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| 1 | Research on evaluations of several grey relational models adapt to grey relational axioms显示文摘Grey relational analysis is an important part of the grey systems theory, and it is the basis of the grey clustering analysis, grey decision-making and grey controlling. To research whether grey relational models satisfy the four grey relational theorems, several kinds of grey relational models are commented. Some problems including the properties of normality, pair symmetry and wholeness are discussed. The phenomenon that the lower value of almost each grey relational model is not equal to zero is proved. The contradiction problems between the properties of wholeness and pair symmetry are verified. Finally, several propositions are constructed to explain the above problems. | Xie Naiming Liu Sifeng | 2009 | Journal of Systems Engineering and Electronics2009，20，2： | 34 |
| 2 | Prediction model of interval grey number based on DGM(1,1)显示文摘In grey system theory,the studies in the field of grey prediction model are focused on real number sequences,rather than grey number ones.Hereby,a prediction model based on interval grey number sequences is proposed.By mining the geometric features of interval grey number sequences on a two-dimensional surface,all the interval grey numbers are converted into real numbers by means of certain algorithm,and then the prediction model is established based on those real number sequences.The entire process avoids the algebraic operations of grey number,and the prediction problem of interval grey number is usefully solved.Ultimately,through an example's program simulation,the validity and practicability of this novel model are verified. | Bo Zeng Sifeng Liu Naiming Xie | 2010 | Journal of Systems Engineering and Electronics2010，21，4： | 19 |
| 3 | Linear Quadratic Differential Game Strategies with Two-pursuit Versus Single-evader显示文摘In order to intercept the future targets that are characterized by high maneuverability, multiple interceptors may be launched and aimed at single target. The scenario of two missiles P and Q intercepting a single target is modeled as a two-pursuit single-evader non-zero-sum linear quadratic differential game. The intercept space is decomposed into three subspaces which are mutually disjoint and their union covers the entire intercept space. The effect of adding the second interceptor arises in the intercept space of both P and Q (PQ-intercept space). A guidance law is derived from the Nash equilibrium strategy set (NESS) of the game. Simulation studies are focused on the PQ-intercept space. It is indicated that 1) increasing the target's maneuverability will enlarge PQ-intercept space; 2) the handover conditions will be released if the initial zero-effort-miss (ZEM) of both interceptors has opposite sign; 3) overvaluation of the target's maneuverability by choosing a small weight coefficient will generate robust performance with respect to the target maneuvering command switch time and decrease the fuel requirement; and 4) cooperation between interceptors increases the interception probability. | LIU Yanfang QI Naiming TANG Zhiwei | 2012 | Chinese Journal of Aeronautics2012，25，6： | 19 |
| 4 | Interval grey number sequence prediction by using non-homogenous exponential discrete grey forecasting model显示文摘This paper aims to study a new grey prediction approach and its solution for forecasting the main system variable whose accurate value could not be collected while the potential value set could be defined. Based on the traditional nonhomogenous discrete grey forecasting model(NDGM), the interval grey number and its algebra operations are redefined and combined with the NDGM model to construct a new interval grey number sequence prediction approach. The solving principle of the model is analyzed, the new accuracy evaluation indices, i.e. mean absolute percentage error of mean value sequence(MAPEM) and mean percent of interval sequence simulating value set covered(MPSVSC), are defined and, the procedure of the interval grey number sequence based the NDGM(IG-NDGM) is given out. Finally, a numerical case is used to test the modelling accuracy of the proposed model. Results show that the proposed approach could solve the interval grey number sequence prediction problem and it is much better than the traditional DGM(1,1) model and GM(1,1) model. | Naiming Xie Sifeng Liu | 2015 | Journal of Systems Engineering and Electronics2015，26，1： | 18 |
| 5 | An optimal one-way cooperative strategy for two defenders against an attacking missile显示文摘This paper investigates a cooperative strategy for protecting an aerial target.The problem is solved as a game among four players(a target,two defenders,and a missile).In this scenario,the target launches two defenders(defender-1 and defender-2)simultaneously,to establish a oneway cooperation system(OCS)against an attacking missile.A new optimal evasion strategy for the target is also derived.During the engagement,the target takes into account the reaction of the attacking missile,and guides defender-1 to the interception point by receiving information from defender-1.Depending on the control effort of the target,defender-2 can choose appropriate launch conditions and use very limited maneuvering capability to intercept the missile.For adversaries with first-order dynamics,simulation results show that the OCS allows two defenders to intercept the missile.During the engagement,even if one defender or communication channel is broken,the OCS still allows an interception to be made,thus increasing the target’s survivability. | Qilong SUN Naiming QI Zheyao XU Yanfang LIU Yong ZHANG | 2017 | Chinese Journal of Aeronautics2017，30，4： | 6 |
| 6 | Guidance laws for attacking defended target显示文摘In this paper,two new guidance laws based on differential game theory are proposed and investigated for the attacker in an attacker-defender-target scenario.The conditions for the attacker winning the game are analyzed when the target and defender using the differential game guidance law based on the linear model.The core ideas underlying the two guidance laws are the attacker evading to a critical safe boundary from the defender,and then maintaining a critical miss distance.The guidance law more appropriate for the attacker to win the game differs according to the initial parameters.Unlike other guidance laws,when using the derived guidance laws there is no need to know the target and the defender’s control efforts.The results of numerical simulations show that the attacker can evade the defender and hit the target successfully by using the proposed derived guidance laws. | Qilong SUN Chenfeng ZHANG Ning LIU Weixue ZHOU Naiming QI | 2019 | Chinese Journal of Aeronautics2019，32，10： | 4 |
| 7 | Ranking grey numbers based on dominance grey degrees显示文摘With respect to the decision making problems where a lot of fuzzy and grey information always exists in the real-life decision making information system, it is difficult for such uncertainty methods as fuzzy mathematics, probability, and interval numbers to deal with. To this end, based on the thought and method of grey numbers, grey degrees and interval numbers, the concept of dominance grey degree is defined. And then a method of ranking interval grey numbers based on the dominance grey degree is proposed. After discussing the relevant properties, the paper finally uses an example to demonstrate the effectiveness and applicability of the model. The result shows that the proposed model can more accurately describe uncertainty decision making problems, and realize the total ordering process for multiple-attribute decision-making problems. | Yong Liu Jeffrey Forrest Naiming Xie | 2014 | Journal of Systems Engineering and Electronics2014，25，4： | 2 |
| 8 | Grey-based approach for estimating software reliability under nonhomogeneous Poisson process显示文摘Due to the randomness and time dependence of the factors affecting software reliability, most software reliability models are treated as stochastic processes, and the non-homogeneous Poisson process(NHPP) is the most used one.However, the failure behavior of software does not follow the NHPP in a statistically rigorous manner, and the pure random method might be not enough to describe the software failure behavior. To solve these problems, this paper proposes a new integrated approach that combines stochastic process and grey system theory to describe the failure behavior of software. A grey NHPP software reliability model is put forward in a discrete form, and a grey-based approach for estimating software reliability under the NHPP is proposed as a nonlinear multi-objective programming problem. Finally, four grey NHPP software reliability models are applied to four real datasets, the dynamic R-square and predictive relative error are calculated. Comparing with the original single NHPP software reliability model, it is found that the modeling using the integrated approach has a higher prediction accuracy of software reliability. Therefore, there is the characteristics of grey uncertain information in the NHPP software reliability models, and exploiting the latent grey uncertain information might lead to more accurate software reliability estimation. | LIU Xiaomei XIE Naiming | 2022 | Journal of Systems Engineering and Electronics2022，33，2： | 1 |
| 9 | Matrix grey clustering model based on object dimension incompatibility attributes constraint and its application in poverty student financial assistance policy design显示文摘 | Hongqi Liu Zhigeng Fang Naiming Xie | 2013 | J of Grey System2013，25，1： | 1 |
| 10 | On novel grey forecasting model based on non-homogeneous index sequence显示文摘 | Xie Naiming Liu Sifeng Yang Yingjie | 2013 | Applied Mathematical Modeling2013，37，7： | 1 |
| 11 | Novel models of grey relational analysis based on visual angle of similarity and nearness 显示文摘 | Liu Sifeng Xie Naiming Forrest Jeffery | 2011 | Grey Systems: Theory and Application2011，1，1： | 1 |
| 12 | Discrete grey forecasting model and its optimization显示文摘 | Xie Naiming Liu Sifeng | 2009 | Applied Mathematical Modelling2009，33，2： | 1 |
| 13 | The relation between Chinese economic development and energy consumption in the different periods显示文摘 | Chaoqing Yuan Sifeng Liu Zhigeng Fang Naiming Xie | | 0，，38： | 1 |
| 14 | A summary on the research of GRA models显示文摘 | Sifeng Liu Yingjie Yang Ying Cao Naiming Xie | 2013 | Grey Systems: Theory and Application2013，，1： | 1 |
| 15 | Discrete grey forecasting model and its optimization显示文摘 | Xie Naiming Liu Sifeng | 2009 | Applied Mathematical Modeling2009，33，2： | 1 |
| 16 | Modeling of disturbance torque in an aerostatic bearings-based nano-satellite simulator显示文摘The disturbance torque of aerostatic bearings is in the same order of the reaction wheel, which causes difficulty in evaluation of the designed attitude control strategy of a nano-satellite based on the aerostatic bearing. Two approaches are proposed to model the disturbance torque. Firstly, the gravity induced moment,the vortex torque, and the damping moment are modeled separately. However, the vortex torque and the damping moment are coupled with each other as both of them are caused by the viscosity. In the second approach, the coupling effect is considered. A nano-satellite is constructed based on aerostatic bearing. The time history of the free rotation rate from an initial speed is measured by the gyro, which is further used to calculate the rotation angle and acceleration. The static vortex torque is measured via the removable micro-torque measurement system. Based on these data, the model parameters are identified and modeling errors are presented. Results show that the second model is more precise.The root mean squire error is less than 0.5×10^(-4) N·m and the relative error of the static vortex torque is 0.16%. | LIU Yanfang HUO Mingying QI Naiming | 2018 | Journal of Systems Engineering and Electronics2018，29，3： | 1 |
| 17 | Capture condition for endo-atmospheric interceptors steered by ALCS and ARCS显示文摘这贡献为飞行器电梯的控制系统(ALCS ) 和态度反应喷气控制系统(弧) 驾驶的阻止的人导弹处理俘获状况。与法律从围住的微分比赛明确的表达导出的指导,俘获地区的存在状况为阻止的人有的盒子被学习可操作性上的优点和活泼上的劣势。为开的俘获地区的存在,在约会终止以后,弧能仅仅关门。而且,也,在最小上贡献可操作性的需要要求了的弧珍视。如果,更多的燃料将被要求弧增加它对可操作性的贡献。最小的要求的燃料发生在二条曲线的正切点:批评参数的曲线和一条候选人限制曲线,它甚至为复杂燃料也真抑制。这些结果的有效性被模拟也表明。 | Yanfang LIU Naiming Qi Tianye WANG | 2014 | Control Theory and Technology2014，12，1： | 1 |
| 18 | China's regional meteorological disaster loss analysis and evaluation based on grey cluster model 显示文摘 | Xie Naiming Xin Jianghui Liu Sifeng | 2014 | Natural Hazards2014，71，2： | 1 |
| 19 | Discrete grey forecasting model and its optimization 显示文摘 | XIE Naiming LIU SiIeng | 2009 | Applied Mathematical Modelling2009，33，2： | 1 |
| 20 | A novel grey relational model based on grey number sequences显示文摘 | Naiming Xie Sifeng Liu | 2011 | Grey Systems:Theory and Application2011，1，2： | 1 |
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