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Research on evaluations of several grey relational models adapt to grey relational axioms

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Journal of Systems Engineering and Electronics 2009年第2期20卷 304-309页

作者： xie naiming Liu Sifeng Coll. of Economic & Management Nanjing Univ. of Aeronautics and Astronautics Nanjing 210016 P. R. China

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.

关键词： grey relational analysis grey system normality whole symmetry

Ranking grey numbers based on dominance grey degrees

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Journal of Systems Engineering and Electronics 2014年第4期25卷 618-626页

作者： Yong Liu Jeffrey Forrest naiming xie College of Economics and Management Nanjing University of Aeronautics and Astronautics School of Business Jiangnan University Mathematics Department Slippery Rock University of USA

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 methods as fuzzy mathematics, it is difficult for such uncertainty 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.

关键词： grey information dominance grey degree intervalgrey number total ordering.

Grey-based approach for estimating software reliability under nonhomogeneous Poisson process

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Journal of Systems Engineering and Electronics 2022年第2期33卷 360-369页

作者： LIU Xiaomei xie naiming College of Economics and Management Nanjing University of Aeronautics and AstronauticsNanjing 211106China College of Science Jiujiang UniversityJiujiang 332005China

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 ***, 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.

关键词： software reliability model stochastic process uncertainty system non-homogeneous Poisson process grey system theory

Expansion modelling of discrete grey model based on multi-factor information aggregation

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Journal of Systems Engineering and Electronics 2014年第5期25卷 833-839页

作者： naiming xie Chaoyu Zhu Jing Zheng College of Economics and Management Nanjing University of Aeronautics and Astronautics

This paper aims to study a novel expansion discrete grey forecasting model, which could aggregate input information more effectively. In general, existing multi-factor grey forecasting models, such as one order and h variables grey forecasting model （GM （1, h））, always aggregate the main system variable and independent variables in a linear form rather than a nonlinear form, while a nonlinear form could be used in more cases than the linear form. And the nonlinear form could aggregate collinear independent factors, which widely lie in many multi-factor forecasting problems. To overcome this problem, a new approach, named as the Solow residual method, is proposed to aggregate independent factors. And a new expansion model, feedback multi-factor discrete grey forecasting model based on the Solow residual method （abbreviated as FDGM （1, h））, is proposed accordingly. Then the feedback control equation and the parameters＇ solution of the FDGM （1, h） model are given. Finally, a real application is used to test the modelling accuracy of the FDGM （1, h） model. Results show that the FDGM （1, h） model is much better than the nonhomogeneous discrete grey forecasting model （NDGM） and the GM （1, h） model.

关键词： multi-variable system Solow residual method dis crete grey forecasting model grey system theory (GST).

Construction mechanism of whitenization weight function and its application in grey clustering evaluation

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Journal of Systems Engineering and Electronics 2019年第1期30卷 121-131页

作者： xie naiming SU Bentao CHEN Nanlei College of Economics and Management Nanjing University of Aeronautics and Astronautics

The clustering evaluation can be used to scientifically classify the objects to be evaluated according to the information aggregation of various evaluation rules. In grey weighted clustering evaluation, the index clustering rule relies on the construction of the whitenization weight function, while the existing construction method of the linear function lacks the construction mechanism analysis and validity explanation. A normative construction principle is put forward by analyzing the construction mechanism of the function. Through proving the normative principle of the function,the basic modal function(BMF) is proposed and characterized by different function forms. Then, a new type of the whitenization weight function and its grey clustering evaluation model algorithm are given by studying the mechanism and nature of the construction of different forms of the function. Finally, the comparative study for self-innovation capability of defense science and technology industry(DSTI) is taken as an example. The results show that the different construction ways of the function have an effect on the clustering result. The proposed construction mechanism can better explain the index clustering rules and evaluation effectiveness,which will perfect the theoretical system of grey clustering evaluation and be applied to practice effectively.

关键词： whitenization weight function grey system theory grey clustering evaluation.

Prediction model of interval grey number based on DGM(1,1)

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Journal of Systems Engineering and Electronics 2010年第4期21卷 598-603页

作者： Bo Zeng Sifeng Liu naiming xie College of Business Planning Chongqing Technology and Business University Chongqing 400067 E R. China College of Economics and Management Nanjing University of Aeronautics and Astronautics Nanjing 210016 P. R. China

In grey system theory,the studies in the field of grey prediction model are focused on real number sequences,rather than grey number ***,a prediction model based on interval grey number sequences is *** 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 *** entire process avoids the algebraic operations of grey number,and the prediction problem of interval grey number is usefully ***,through an example＇s program simulation,the validity and practicability of this novel model are verified.

关键词： grey system theory prediction model interval grey number grey number band grey number layer DGM(1 1) model.

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

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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

考虑团队交互学习效应的单工作组可中断任务调度模型

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计算机集成制造系统 2022年第1期28卷 161-174页

作者：李斌谢乃明南京航空航天大学经济与管理学院江苏南京211106

工作组完成工作任务时团队成员间存在交互学习效应,考虑工作组规模、人员结构等因素可以更好地配置资源实现优化调度。基于标准加工时间和单人学习效应定义了团队交互学习效应,给出了基于团队交互学习效应和人员加工可中断约束的工时表... 详细信息

工作组完成工作任务时团队成员间存在交互学习效应,考虑工作组规模、人员结构等因素可以更好地配置资源实现优化调度。基于标准加工时间和单人学习效应定义了团队交互学习效应,给出了基于团队交互学习效应和人员加工可中断约束的工时表征公式,构建了以最大完工时间最小为目标的单工作组可中断任务调度模型,设计了基于精英保留遗传算法(e-GA)的模型求解策略,并设计了不同规模、不同人员结构的测试算例验证所构建模型和算法的有效性。实验结果表明,所构建的模型和算法能够实现优化调度。

关键词：团队交互学习效应单工作组调度人员加工可中断精英保留遗传算法

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广义灰色关联分析模型的统一表述及性质

系统工程理论与实践 2019年第1期39卷 226-235页

作者：韦保磊谢乃明南京航空航天大学经济与管理学院南京211106 南京航空航天大学灰色系统研究所南京211106

系统地研究了初值化、始点零化和初值-始点零化三种关联序列算子的幂等、线性和仿射变换性质,给出了灰色关联接近性公理的数学定义,阐述了灰色关联度正定性、仿射性和仿射保序性的物理意义.揭示广义灰色关联度及其改进均是以序列插值曲... 详细信息

系统地研究了初值化、始点零化和初值-始点零化三种关联序列算子的幂等、线性和仿射变换性质,给出了灰色关联接近性公理的数学定义,阐述了灰色关联度正定性、仿射性和仿射保序性的物理意义.揭示广义灰色关联度及其改进均是以序列插值曲线之间面积为基础进行构造的内涵,通过引入分辨系数,分别给出了广义灰色关联度和改进广义灰色关联度的统一表述形式,证明了分辨系数与关联序的独立性,研究了其正定性、平行性、一致性、仿射性、平行保序性、一致保序性、仿射保序性和适用性.

关键词：灰色系统关联序列算子广义灰色关联度改进广义灰色关联度