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Interval grey number sequence prediction by using non-homogenous exponential discrete grey forecasting model

Journal of Systems Engineering and Electronics 2015年第1期26卷 96-102页

作者： Naiming Xie Sifeng Liu College of Economics and Management Nanjing University of Aeronautics and Astronautics Institute of grey System Studies Nanjing University of Aeronautics and Astronautics

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.

关键词： grey number grey system theory interval discrete grey forecasting model non-homogeneous exponential sequence

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Fundamental definitions and calculation rules of grey mathematics: a review work

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Journal of Systems Engineering and Electronics 2015年第6期26卷 1254-1267页

作者： Qiaoxing Li Sifeng Liu Jeffrey Yi-Lin Forrest School of Management Guizhou University School of Economics and Management Nanjing University of Aeronautics and Astronautics Centre of Computational Intelligence De Montfort University School of Business Slippery Rock University

grey mathematics is the mathematical foundation of the grey system theory. Recently, some important results have been achieved. In order to accelerate the development of grey mathematics, the results are summarized and redefined. This paper includes the fundamental definitions and calculation rules of the grey hazy set, grey number, grey matrix and grey function. grey mathematics includes four types of operation, i.e. the grey operation, the whitened operation, the covered operation and the only potential true operation. According to its intrinsic quality, the covered operation, which differs from the interval one, is called as the whole-proximate calculation that means the proximate calculation spreads through the whole range of the covered set of every grey number, and we confirm that it may be a new branch of computational or applied mathematics. The overview should develop the grey system theory and grey mathematics.

关键词： grey mathematics grey hazy set grey number covered operation grey system theory.

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维普期刊数据库

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An improved interval model updating method via adaptive Kriging models

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Applied Mathematics and Mechanics(English Edition) 2024年第3期45卷 497-514页

作者： Sha WEI Yifeng CHEN Hu DING Liqun CHEN Shanghai Key Laboratory of Mechanics in Energy Engineering Shanghai Frontier Science Center of MechanoinformaticsShanghai Institute of Applied Mathematics and MechanicsSchool of Mechanics and Engineering ScienceShanghai UniversityShanghai 200072China Shanghai Institute of Aircraft Mechanics and Control Shanghai 200092China

Interval model updating(IMU)methods have been widely used in uncertain model updating due to their low requirements for sample ***,the surrogate model in IMU methods mostly adopts the one-time construction *** makes the accuracy of the surrogate model highly dependent on the experience of users and affects the accuracy of IMU ***,an improved IMU method via the adaptive Kriging models is *** method transforms the objective function of the IMU problem into two deterministic global optimization problems about the upper bound and the interval diameter through universal grey *** optimization problems are addressed through the adaptive Kriging models and the particle swarm optimization(PSO)method to quantify the uncertain parameters,and the IMU is *** the construction of these adaptive Kriging models,the sample space is gridded according to sensitivity *** sampling is then performed in key subspaces based on the maximum mean square error(MMSE)*** interval division coefficient and random sampling coefficient are adaptively adjusted without human interference until the model meets accuracy *** effectiveness of the proposed method is demonstrated by a numerical example of a three-degree-of-freedom mass-spring system and an experimental example of a butted cylindrical *** results show that the updated results of the interval model are in good agreement with the experimental results.

关键词： interval model updating(IMU) non-probabilistic uncertainty adaptive Kriging model surrogate model grey number

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Generalized dominance-based rough set approach to security evaluation with imprecise information

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High Technology Letters 2010年第3期16卷 254-262页

作者： Zhao Liang Xue Zhi School of Electronic and Electric Engineering Shanghai Jiaotong University Shanghai 200240 P.R. China

The model of grey multi-attribute group decision-making （MAGDM） is studied, in which the attribute values are grey numbers. Based on the generalized dominance-based rough set approach （G-DR- SA）, a synthetic security evaluation method is presented. With-the grey MAGDM security evaluation model as its foundation, the extension of technique for order performance by similarity to ideal solution （TOPSIS） integrates the evaluation of each decision-maker （DM） into a group＇s consensus and obtains the expected evaluation results of information system. Via the quality of sorting （QoS） of G-DRSA, the inherent information hidden in data is uncovered, and the security attribute weight and DMs＇ weight are rationally obtained. Taking the computer networks in a certain university as objects, the example illustrates that this method can effectively remove the bottleneck of the grey MAGDM model and has practical significance in the synthetic security evaluation.

关键词： security evaluation grey number multi-attribute group decision-making (MAGDM) generalized dominance-based rough set approach (G-DRSA)

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The Further Discussion of Distribution and Characters of grey Potential Degrees

The Further Discussion of Distribution and Characters of Gre...

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第25届全国灰色系统会议

作者： Aiqing Ruan Yinao Wang City College Wenzhou University College of Economics and Management Nanjing University of Aeronautics and Astronautics College of Mathematics and Information Science Wenzhou University

grey number has become a very important and useful tool to describe the pay-off matrix of game due to the inevitable defect of information and the limited rationality of human. The conception system of grey Potential Degrees, including grey Superiority Potential Degree, grey Inferior Potential Degree and grey Total Potential Degree of two grey numbers is built up in exiting research. This paper is to further discuss the distribution, the characters and the changing of these grey Potential Degrees. Distribution of grey Potential Degree is discussed in the paper and grey Superiority Degree is divided into three areas, Absolutely Superiority, Relative Superiority and No Superiority. And grey Inferior Potential Degree is divided into three parts, Absolutely Inferiority, Relative Inferiority and No Inferiority. It is found that any two grey numbers could be in some special situation of No Superiority to Each other, No Inferiority to Each other, Unit Superiority Potential. When they are same grey numbers, all grey Potential Degrees are in value of zero. grey Potential Degrees of grey numbers can be in mutual influence. They are connected with the length of grey numbers. According to the dimension of position and the dimension of length of grey umbers, the changing and tendency of three kinds of grey Potential Degrees are stimulated, accounted and figured in paper. The growing tendencies of grey Potential Degrees are presented when one grey number moves from left side to right side of the other grey number. Closer the lengths of two grey numbers are, nearer the grey Superiority Potential Degree and grey Inferior Potential Degree.

关键词： grey number grey potential degree distribution

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