Some results about grey mathematics

Li, Qiaoxing; Liu, Sifeng

doi:10.1108/03684920910943976

Cited by 14 publications

(18 citation statements)

References 8 publications

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“…Some are based on the geometric features of interval grey numbers (Luo, 2009;Zeng et al 2013), and the fluctuation range of the upper and lower boundaries (Li et al 2007;Wu and Liu, 2009). Combination of models from other theory is also studied, such as the evolutionary analysis idea in grey hazy set (Li and Liu, 2009) and the classic statistical methods in normal distribution theory (Teng and Huang, 2013). Prediction model for Heterogeneous Data is first proposed by Zeng (2013).…”

Section: Introductionmentioning

confidence: 99%

A greyness reduction framework for prediction of grey heterogeneous data

Yang

Liu

2020

Soft Comput

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Existing operational rules of interval grey numbers do not make full use of possible background information when determining the interval boundaries, and this may result in inconsistent results if applying different logical operations. This paper finds that multiplication and division rules of interval grey numbers do not meet the calculation rule of inverse operators. Direct solution and inverse solution of the same interval grey number object may differ not only in numerical ranges but also in greyness degrees. To improve the accuracy of grey number calculation, new operational rules for multiplication and division of interval grey numbers are proposed. Then the traditional prediction modeling method of grey heterogeneous data is refined and expanded by integrating a greyness reduction preprocessing, which is based on the proposed calculation rules. Application of the expanded heterogeneous interval grey number prediction model to a stock replenishment scheduling problem in emergency rescue scenarios is included to illustrate the new operational rules of grey numbers and their application in prediction algorithm, and the proposed approach is compared with other existing methods to demonstrate its effectiveness.

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Section: Introductionmentioning

confidence: 99%

A greyness reduction framework for prediction of grey heterogeneous data

Yang

Liu

2020

Soft Comput

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“…To obtain a reliable prediction, certain laws governing the phenomena of system development must be discovered on the basis of either natural principles or real observation. However, in the practical world, searching the available natural principles is very hard either in the physical system or in the generalized system (Li and Liu, 2009). Therefore, forecasting the further system development directly from previous observation (data) seems to be a practicable alternative.…”

Section: Introductionmentioning

confidence: 99%

Property of derived grey verhulst model with multiple transformation

Cui

Xie

et al. 2014

Grey Systems: Theory and Application

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Purpose – The purpose of this paper is to study the properties of derived grey verhulst prediction model with multiplication transformation and reduce its modeling complexity. Design/methodology/approach – The paper discussed the parameter characteristics of grey derived verhulst model under multiple transformation, and demonstrated its effect on its simulative value and predictive value by investigating the multiple transformation acting on the raw data sequence of this grey model. The parameter characteristics of this model under multiple transformations and its effect of the simulation value and forecasting value are analyzed by studying the properties of multiply transformation of this model. Findings – The research finding shows that the modeling accuracy of derived grey verhulst model is in no relation to multiple transformations. Practical implications – The above results imply that the data level can be reduced; the process of building derived grey verhulst model can be simplified; but the simulative and predictive accuracy of this model remain unchanged. Originality/value – The paper succeeds in realising the properties of derived grey verhulst model by using the method of multiplication transformation, which is helpful to understand the modeling mechanism and expand the application range of derived grey verhulst model.

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“…The parameters' properties of GM (n, h) model on the basis of multiple transformation and the relationship of GM (n, h) model and other grey models were studied (Xie and Liu, 2009b). From the grey hazy set, Li and Liu (2009) redefine grey number and the operation of grey-number element. The accuracies of different grey models such as GM (1,1), Grey Verhulst model, modified grey models using Fourier series is investigated (Kayacan et al, 2010).…”

Section: Introductionmentioning

confidence: 99%

Study on parameters characteristics of NGM (1,1,k) prediction model with multiplication transformation

Cui

Zeng

2012

Grey Systems: Theory and Application

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Purpose -The purpose of this paper is to study the properties of the NGM (1,1,k) prediction model with multiplication transformation and reduce its modeling complexity. Design/methodology/approach -The authors improved this model by putting forward a formula to solve its parameters, building an algorithm for optimizing the NGM (1,1,k) model in terms of the least modeling error and designing a key technology for the implementation of this algorithm. The optimized NGM (1,1,k) model is built accordingly. The parameter characteristics of the two models under multiple transformations and its effect of the simulation value and forecasting value are analyzed by studying the properties of multiple transformation of the two models. Findings -The research finding shows that the modeling accuracies of the NGM (1,1,k) model and the optimized NGM (1,1,k) model are all in no relation to multiple transformations. Practical implications -The above results imply that the data level can be reduced; the process of building the NGM (1,1,k) model and the optimized NGM (1,1,k) model can be simplified; but the simulative and predictive accuracy of the two models remain unchanged. Originality/value -The paper succeeds in realising the properties of NGM (1,1,k) model and the optimized NGM (1,1,k) model by using the method of multiplication transformation, which is helpful for understanding the modeling mechanism and expanding the application range of the NGM (1,1,k) model.

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Some results about grey mathematics

Cited by 14 publications

References 8 publications

A greyness reduction framework for prediction of grey heterogeneous data

A greyness reduction framework for prediction of grey heterogeneous data

Property of derived grey verhulst model with multiple transformation

Study on parameters characteristics of NGM (1,1,k) prediction model with multiplication transformation

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