose the enemy fighters have m attributes such as speed, angle, and distance. is for t 1 , t 2 ,..., t p the attribute value of the jth (j = 1, 2,..., m) attribute at time, where is represented by an interval intuitionistic fuzzy number. Meanwhile, λ(t) = (λ(t 1 ), λ(t 2 ),..., λ(t p )) T is the time weight vector for each period and satisfies λ(t k ) ≥ 0, and k = 1, 2,..., p; then the data aggregation operator DIVIFPWGA is:

[0021]

[0022] In the existing algorithms, when the aggregation operator processes dynamic decision-making problems, it is difficult to describe the fuzzy characteristics of the decision-making information; at the same time, the existing weighted average operator does not consider the relationships between the aggregated air combat data. For this reason, the DIVIFPWGA operator is proposed, which can be used to handle dynamic interval-valued intuitionistic fuzzy multi-attribute decision-making problems with interrelationships.

[0023] Furthermore, the attributes of the target fighter mainly include air combat ability, distance, speed, and angle, and their weights are closely related to the importance of the attributes themselves. The fuzzy distance is used to measure the deviation between the air combat target attributes and other attributes. The smaller the deviation value, the smaller the contribution value of the attribute in the decision-making process, and the corresponding weight should be smaller; conversely, the larger the deviation value, the larger the contribution value of the attribute in the decision-making process, and the corresponding weight is larger. According to the above description, when the weights of the target fighter attributes are completely unknown, the maximum deviation model is as follows:

[0024]

[0025] Among them, D(ω) represents the total deviation of all attributes between all target fighter planes and other fighter planes. represents the Hamming distance between two air combat targets under any two attributes; since the attribute values of the target fighter plane are in the form of interval-valued intuitionistic fuzzy numbers, the commonly used Hamming distance is selected to measure the distance between interval-valued intuitionistic fuzzy numbers.

[0026]

[0027] To solve the maximum deviation model, the Lagrangian function is constructed as follows:

[0028]

[0029] Taking the partial derivative of Equation (5), the attribute weights of the target fighter plane are obtained:

[0030]

[0031] Furthermore, the time weight vector λ(t) is obtained by the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS). On the one hand, this method integrates the decision maker's preference for time information; on the other hand, since the vector characteristics of the time weights are relatively obvious, the Dice similarity coefficient is used instead of the Euclidean distance to determine the closeness of the actual time weights to the positive and negative ideal solutions. Specifically:

[0032] Let λ(t k )=(λ(t 1 ),λ(t 2 ),...,λ(t p )) T be the time series weight vector, representing the importance of different time points, and satisfying λ(t k )∈[0,1]. Let where θ∈[0,1] represents the preference degree of the pilot of our fighter plane, i.e., the decision maker, for the time series, and its value is set according to the decision maker's experience and preference; the closer θ is to 0, the more the decision maker prefers the current moment; the closer θ is to 1, the more the decision maker prefers historical information. Using the principle of maximizing information entropy, an (M - 1) non-linear model is established:

[0033]

[0034] When λ(t k )=(0,0,....,1) T , θ = 0, indicating that the decision maker completely prefers recent decision information. Denote the positive ideal solution of the time weight as: λ(tk ) + =(0, 0,...., 1) T ; when λ(t k )=(1, 0,...., 0) T At this time, θ = 1, indicating that the decision - maker completely prefers the previous - period data. Denote the negative ideal solution of the time weight as: λ(t k ) - =(1, 0,...., 0) T ; The similarity degree between the time - weight vector and the positive and negative ideal solutions is:

[0035]

[0036]

[0037] Then the correlation coefficient c between the time - weight vector and the ideal solution is:

[0038]

[0039] where S = s(λ(t k ), λ(t k ) + ) + s(λ(t k ), λ(t k ) - )

[0040] Furthermore, establish the (M - 2) non - linear model:

[0041]

[0042] To make the time - weight value include both subjective preference and objective reality, combine (M - 1) and (M - 2) to give the (M - 3) non - linear model:

[0043]

[0044] Obtain the time - weight vector by solving equation (12); where q is the balance coefficient of the two non - linear models, satisfying q ∈ [0, 1], and is determined by different decision - makers; the closer q is to 1, the more the time - weight set by the decision - maker tends to subjective preference; the closer q is to 0, the more the time - weight set by the decision - maker tends to objective reality.

[0045] Furthermore, the comprehensive interval intuitionistic fuzzy value of each enemy fighter T i at different times t k is: For:

[0046]

[0047] As a further step, for each enemy fighter T i at each moment t k the comprehensive interval intuitionistic fuzzy value

[0048]

[0049] As a further step, obtain the score function of the comprehensive interval intuitionistic fuzzy value and the accuracy function Specifically: for any interval-valued intuitionistic fuzzy number there is:

[0050]

[0051]

[0052] wherein,

[0053] For any two interval intuitionistic fuzzy numbers and satisfy:

[0054]

[0055] When increases, the corresponding interval intuitionistic fuzzy number becomes larger.

[0056] Due to the adoption of the above technical solutions, the present invention can achieve the following technical effects: The present invention uses the IVIFPWGA operator and the DIVIFPWGA operator to solve the correlation problem of decision-making data at different times, and at the same time designs a method for solving the time weights of TOPSIS based on time series preferences, which not only considers the fuzzy uncertainty of air combat targets but also considers the dynamic characteristics of enemy fighter information. Through the proposed dynamic decision-making method, the complexity of attribute weights and time weights is solved, the reliability of decision-making results is improved, the time complexity of the algorithm is effectively reduced, and the threat assessment of air combat targets can be more accurately carried out, meeting the requirements for threat assessment and dynamic decision-making in the battlefield environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 is a dynamic decision-making process diagram based on attribute weights and time weights;

[0058] Figure 2 is a comparison diagram of the sorting results of each target within the time from t 1 to t 4 ;

[0059] Figure 3It is a sensitivity analysis diagram of speed;

[0060] Figure 4 It is a sensitivity analysis diagram of angle;

[0061] Figure 5 It is a sensitivity analysis diagram of distance. Specific implementation manners

[0062] The embodiments of the present invention are implemented on the premise of the technical solution of the present invention, and detailed implementation manners and specific operation processes are given, but the protection scope of the present invention is not limited to the following embodiments.

[0063] Such as Figure 1 As shown, this embodiment provides a dynamic decision-making method for solving the complexity of attribute weights and time weights. To verify the feasibility and effectiveness of the present invention, threat assessments of air combat targets, impact analysis of time factors on decision-making results, and sensitivity analysis experiments of attribute parameters are carried out.

[0064] (1) Threat assessment experiment of air combat targets

[0065] Taking the threat assessment of air combat targets as an example, the target attributes mainly include air combat ability, distance, speed, and angle, corresponding to the threat degrees of air combat ability, distance, speed, and angle.

[0066] Threat degree of air combat ability. The air combat ability can be divided into 5 levels from strong to weak, and the threat level of the target's air combat ability is represented in the form of interval intuitionistic fuzzy, as shown in Table 1.

[0067] Table 1

[0068]

[0069] Threat degree of distance. By the distance of the target from us, the attack intention of the enemy and the probability of successful attack are judged. Of course, the closer the target is, the greater the threat to us; on the contrary, the threat is smaller. The interval intuitionistic fuzzy form of the threat degree of distance is:

[0070]

[0071] Threat degree of speed. The target speed is directly related to the length of the reaction time of the weapon system and the size of the damage probability. The faster the target speed, the greater the impact on us and the greater the threat. The interval intuitionistic fuzzy form of the threat degree of speed is:

[0072]

[0073] Angle threat level. The target attack angle can be the magnitude of the perpendicular distance from the protected area of our side to the extension line of the projection of the instantaneous velocity of the air raid target on the horizontal plane. A larger attack angle means less threat. The interval intuitive fuzzy form of the angle threat level is as follows:

[0074]

[0075] where k i , l i , a i , β i , and γ i are determined by the accuracy of each attribute data information and the engagement environment, satisfying 0 ≤ k i + l i ≤ 1, 0 ≤ a i + β i ≤ 1,

[0076] After the above process, the threat assessment of each target can be transformed into the target threat assessment under the interval intuitionistic fuzzy condition. There are 4 fighter jets as an example, T = {T 1 , T 2 , T 3 , T 4}, the distance threat degree parameter k = 0.7, l = 0.2, the speed threat degree parameter α = 0.7, β = 0.3, and the angle threat degree parameter γ = 0.2. The data is shown in Table 2. t 1 - t 4 are the data information of four adjacent times, and t 4 is the latest data. Use the dynamic decision-making method of the present invention to complete the target threat ranking analysis. First, calculate the interval intuitionistic fuzzy matrix of each corresponding target with reference to Table 1 and Table 2, as shown in Table 3. According to the above formula, the attribute weight θ = 0.3 and the time weight q = 0.5 are obtained. Then, use the IVIFPWGA operator to reorganize the elements in . Next, use the DIVIFPWGA operator to aggregate the comprehensive interval intuitionistic fuzzy of different times to obtain the intuitionistic fuzzy comprehensive interval of each target. Finally, calculate the score function and accuracy function of the 4 fighter jets. Based on the above function values, the evaluation result is: Target2 > Target 3 > Target 4 > Target 1.

[0077] Table 2

[0078]

[0079] Table 3

[0080]

[0081]

[0082] (2) Experimental analysis of the influence of time factors on decision-making results

[0083] Figure 2 For the ranking result comparison and analysis of each target within t 1 -t 4 time. It can be seen from Figure 2 that the threat of the same target changes continuously within a period of time, and the order of the targets is the same at different times, but the magnitude of the threat may be different. The static evaluation method that only considers a single time may not ideally exhibit the dynamic characteristics. For example, only considering time t 4 The obtained threat assessment result is: Target 2>Target 1>Target 3>Target 4, while the dynamic assessment result obtained by the method of the present invention is: Target 2>Target 3>Target 4>Target 1. This is because the method proposed in this invention not only considers the decreasing trend of the speed, angle and distance threats of Target 4 during the whole evaluation process, but also considers the sudden increase in the speed, angle and distance threats of Target 3. Therefore, the obtained threat assessment result is more reliable.

[0084] To illustrate the advantages of the method proposed in the present invention, the dynamic evaluation results are compared at time t 4 and compared with the results in [Literature: Y.Zhang, Q.Feng, D.Zhou, Dynamic Multi-attribute Threat Assessment forAirCombat Based on Intuitionistic Fuzzy Set.Electronics Optics&Control.2015.]. The target with the highest threat achieved by the present invention is consistent with the target achieved by other methods, which shows the correctness of the method in this paper. Generally speaking, the ranking results obtained by the three methods are different. Only dealing with t 4The threat information of each target at a moment, and the obtained target threat assessment result has instantaneity. In other methods, the threat assessment of each target is set to be dynamic, which can reflect the time and battlefield situation changes of each target. However, the relationship between data is not considered in information processing, and only a simple solution of weights is given. This invention reflects the dynamic characteristics of the target, uses the power-weighted geometric mean operator to connect the correlation between data, and considers the accuracy of weights at the same time. Therefore, the obtained threat assessment result can become more reliable; at the same time, compared with other methods, it has a slight advantage in processing time, and the running time is also reduced by 3.01%.

[0085] (3) Sensitivity analysis experiment of attribute parameters

[0086] To analyze the influence degree of the interval intuitionistic fuzzy set on the fuzzy uncertainty degree in the decision-making process of each target under each attribute, the sensitivity analysis of attribute parameters is carried out below. By slightly adjusting the membership degree and non-membership degree ranges of the intuitionistic fuzzy numbers of each target with corresponding attributes, the adjustment formula is:

[0087]

[0088] where q = -Δσ l / h,...,-1,0,1,...,Δσ l / h, h is used as the step size, and the change intervals of the membership degree and non-membership degree of the four attributes are Here, the change intervals of the membership degree and non-membership degree are selected as By changing the speed, angle, and distance of the target in turn, the sensitivity analysis corresponds to Figure 3 、 Figure 4 and Figure 5 shown.

[0089] Generally speaking, when the interval intuitionistic fuzzy values under different attributes change slightly, although it does not have a great impact on the final ranking, the responses of the 4 targets to the changes of different attributes are different. The coping strategies for different targets can be analyzed through the response degrees of different targets to the changes of each attribute.

[0090] From Figure 3 it can be seen that the responses of each target to the change of speed are generally stable; it shows that in terms of speed, each target is evenly matched, and the threat degree to us changes little with the change of the membership degree and non-membership degree. From Figure 4It can be seen that Target 4 is relatively sensitive to the change of the course, and as the membership degree in the intuitionistic fuzzy value of the course interval increases, the score function value decreases; this indicates that the threat level of Target 4 to our side shows a downward trend as the course membership degree increases. As can be seen from Figure 5, Target 4 is relatively sensitive to the change of the distance. As the intuitionistic fuzzy value of the distance interval changes, the score function value shows a trend of first rising slightly and then decreasing overall; this indicates that the change of Target 4 in terms of distance poses a relatively small threat to our side.

[0091] The foregoing description of the specific exemplary embodiments of the present invention is for purposes of illustration and exemplification. These descriptions are not intended to limit the present invention to the precise forms disclosed, and obviously, many changes and variations are possible in light of the above teachings. The purpose of selecting and describing the exemplary embodiments is to explain the specific principles of the present invention and its practical applications, so that those skilled in the art can implement and utilize various different exemplary embodiments of the present invention, as well as various different selections and changes. The scope of the present invention is intended to be defined by the claims and their equivalents.

Claims

1. A dynamic decision-making method for solving the complexity of attribute weights and time weights, characterized in that, it includes: Extract the decision-making information of each target fighter according to the battlefield environment; Convert the target fighter attribute information into an interval intuitionistic fuzzy matrix at different times t k to obtain a decision matrix Use the deviation maximization method to obtain the attribute weight w(t) of each said target fighter; Using the data aggregation operator IVIFPWGA to aggregate the elements in the decision matrix k at different times t k Decision matrix in to obtain the comprehensive interval intuitionistic fuzzy values of each enemy fighter T i at different times t i at different times t k ​ Obtain the time weight vector λ(t) through the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS); Using the data aggregation operator DIVIFPWGA to aggregate the comprehensive interval intuitionistic fuzzy values at different times t k to obtain the comprehensive interval intuitionistic fuzzy values of each enemy aircraft T at each time t i k to obtain the comprehensive interval intuitionistic fuzzy values ​ Obtain the score function of the comprehensive interval intuitionistic fuzzy value and the accuracy function of Sort the score function to obtain a decision result; The decision matrix Specifically: Let the set of target fighter jets be \(T = \{T 1 , T 2 , \cdots, T n \}\), and the set of attributes be \(G = \{G 1 , G 2 , \cdots, G m \}\). By collecting the attribute information of each target fighter jet at each moment \(t k \), a decision matrix Let the time vector be: \(\lambda(t k )=( \lambda(t 1 ), \lambda(t 2 ), \cdots, \lambda(t p )) T , which satisfies The attribute weight is \(\omega(t k )=( \omega 1 (t k ), \omega 2 (t k ), \cdots, \omega m (t k )) T , and it satisfies \(\omega j (t_k)\in[0 , 1]\) and The data aggregation operator IVIFPWGA converts the target fighter information into elements in the decision matrix for aggregation, obtaining the comprehensive interval intuitionistic fuzzy values of each enemy fighter at different times: Let be the interval-valued intuitionistic fuzzy numbers of the attribute intervals of a group of enemy fighters. Then the definition of the data aggregation operator IVIFPWGA is as follows: is the normalized Hamming distance between two interval-valued intuitionistic fuzzy numbers; The data aggregation operator DIVIFPWGA utilizes the non - linear property of the power - weighted geometric mean operator to connect the inter - relationships of the aggregated data: Suppose there are m attributes of the enemy fighter jets. is t 1 , t 2 ,..., t p is the attribute value of the j - th (j = 1, 2,..., m) attribute at time t, where is represented by the interval - valued intuitionistic fuzzy number, and at the same time, λ(t)=(λ(t 1 ), λ(t 2 ),..., λ(t p )) T is the time - weight vector of each period, and satisfies λ(t k )≥0, and k = 1, 2,..., p; then the data aggregation operator DIVIFPWGA is: When the attribute weights of the target fighters are completely unknown, the maximum deviation model is as follows: where D(ω) represents the total deviation value of all attributes between all target fighter jets and other fighter jets. represents the Hamming distance between two air combat targets under any two attributes: To solve the said maximum deviation model, construct the Lagrangian function as: Take the partial derivative of Equation (5) to obtain the attribute weights of the target fighters: Obtain the time weight vector λ(t) through the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS), specifically: Let λ(t k ) = (λ(t 1 ), λ(t 2 ),..., λ(t p )) T be the time - series weight vector, representing the importance at different time points, and satisfying λ(t k ) ∈ [0, 1]. Let where θ ∈ [0, 1], representing the preference degree of the pilot of our fighter plane, i.e., the decision - maker, for the time series. Its value is set according to the experience and preference of the decision - maker; the closer θ is to 0, the more the decision - maker prefers the current moment; the closer θ is to 1, the more the decision - maker prefers historical information. Establish a (M - 1) non - linear model using the principle of maximizing information entropy: When λ(t k ) = (0, 0,...., 1) T At this time, θ = 0, indicating that the decision maker completely prefers recent decision information. Denote the positive ideal solution of the time weight as: λ(t k ) + = (0, 0,...., 1) T ; When λ(t k ) = (1, 0,...., 0) T At this time, θ = 1, indicating that the decision maker completely prefers previous data. Denote the negative ideal solution of the time weight as: λ(t k ) - = (1, 0,...., 0) T ; The similarity degree between the time weight vector and the positive and negative ideal solutions is: Then the correlation coefficient c between the time weight vector and the ideal solution is: where S = s(λ(t k ), λ(t k )) + ) + s(λ(t k ), λ(t k )) - ).

2. The dynamic decision-making method for solving the complexity of attribute weights and time weights according to Claim 1, characterized in that, Establish the (M-2) non-linear model: To make the time weight value include both subjective preferences and objective reality, combine (M-1) and (M-2) to give the (M-3) non-linear model: Obtain the time weight vector by solving Equation (12); Where q is the balance coefficient of the two non-linear models, satisfying q ∈ [0, 1], which is determined by different decision-makers; the closer q is to 1, the more the time weight set by the decision-maker tends to subjective preferences; the closer q is to 0, the more the time weight set by the decision-maker tends to objective reality.

3. The dynamic decision-making method for solving the complexity of attribute weights and time weights according to Claim 1, characterized in that, Each enemy fighter plane T i At different times t k The comprehensive interval intuitionistic fuzzy value Is as follows:

4. The dynamic decision-making method for solving the complexity of attribute weights and time weights according to Claim 1, characterized in that, Each enemy fighter plane T i At each moment t k Comprehensive interval intuitionistic fuzzy value 5. The dynamic decision-making method for solving the complexity of attribute weights and time weights according to Claim 1, characterized in that, Obtain the score function of the comprehensive interval intuitionistic fuzzy value and the accuracy function Specifically: For any intuitionistic fuzzy number of interval values there is: There is: Among them, For any two interval intuitionistic fuzzy numbers and satisfy: When increases, the corresponding interval intuitionistic fuzzy number becomes larger.

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