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Article
Publication date: 7 August 2009

Yong Wei and Dahong Hu

The purpose of this paper is to introduce the new class ratio dispersion, the new smooth degree sequence and the comparison criterion of the new smooth degree and to propose the…

126

Abstract

Purpose

The purpose of this paper is to introduce the new class ratio dispersion, the new smooth degree sequence and the comparison criterion of the new smooth degree and to propose the new prior check of grey modeling in order to meet the modeling demand of the optimized grey models which have the white exponential law of coincidence.

Design/methodology/approach

This paper introduces the corresponding new concepts and new comparison criterion which can reflect the approach degree of the raw data and the normal geometric progression by analogy with the traditional class ratio dispersion, smooth degree sequence and comparison criterion.

Findings

To the optimized grey models, the new concepts and the new comparison criterion can be regarded as the prior check of grey modeling.

Originality/value

First, the new concepts and the new comparison criterion can reflect the approach degree of the raw data and the normal geometric progression, and this paper proposes the prior check of grey modeling to the optimized grey models. Second, this paper proposes the quantificational valuation criterion – the concept of the smooth degree which can reflect the approach degree of a single sequence and the normal geometric progression, and ends the status quo that there is only the comparison criterion of the smooth degree between two sequences but not the quantificational valuation criterion of a single sequence.

Details

Kybernetes, vol. 38 no. 7/8
Type: Research Article
ISSN: 0368-492X

Keywords

Article
Publication date: 28 October 2013

Jing Ye, Bingjun Li and Fang Liu

This paper aims to find an effective and standardized function transformation method to apply in both high-growth original data sequences and low-growth original data sequences

Abstract

Purpose

This paper aims to find an effective and standardized function transformation method to apply in both high-growth original data sequences and low-growth original data sequences, which can improve the accuracy of model prediction in GM(1, 1) forecast.

Design/methodology/approach

In GM(1, 1) forecast, many original data sequences need to meet the quasi-exponential characteristic by methods of function transformation. However, many methods of function transformation have complex transformation processes or narrow application range. On the basis of the research results of Ye and Li, the paper presents a standardized approach based on to original data sequences and designs four situations of the standardized approach. By using high-growth and low-growth original data sequences as the objects, respectively, the paper verifies the effectiveness of the proposed method and compares the forecasting effects of GM(1, 1) based on function transformation with the original GM(1, 1).

Findings

Most of the results show that function transformations can improve the accuracy of the conventional GM(1, 1) forecast, and transform is a powerful tool to effectively process original data sequence of GM(1, 1) modeling.

Practical implications

GM(1, 1) forecast have been widely used in many fields such as agriculture, economy, meteorology, and geology. The proposed method in this paper can effectively apply to prediction of high-growth original data sequences and low-growth original data sequences, to some extent, enrich and deepen application of GM(1, 1) forecast.

Originality/value

The paper succeeds in providing a standardized approach based on and designs four intensity levels for different data sequences based on the standardized approach.

Details

Grey Systems: Theory and Application, vol. 3 no. 3
Type: Research Article
ISSN: 2043-9377

Keywords

Article
Publication date: 5 February 2018

Tianxiang Yao and Hong Gao

Buffer operators can be utilized to improve the smooth degree of the raw data sequence, and to increase the simulation accuracy of the model. The purpose of this paper is to…

Abstract

Purpose

Buffer operators can be utilized to improve the smooth degree of the raw data sequence, and to increase the simulation accuracy of the model. The purpose of this paper is to analyze the cause of increase in the simulation accuracy of the buffer operator.

Design/methodology/approach

This paper probed into the modeling mechanism of several typical buffer operators such as the arithmetic buffer operators, the buffer operators with monotonic function and weighted buffer operators. The paper also gives an example of the buffer operator sequence.

Findings

The results indicate that after applying an infinite buffer operator, whether the authors adopt a weakening buffer operator or a strengthen buffer operator, the raw sequence can be changed into a constant sequence. Because the discrete GM(1,1) model can completely simulate constant sequence, the simulation accuracy is 100 percent. Because the discrete GM(1,1) model is the accurate form of the GM(1,1) model, after applying an infinite buffer operator, the GM(1,1) model can have a very high simulation accuracy. The buffer operator model can increase the simulation accuracy of both the GM(1,1) model and the discrete GM(1,1) model.

Originality/value

The paper analyses the cause of increasing simulation accuracy of the buffer operator model. The paper may indicate that possible results can be studied in the future. All the buffer operator models have similar properties. After applying an infinite buffer operator, the raw sequence can be changed into a constant sequence. A fixed-point axiom may be the basic cause.

Details

Grey Systems: Theory and Application, vol. 8 no. 1
Type: Research Article
ISSN: 2043-9377

Keywords

Article
Publication date: 27 January 2012

Chaoyu Zhu and Naiming Xie

The purpose of this paper is to propose a model for effective data filling and precise prediction, which is used to solve the prediction problem of sequential data with the…

266

Abstract

Purpose

The purpose of this paper is to propose a model for effective data filling and precise prediction, which is used to solve the prediction problem of sequential data with the characteristics of poor information, high growth and containing extraordinary points.

Design/methodology/approach

After proving that the three principles of smooth sequence are not a sufficient condition for the judgement of sequence smoothness, judgement rules for sequence smoothness based on smoothness efficiency is introduced. Based on the non‐homogenous discrete grey model (NDGM) model which fits for high growth sequence, model error caused by equal weight mean value is analyzed, and mean value generation weight efficiency is optimized by the method of differential. Prediction steps that fit sequences with high growth, poor information and containing extraordinary points is established on the basis of equal weight mean value generation efficiency.

Findings

The results are convincing: previous judgement rules used for sequence smoothness do not fit for the high growth sequence, new judgement rules introduced are more effective for high growth sequence. Sequence filling algorithm based on differential ration not only improve the filling of high growth sequence, but also enhance the prediction precision of these sequences.

Practical implications

The method exposed in the paper can be used to solve the prediction problem of sequences with poor information, high growth and containing extraordinary points, and it was proved in the cases of large and medium company new products income and Ufida Software Company. What is more, the method is also helpful in aspects of corporate financial control and strategy‐making process.

Originality/value

The paper succeeds in proposing a new interpolation algorithm that is superior to ordinary mean value generation method in the aspects of generation and prediction and to grey interpolation algorithm in the aspect of information volume by defining sequence smoothness efficiency and introducing smoothness judgement rules that are easy to compute and fits for high growth sequence and not limited to monotonicity sequence.

Details

Grey Systems: Theory and Application, vol. 2 no. 1
Type: Research Article
ISSN: 2043-9377

Keywords

Article
Publication date: 1 March 1993

H. UGOWSKI

Novel necessary and sufficient existence conditions for convolution inverses of real finite sequences are derived. These conditions are obtained with the aid of well known…

Abstract

Novel necessary and sufficient existence conditions for convolution inverses of real finite sequences are derived. These conditions are obtained with the aid of well known conditions expressed in terms of the Fourier and z‐transforms. The conditions given in the paper imply suitable algorithms, which are convenient for checking the existence of convolution inverses of any real finite sequences.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 12 no. 3
Type: Research Article
ISSN: 0332-1649

Article
Publication date: 19 August 2011

Yong Wei, Xin‐hai Kong and Da‐hong Hu

The purpose of this paper is to perfect the axiom systems of buffer operator via adding the axiom of invariable trend.

179

Abstract

Purpose

The purpose of this paper is to perfect the axiom systems of buffer operator via adding the axiom of invariable trend.

Design/methodology/approach

Based on the three axioms of buffer operator, for any given data sequence of system behavior and any set of data satisfying the axiom of fixed point, it is proved that there always exists a buffer operator satisfying that the set of data is the buffer sequence of the given data sequence, and a specific constructor method of buffer operator is provided. Finally, the axiom of invariable trend is proposed to add in the axiom systems of buffer operator.

Findings

The results are convincing that although the raw sequence suffered from certain disturbance may be enlarged or reduced, the trend is in line with the original law. All predictions must be on the premise of this trend to forecast, or prediction will be considered invalid.

Practical implications

The method exposed in the paper can be used to construct a specific buffer operator between two sequences satisfying the axiom of fixed point.

Originality/value

The paper succeeds in providing a kind of universal constructor method for buffer operator, and adding the axiom of invariable trend to perfect the axiom systems of buffer operator and ensure the consistency of variation trend between the predicted values and the actual values.

Details

Grey Systems: Theory and Application, vol. 1 no. 2
Type: Research Article
ISSN: 2043-9377

Keywords

Article
Publication date: 26 September 2008

Kai‐Fu Zhang, Hui Cheng and Yuan Li

Complex products, such as aircrafts and ships, are assembled from many parts and there are many available assembly sequences. Selecting the best from the available assembly…

Abstract

Purpose

Complex products, such as aircrafts and ships, are assembled from many parts and there are many available assembly sequences. Selecting the best from the available assembly sequences is challenging because of many factors, such as assembly performance, assemblability, assembly cost, assembly quality and assembly time. The purpose of this paper is to investigate a new and efficient algorithm aimed at this goal.

Design/methodology/approach

A new and efficient algorithm evaluating assembly sequences based on multi‐objective harmonious colony‐decision method is presented. This algorithm mainly includes three key steps: first, presenting the priority relationship between assembly sequences and the coefficient matrix for these objectives: assembly performance, assemblability, assembly cost, assembly quality, assembly time, and so on by several experts; second, calculating the maximum of harmonious values and harmonious priority value; third, if the maximum of harmonious priority value is not negative, the algorithm ends. Then the priority relationships of assembly sequences are obtained and the optimal assembly sequence can be selected.

Findings

This algorithm can efficiently support several experts to evaluate assembly sequences according to plenty of evaluation objectives and then to output a harmonious and recognized priority relationship of assembly sequences.

Practical implications

The algorithm is applied successfully to evaluate assembly sequences and select the optimal assembly sequence for component of aircraft's wing with fixtures.

Originality/value

This algorithm provides a new method to synthetically evaluate assembly sequences for complex product according to multi‐objectives.

Details

Assembly Automation, vol. 28 no. 4
Type: Research Article
ISSN: 0144-5154

Keywords

Article
Publication date: 27 January 2012

Tianxiang Yao, Jeffery Forrest and Zaiwu Gong

The purpose of this paper is to expand discrete GM (1,1) model and solve the problem of non‐equidistance grey prediction problem with integral interval or digital interval.

1165

Abstract

Purpose

The purpose of this paper is to expand discrete GM (1,1) model and solve the problem of non‐equidistance grey prediction problem with integral interval or digital interval.

Design/methodology/approach

Discrete GM (1,1) model can be utilized to simulate exponential sequence without errors, but it can't be utilized to simulate non‐equidistance data sequence. This paper applied optimization theories to establish generalized discrete GM (1,1) model. First, this paper established the time response of simulation sequence directly. Second, this paper established the steps of non‐equidistance data sequence. Finally, this paper utilized examples to test the method put forward.

Findings

The results indicate the generalized discrete GM (1,1) (GDGM) model can perfectly simulate non‐equidistance exponential series. Discrete GM (1,1) model is only the special form of GDGM model.

Practical implications

Though grey forecasting models are widely used, most of the forecasting models are based on the equal distance sequence. Due to many reasons, the raw data available usually is incomplete. There are mainly four reasons which caused non‐equidistance sequence. So generalized discrete GM (1,1) model can be utilized to simulate non‐equidistance sequence and has great application values.

Originality/value

The paper succeeds in establishing a generalized discrete GM (1,1) model which can be utilized to solve non‐equidistance data sequence forecasting. The GDGM model can be solved by MATLAB or other corresponding software.

Details

Grey Systems: Theory and Application, vol. 2 no. 1
Type: Research Article
ISSN: 2043-9377

Keywords

Article
Publication date: 17 May 2011

Lu Zhong, Sun Youchao, Okafor Ekene Gabriel and Wu Haiqiao

Maintenance disassembly that involves separating failed components from an assembly or system plays a vital role in line maintenance of civil aircraft, and it is necessary to have…

Abstract

Purpose

Maintenance disassembly that involves separating failed components from an assembly or system plays a vital role in line maintenance of civil aircraft, and it is necessary to have an effective and optimal sequence planning in order to reduce time and cost in maintenance. The purpose of the paper is to develop a more effective disassembly sequence planning method for maintenance of large equipment including civil aircraft systems.

Design/methodology/approach

The methodology involves the following steps: a component‐fastener graph is built to describe the equipment in terms of classifying components into two categories that are functional components and fasteners; interference matrix is developed to determine the removable component, and a disassembly sequence planning of functional components is proposed based on Dijkstra's algorithm; the disassembly sequence planning including fasteners is presented based on particle swarm optimization.

Findings

An application case, which takes the nose landing gear system of a regional jet as a study object, shows that the disassembly sequence planning method proposed in the paper can reduce the calculation complexity greatly, and its effectiveness is greater than that of a genetic algorithm‐based method, in most situations.

Practical implications

The method proposed herein can acquire the optimal maintenance disassembly sequence, which can reduce the cost and time for maintenance of large equipment.

Originality/value

A novel and effective disassembly sequence planning solution for maintenance of large equipment is presented, which can be applied to the line maintenance of civil aircraft.

Details

Aircraft Engineering and Aerospace Technology, vol. 83 no. 3
Type: Research Article
ISSN: 0002-2667

Keywords

Article
Publication date: 3 August 2012

Ke Zhang, Wei Ye and Liping Zhao

This paper attempts to extend classic absolute degree of grey incidence so that the extended model can be used for grey number sequences.

Abstract

Purpose

This paper attempts to extend classic absolute degree of grey incidence so that the extended model can be used for grey number sequences.

Design/methodology/approach

The classic absolute degree of grey incidence was extended according to basic principles of grey incidence analysis. First, modelling methods and theories of the classic grey incidences were summarized. Then, the zeroing starting operator in grey incidence was extended for grey sequence. Third, the parameters in classic incidence degree were redefined, and an absolute degree of grey incidence for grey number sequences was proposed. The degree can not only be applied to grey number sequence, but also contains the uncertain information of analysis result. Fourth, two non‐linear programming models were constructed to estimate the grey coverage interval of absolute degree of incidences. Finally, the comparison method of grey numbers was introduced for sorting the different absolute degrees of incidences.

Findings

A theoretically feasible absolute degree of grey incidence was constructed for grey sequence. A case study showed that the proposed incidence degree was an effective method for grey sequence incidence analysis.

Practical implications

The method exposed in the paper can be used for grey sequences clustering, grey decision making, multi‐attribute decision making theory, uncertain target recognition and other related fields.

Originality/value

The paper succeeded in establishing an incidence analysis model for grey sequences which was still a research gap in grey system theory.

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