1.Introduction

Most moderncombat situationsare cluster combats,which require the pilots to face the enemy multi-target.According to the air combat situation,the enemy target threat is to make a reasonable assessment,and improve the operational efficiency of multi-target attack and self-survival probability.Therefore,it is practically significant to review the threat assessment[1,2].

当摊铺好的混合料达到30m时，即可根据确定的碾压方案进行碾压。碾压分初压、复压、终压三个阶段，现场测温员负责设置碾压指示牌，指示牌交替向前，现场由专人负责记录碾压情况。

Since Zadeh put forward the fuzzy set[3]and applied it to multiple attribute decision making,the fuzzy multiattribute problem has been developed rapidly.Intuitionistic fuzzy sets[4]were proposed by the Bulgarian scholar Atanassov in1986.On the basis of conventional fuzzy sets,a new attribute parameter-hesitation,the nonmember ship function is added which can describe the characterization of fuzzy nature more precisely[5].Nowadays,intuitionistic fuzzy sets have attracted much attention.As the air combat process is dynamic and continuous,using a static data description method for processing air combat threat assessment can lead to loss of information in air combat situations before the current time.It is difficult for a continuous air combat situation to make objective and comprehensive analysis,resulting in the greatly reduced rationality of the assessment.Finally,many scholars used the technique for order of preference by similarity to ideal solution(TOPSIS)method[6]for threat assessment.The basic principle of the TOPSIS method is that the chosen alternative should have the“shortest distance”from the ideal solution and the “farthest distance”from the “negativeideal”solution.The TOPSIS method introduces two “reference”points,but it does not consider the relative importance of the distances from these points.The TOPSIS method uses vector normalization to eliminate the units of criterion functions.The normalized value of the TOPSIS method depends on the evaluation unit of a criterion function.The VlseKriterijumska Optimizacija I Kompromisno Resenje(VIKOR)method[7–10]of compromise ranking determines a compromise solution,providing a maximum“group utility”for the “majority”and a minimum of individual regret for the “opponent”.The VIKOR method avoids the shortcomings of the TOPSIS method which has very strong superiority[11].

Therefore,assessment and sequencing of air target threat based on intuitionistic fuzzy entropy(IFE)[12–14]and dynamic VIKOR are proposed in this study.The target attribute weight is calculated by the IFE algorithm which aims at combat information uncertainty.Time series weight is gained by the poison distribution method which aims at high dynamic enemy operations.The dynamic VIKOR threat assessment method is carried out to attain the air combat hybrid formation.A multi-target threat assessment model is established to improve the sci-entific rationality of multi-target threat assessment for air combat.

内生动力、益贫市场与政策保障：打好脱贫攻坚战实现“真脱贫”的路径框架…………………左 停 金 菁 于乐荣（47）

2.Alternative attribute weight determine based on IFE

2.1 Preliminaries

We assume a finite set[15,16]of possible alternatives X={xi}(i=1,2,...,m),a finite set of attributes according to the desirability judgment of alternatives A={ai}(j=1,2,...,n),and the time sequence T={tk}(k=1,2,...,p).

Definition 1 Let X be a finite universal set.An intuitionistic fuzzy set(IFS)A in X may be mathematically expressed as

where the functions μA:X → [0,1]and νA:X → [0,1].

Membership and non-membership degrees of an element are defined as x∈X to A∈X,respectively,in such a way that they satisfy the condition:0≤ μA(x)+νA(x)≤1,for any x∈X.

3)当1/π>Fr>1/(2π)时(这时层结稳定度有所加强),该大气波动不仅出现在地形附近,还出现在地形的下风方,其波长与地形的水平尺度无关,该波长仅取决于背景场,且波动向上仍有所减弱。

Definition 2 Let A={〈x,μA(x),vA(x)?|x ∈ X}and B={〈x,μB(x),vB(x)?|x ∈ X}be two IFSs in the set X and λ≥0,then

If|A|=1,i.e.,there is only one element x in A,then the IFS A usually is denoted by A= 〈μA(x)-νA(x)?for short.

Let γA(x)=1- μA(x)- νA(x),which is called the intuitionistic index of an element x in the IFS A.It is the degree of indeterminacy membership of the element x to A.Obviously 0≤γA(x)≤1.

The VIKOR method can be layered between individual attributes and all attributes,for example,in the combat threat assessment process,if the enemy has airborne warning and control system(AWACS),which has lower maneuvering ability but higher battle field situation control ability.The new threat level can be implemented by the VIKOR method while the TOPSIS method is incapable of action.At the same time,we can see that the result computed by TOPSIS is very close,it can cause various threats of almost all illusions.However,in order to facilitate the process of air combat prompt pilots through the VIKOR method,it can be more significant to reflect the extent of the differences between the various threats.

(ii)AB = {〈x,μA(x)μB(x),μA(x)+ μB(x)-μA(x)μB(x)?}

(iii)λA={〈x,1-(1- μA(x))λ,(μA(x))λ?}

(iv)Aλ ={〈x,(μA(x))λ,1-(1- μA(x))λ?}.

2.2 Alternative attribute weight determination

The IFE method uses probability theory as a mathematical tool of metric information.Overcome the effects of uncertain information by intuition and ambiguity,and the full measure of uncertain information of IFS through the establishment of the entropy minimization nonlinear programming model for solving the calculation of attribute weights.The algorithm is as follows:

Step 1 Construct the dynamic intuitionistic fuzzy decision matrix at time tk,as expressed in(2).

where fij(tk) = 〈μij(tk),νij(tk)?, μij(tk) ≥ 0,νij(tk) ≥ 0,and μij(tk)is the membership of alternative xiwith respect to attribute aiat the time tk,νij(tk)is the non-membership of alternative xiwith respect to attribute aiat the time tk.

The attribute weight can be calculated as(7).

Effect of different time points in air combat target data on threat assessment is not the same.Change of the air combat situation to make a comprehensive and objective assessment must be a different time point of time series empowerment.The actual combat process is closer at the moment and collected information of target threat assessment is more important.In this study,the weight of time series is calculated by an inverse form of the Poisson distribution.η =(η1,η2,...,ηp),

where ωj(tk)is the weight for attribute aiat the time tk.

Step 4 Compute the attribute weights: ω(tk) =(ω1(tk),ω2(tk),...,ωn(tk));and the Lagrange function is defined as(5).

Compute the partial derivative of(5)with respect to each variable,

Step 2 Calculate IFE at the time tk,according to(3).

3.Dynamic VIKOR method in decision making process

3.1 Time series weight determination based on Poisson distribution method

Step 3 The alternative attribute weight nonlinear programming model is constructed as

where

眼看着生意越做越顺，2010年5月，李志勇成立了自己的食用菌有限公司，取了个响亮的名字一一“山大王”。围绕着“创品牌、拓市场、建基地、强服务”的理念，山大王公司采用最为合理的“公司+基地+农户”经营模式，产值及营业额连年递增，产业规模不断扩大。

3.2 Dynamic VIKOR method in decision making process based on time series weight

Based on attribute weight and time series weight,the method is presented in a step by step algorithm as follows:

Step 1 Construct the dynamic intuitionistic fuzzy decision matrix F(tk)by(2).

Step 2 Construct the weighted intuitionistic fuzzy decision matrix Z;

where

Step 3 Determine the positive ideal solution(PIS)and negativeideal solution(NIS)of weighted intuitionistic fuzzy decision matrix Z.

The PIS is given by

where(benefit criteria)andcriteria).

时间序列分析提示，1991-2010年间AP患者的中位年龄呈下降趋势(均方根误差为1.275，可决系数为0.702，图1)。

Using the same simulation parameters,the simulation data do not change at time T3.At time T2,target 4 accelerates motion value changed from 〈0.73,0.19?to 〈0.80,0.15?.The result is 0.0636,0.9689,0.7305,0.5000 when υ =0.5.The sequencing result is m1＞m4＞m3＞m2.In this study,the dynamic process of the combat situation and threat assessment is combined.When target 4 has a tendency to accelerate the movement,raise the threat level to get a more reasonable assessment of the threat.

where(benefit criteria)and(cost criteria).

小虫的心情极好与风无关，而是受了姑父的鼓舞。能被姑父器重，是小虫到凌州以来最大的心愿。平时，小虫和姑父之间像隔着一座高大的山坡，姑父在山巅，小虫在山谷。这些年小虫一直怀着无比崇敬的心情，就这么仰视着姑父。小虫非常希望自己能干件漂亮的活儿，让姑父瞧瞧。现在，机会来了。

Step 4 Compute Si,Ri,Qi.

where Siis the maximizing group effect,it is the weighted Hamming distance between the evaluation value of the ith scheme and the ideal solution.Riis the minimizing individual regret,it is the weighted Chebyshev distance between the evaluation value of the ith scheme and the negative ideal solution.ωjis the weight of each evaluation criterion.υ is the decision-making mechanism coefficient.Step 5 Sequence the alternatives according to the relations of Si,Ri,Qi.The smaller the value is,the better the corresponding alternatives are.

4.Numerical examples and discussion

We assume that we encounter four enemy aircraft in combat and each enemy’s plane has four attributes.Its objective information is to select the current and previous two times sample data.The information is presented in Table 1.

Table 1 Target data information

Angle threat factor m1 ?0.76,0.10??0.68,0.15??0.75,0.15??0.80,0.15?m2 ?0.80,0.15??0.70,0.15??0.60,0.20??0.90,0.10?t1 m3 ?0.78,0.15??0.72,0.13??0.65,0.15??0.75,0.15?m4 ?0.65,0.28??0.80,0.20??0.55,0.30??0.80,0.11?m1 ?0.78,0.10??0.65,0.20??0.70,0.20??0.80,0.11?m2 ?0.83,0.10??0.65,0.20??0.70,0.15??0.85,0.10?t2 m3 ?0.75,0.20??0.85,0.15??0.82,0.18??0.73,0.19?m4 ?0.70,0.20??0.64,0.21??0.76,0.15??0.75,0.15?m1 ?0.76,0.13??0.70,0.15??0.60,0.25??0.75,0.18?m2 ?0.85,0.1? ?0.75,0.15??0.75,0.10??0.85,0.05?t3 m3 ?0.75,0.25??0.70,0.15??0.75,0.25??0.70,0.15?m4 ?0.75,0.15??0.68,0.20??0.70,0.18??0.60,0.20?Time Target Combat capability factor Velocity threat factor Distance threat factor

According to(7),the attribute weight is shown as follows:

ω(t1)=(0.265 4,0.219 0,0.168 4,0.347 2)ω(t2)=(0.263 3,0.206 4,0.249 9,0.280 4)ω(t3)=(0.325 4,0.215 8,0.234 1,0.224 7).

According to(8),the time series weight is shown as follows when φ=1.5:

η=(0.200 0,0.266 7,0.533 3).

（2） 净化。将上述液体上样Oasis PRiME HLB型柱，以1滴/s的速度过柱，收集洗脱液于试管中，再用3 mL乙腈-水（80∶20，V∶V） 溶液淋洗小柱，收集全部流出液后，在40℃下用氮气吹至液面低于1 mL，并用50%甲醇水溶液定容至1.00 mL，漩涡混匀，过0.22 μm微孔滤膜，经液相色谱-串联质谱测定。

According to(10)and(11),the PIS and NIS are given as follows:

术前访视以及手术全程,需加强心理护理,主动介绍手术室环境、医护人员、手术操作的基本流程以及需要注意事项,将患者送入手术室后,护理人员通过简短的语言安慰鼓励患者,缓解患者的紧张,增强成功手术治疗信心,麻醉开始后与患者交流,分散患者注意力,缓解患者焦虑。

According to(12)–(14),set υ =0.5,we can calculate the results as follows:

Finally,the most threatening target is m1,the optimal sequencing result is given by m1＞m3＞m4＞m2.By comparing the proposed methods,the TOPSIS method is utilized in assessing the air threat by the same assumption.The TOPSIS method was firstly developed by Hwang and Yoon in 1981.The basic approach of this method is choosing an alternative that should have the shortest distance from the positive ideal solution and the farthest distance from the negative ideal solution.The positive ideal solution maximizes the benefit criteria and the minimizes conflicting criteria.However,the negative ideal solution maximizes the conflicting criteria and minimizes the benefit criteria.This method has been applied in many combat threat assessment problems.The rationality of this method has been proved by many combat examples.The assessment results which are calculated by the TOPSIS method are 0.586 0,0.448 5,0.581 5,0.571 7 in 0.036 2 s.The sequencing result is m1＞m3＞m4＞m2.The result of two methods is the same.And the result is consistent with the method which is proposed by this study[17].We conclude that the threat assessment result is rational and effective.

水花鱼苗下塘后就要及时的投饵，保证鱼苗有充足的适口饵料。投饵一般投喂豆浆，初期每天用3～4kg/亩的黄豆，充分浸泡后打浆，按照 “三边两满塘”的方法泼洒投喂，而后根据水质肥瘦，适当的调节投饵量。20天左右可以适当增加菜籽饼、菜籽粕和黄豆一起打浆投喂。30天左右可以逐渐驯化投喂粉状配合饲料。

Moreover,the method has some advantages compared with the TOPSIS method.Dynamic character and flexible parameter υ are the obvious characteristics of the proposed method.The assessment and sequencing results of different υ are presented in Table 2.

Table 2 Results of different υ

ID υ Q Result Time/s 1 0.0 0.000 0,0.843 2,0.659 0,1.000 0 m1＞m3＞m2＞m4 0.038 5 2 0.1 0.017 9,0.858 9,0.593 1,0.913 6 m1＞m3＞m2＞m4 0.039 2 3 0.2 0.035 8,0.874 5,0.527 2,0.827 3 m1＞m3＞m4＞m2 0.039 0 4 0.3 0.053 7,0.890 2,0.461 3,0.740 9 m1＞m3＞m4＞m2 0.039 0 5 0.4 0.071 6,0.905 9,0.395 4,0.654 6 m1＞m3＞m4＞m2 0.039 1 6 0.5 0.089 5,0.921 6,0.329 5,0.568 2 m1＞m3＞m4＞m2 0.040 0 7 0.6 0.107 4,0.937 3,0.263 6,0.481 9 m1＞m3＞m4＞m2 0.039 7 8 0.7 0.125 3,0.953 0,0.197 7,0.395 5 m1＞m3＞m4＞m2 0.040 6 9 0.8 0.143 2,0.968 6,0.131 8,0.309 1 m3＞m1＞m4＞m2 0.038 7 10 0.9 0.161 1,0.984 3,0.065 9,0.222 8 m3＞m1＞m4＞m2 0.038 5 11 1.0 0.179 0,1.000 0,0.000 0,0.136 4 m3＞m4＞m1＞m2 0.038 1

We use modified VIKOR assessment result(1-Q)in order to facilitate comparison and display the results in Fig.1.

Fig.1 shows that results change when we use different υ values.In the first group υ =0.0-0.1,the sequencing result is m1＞m3＞m2＞m4.In the second group υ =0.2-0.7,the sequencing result is m1＞m3＞m4＞m2.In the third group υ=0.8-0.9,the sequencing result is m3＞m1＞m4＞m2.While in the fourth group υ =1,the sequencing result is m3＞m4＞m1＞m2.

We conclude that,the threat level superimposed when targets 3 and 4 consider all of the threat attributes,has a beyond tendency.The threat degree of target 3 exceeds target 1 when υ=0.8;the threat degree of target 4 exceeds target 2 when υ=0.2;the threat degree of target 4 exceeds target 1 when υ=1.0.Targets 1 and 2 have the threat degree when considering the single attribute.However,they have a lower threat degree when considering all of the threat attributes.The results based on the TOPSIS method are consistent with the results based on VIKOR when υ=0.2-0.7,which is in line with the results of most sorting.Calculation time is given in Table 2.We also conclude that,all the calculation time of different methods is about 0.038–0.040 s with the maximum time difference of 0.001 9 s with similar efficiency.

(i)A+B={〈x,μA(x)+ μB(x)- μA(x)μB(x),vA(x)μB(x)?}

区域构造发育，主要为一套趋于NNE向的构造体系(图1)。区域岩浆岩不甚发育，仅在局部地段见有煌斑岩细脉出露。

Fig.1 Result figures

The NIS is given by

孙莉军介绍到，当前，工业区已建立起一个立体的环境监测网络，不仅对地面的生产企业实行监控，而且对大气实施自动监测。通过与国家安全科学研究院合作，工业区在30家重点企业周围安装VOCs网格化监控系统传感器，依托监测体系的实时数据，分析各项污染物浓度趋势，形成月度报告，为改善区域环境质量提供依据。同时，工业区推进雨水三级应急体系建设，包括24个入河口水闸，企业雨水应急阀门和河道联闸联控系统，进一步降低工业区水污染风险，提升水污染突发事故的应急处置能力。

学生学习知识的过程是符合客观的现实规律的。每个人的知识构建的学习都是由浅入深，符合知识的构建发展的规律，教学的过程需要符合客观规律，每个学生都是从基础知识学过来的尽量要满足每个人的需求，由浅入深的教学，在讲解二次函数的时候，先更具方程画出函数的图形，在来研究每个点的规律，然后考虑怎么将二次方程转化为标准方程，研究的问题越来越广，还可以研究每个函数的对称轴，使学生较好的分析和掌握二次函数的关系和性质，才能为以后的运用过程打下良好的基础。

5.Conclusions

The modern combat process is always an uncertain,dynamic and hybrid formation.Considering that the traditional air target threat assessment methods are difficult to reflect the combat characteristics,an algorithm is proposed to solve the multi-target threat assessment problems.The target attribute weight is calculated by the IFE algorithm and the time series weight is gained by the Poisson distribution method based on multi-times data.Assessment and sequencing of the air multi-target threat model based on IFE and dynamic VIKOR are established.Finally,a simulation example indicates that the method is reasonable and effective.And this method improves the scientific rationality of multi-target threat assessment for air combat.

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